OXIDATION

Oxidation is defined as the addition of an oxygen/electronegative element to a substance or removal of a hydrogen/ electropositive element from a susbtance. For example,

REDUCTION

Reduction is defined as the removal of oxygen/electronegative elements from a substance or addition of hydrogen or electropositive elements to a substance. For example,

REDOX REACTION IN TERMS OF ELECTRON TRANSFER REACTION

A few examples of redox reaction on the basis of electronic concept are given below:
According to the electronic concept every redox reaction consists of two steps known as half reactions.
(i) Oxidation reaction: Half reactions that involve loss of electrons are called oxidation reactions.
(ii) Reduction reaction: Half reactions that involve gain of electrons are called reduction reactions.
Oxidizing agent: Acceptor of electrons.
Reducing agent: Donar of electrons.

OXIDATION NUMBER

It is the oxidation state of an element in a compound which is the charge assigned to an atom of a compound is equal to the number of electrons in the valence shell of an atom that are gained or lost completely or to a large extent by that atom while forming a bond in a compound.

Rules for Assigning Oxidation Numbers

(i) The oxidation number of an element in its elementary form is zero.
For example, H2, 02, N2 etc. have oxidation number equal to zero.
(ii) In a single monatomic ion, the oxidation number is equal to the charge on the ion. For example, Na+ ions have an oxidation number of +1 and Mg2+ ions have +2.
(iii) Oxygen has oxidation number -2 in its compounds.
(iv) In non-metallic compounds of hydrogen like HCl, H2S, H2O oxidation number of hydrogen = + 1 but in metal hydrides oxidation number of hydrogen = -1 [LiH, NaH, CaH2 etc.]
(v) In compounds of metals and non-metals metals have positive oxidation number while non-metals have negative oxidation number. For example, In NaCl. Na has +1 oxidation number while chlorine has -1.
(vi) If in a compound there are two non-metallic atoms the atoms with high electronegativity are assigned negative oxidation number while other atoms have positive oxidation number.
(vii) The algebraic sum of the oxidation number of all atoms in a compound is equal to zero.
(viii) In polyatomic ion the sum of the oxidation no. of all the atoms in the ion is equal to the net charge on the ion.
For example, in (C03)2—Sum of carbon atoms and three oxygen atoms is equal to -2.
Fluorine (F2) is so highly reactive non-metal that it displaces oxygen from water.

DISPROPORTIONATION REACTION

In a disproportionation reaction an element in one oxidation state is simultaneously oxidized and reduced. For example,

Hence, the oxygen of peroxide, which is present in -1 oxidation state is connected to zero oxidation state and in 02 and in H2O decreases to -2 oxidation state.

FRACTIONAL OXIDATION NUMBERS

Elements as such do not have any fractional oxidation numbers.
When the same elements are involved in different bonding in a species, their actual oxidation states are whole numbers but an average of these is fractional. For example, In C302

Fractional O.N. of a particular element can be claculated only if we know about the structure of the compound or in which it is present.

BALANCING OF REDOX REACTIONS

Oxidation Number Method:

Following steps are involved:
(a) Write the correct formula for each reactant and product.
(b) By assigning the oxidation change in oxidation number can be identified.
(c) Calculate the increase and decrease in oxidation number per atom with respect to the reactants. If more than one atom is present then multiply by suitable coefficient.
(d) Balance the equation with respect to all atoms. Balance hydrogen and oxygen atoms also.
(e) If the reaction is carried out in an acidic medium, use H+ ions in the equation. If it is in basic medium use OH– ions.
(f) Hydrogen atoms in the expression can be balanced by adding (H20) molecules to the reactants or products.
If there are the same number of oxygen atoms on both sides of the equation then it represents the balanced redox reaction.

Half Reaction Method:

In this method two half equations are balanced separately and then added together to give a balanced equation.

REDOX REACTIONS AS THE BASIS FOR TITRATION

Potassium Permanganate Titration:

In these titrations potassium permanganate (pink in colour) acts as an oxidising agent in the acidic medium while oxalic acid or some ferrous salts acts as a reducing agent.
The ionic equation can be written as:

These are the examples of redox titration.
On both these titrations, potassium permanganate itself acts as indicator.
It is commonly known as a self indicator.
The appearance of pink colour in the solution represents the end points.

Potassium Dichromate Titration :

In place of potassium permanganate, potassium dichromate can also be used in the presence of dil. H2S04.
The ionic equation for the redox reaction with FeS04 (Fe2+ ions) is given.

LIMITATION OF CONCEPT OF OXIDATION NUMBER

According to the concept of oxidation number, oxidation means increase in oxidation number – by loss of electrons and reduction means decrease in oxidation number by the gain of electrons. However, during oxidation there is decrease in electron density while increase in electron density around the atom undergoing reduction.

REDOX REACTIONS AND ELECTRODE

Processes-Electrochemical Cells

A device in which the redox reaction is carried indirectly and the decrease in energy appears as the electrical energy are called electrochemical cell.

Electrolytic Cell

The cell in which electrical energy is converted into chemical energy. Example, when a lead storage battery is recharged, it acts as electrolytic cell.

IMPORTANT TERMS AND DEFINITIONS

SYSTEM

Refers to the portion of the universe which is under observation.

SURROUNDINGS

Everything else in the universe except the system is called surroundings.
The Universe = The System + The Surroundings.

OPEN SYSTEM

In a system, when there is exchange of energy and matter taking place with the surroundings, then it is called an open system.
For Example: Presence of reactants in an open beaker is an example of an open system.

CLOSED SYSTEM

A system is said to be a closed system when there is no exchange of matter ‘ but exchange of energy is possible. For example: The presence of reactants in a closed vessel made of conducting material.

ISOLATED SYSTEM

In a system, when no exchange of energy or matter takes place with the surroundings, it is called an isolated system.
For example: The presence of reactants in a thermoflask, or substance in an insulated closed vessel is an example of an isolated system.

HOMOGENEOUS SYSTEM

A system is said to be homogeneous when all the constituents present are in the same phase and is uniform throughout the system.
For example: A- mixture of two miscible liquids.

HETEROGENEOUS SYSTEM

A mixture is said to be heterogeneous when it consists of two or more phases and the composition is not uniform.
For example: A mixture of insoluble solid in water. ’

THE STATE OF THE SYSTEM

The state of a thermodynamic system means its macroscopic or bulk properties which can be described by state variables:
Pressure (P), volume (V), temperature (T) and amount (n) etc.
They are also known as state functions.

ISOTHERMAL PROCESS

When the operation is carried out at constant temperature, the process is said to be isothermal. For isothermal processes, dT = 0 Where dT is the change in temperature.

ADIABATIC PROCESS

It is a process in which no transfer of heat between system and surroundings takes place.

ISOBARIC PROCESS

When the process is carried out at constant pressure, it is said to be isobaric. i.e. dP = 0

ISOCHORIC PROCESS

A process when carried out at constant volume, it is known as isochoric in nature.

CYCLIC PROCESS

If a system undergoes a series of changes and finally returns to its initial state, it is said to be a cyclic process.

REVERSIBLE PROCESS

When in a process, a change is brought in such a way that the process could, at any moment, be reversed by an infinitesimal change. The change r is called reversible.

INTERNAL ENERGY

It is the sum of all the forms of energies that a system can possess.
In thermodynamics, it is denoted by AM which may change, when
— Heat passes into or out of the system
— Work is done on or by the system
— Matter enters or leaves the system.

CHANGE IN INTERNAL ENERGY BY DOING WORK

Let us bring the change in the internal energy by doing work.
Let the initial state of the system be state A and Temp.
TA Internal energy = uA
On doing’some mechanical work the new state is called state B and the temp. TB.
It is found to be :TB > TA
uB is the internal energy after change.
∴ Δu = uB – uA

CHANGE IN INTERNAL ENERGY BY TRANSFER OF HEAT

Internal energy of a system can be changed by the transfer of heat from the surroundings to the system without doing work.
Δu = q, Where q is the heat absorbed by the system.
It can be measured in terms of temperature difference.
q is +ve when heat is transferred from the surroundings to the system. q is -ve when heat is transferred from the system to surroundings.
When change of state is done both by doing work and transfer of heat.
Δu = q + w

FIRST LAW OF THERMODYNAMICS (LAW OF CONSERVATION OF ENERGY):

It states that energy can neither be created nor be destroyed. The energy of an isolated system is constant.
Δu = q + w.

WORK (PRESSURE-VOLUME WORK)

Let us consider a cylinder which contains one mole of an ideal gas in which a frictionless piston is fitted.

WORK DONE IN ISOTHERMAL AND REVERSIBLE EXPANSION OF IDEAL GAS

ISOTHERMAL AND FREE EXPANSION OF AN IDEAL GAS

For isothermal expansion of an ideal gas into vacuum W = 0

ENTHALPY (H):

It is defined as the total heat content of the system.
It is equal to the sum of internal energy and pressure-volume work.
Mathematically, H = U + PV

CHANGE IN ENTHALPY

Change in enthalpy is the heat absorbed or evolved by the system at constant pressure.
ΔH = qp
For exothermic reaction (System loses energy to Surroundings),
ΔH and qp both are -Ve.
For endothermic reaction (System absorbs energy from the Surroundings).
ΔH and qp both are +Ve.

EXTENSIVE PROPERTY

An extensive property is a property whose value depends on the quantity or size of matter present in the system.
For example: Mass, volume, enthalpy etc. are known as extensive property.

INTENSIVE PROPERTY

Intensive properties do not depend upon the size of the matter or quantity of the matter present in the system.
For example: temperature, density, pressure etc. are called intensive properties.

HEAT CAPACITY

The increase in temperature is proportional to the heat transferred.
q = coeff. x ΔT
q = CΔT, Where, coefficient C is called the heat capacity.
C is directly proportional to the amount of substance.
Cm = C/n
It is the heat capacity for 1 mole of the substance.

MOLAR HEAT CAPACITY

It is defined as the quantity of heat required to raise the temperature of a substance by 1° (kelvin or Celsius).

SPECIFIC HEAT CAPACITY

It is defined as the heat required to raise the temperature of one unit mass of a substance by 1° (kelvin or Celsius).
q = C x m x ΔT where, m = mass of the substance and ΔT = rise in temperature.

RELATION BETWEEN Cp AND Cv FOR AN IDEAL GAS

At constant volume heat capacity = Cv
At constant pressure heat capacity = Cp
At constant volume qv= CvΔT = ΔU
At constant pressure qp = Cp ΔT = ΔH
For one mole of an ideal gas
ΔH = ΔU + Δ (PV) = ΔU + Δ (RT)
ΔH = ΔU + RΔT
On substituting the values of ΔH and Δu, the equation is modified as :Cp ΔT = CvΔT + RΔT
or Cp-Cv = R

MEASUREMENT OF ΔU and ΔH-CALORIMETRY

DETERMINATION OF ΔU:

ΔU is measured in a special type of calorimeter, called bomb calorimeter.

WORKING OF CALORIMETER:

The calorimeter consists of a strong vessel called (bomb) which can withstand very high pressure.
It is surrounded by a water bath to ensure that no heat is lost to the surroundings.

PROCEDURE:

A known mass of the combustible substance is burnt in the pressure of pure dioxygen in the steel bomb.
Heat evolved during the reaction is transferred to the water and its temperature is monitored.

ENTHALPY CHANGES DURING PHASE TRANSFORMATION

ENTHALPY OF FUSION

Enthalpy of fusion is the heat energy or change in enthalpy when one mole of a solid at its melting point is converted into liquid state.

ENTHALPY OF EVAPORATION

It is defined as the heat energy or change in enthalpy when one mole of a liquid at its boiling point changes to gaseous state.

ENTHALPY OF SUBLIMATION

Enthalpy of sublimation is defined as the change in heat energy or change in enthalpy when one mole of solid directly changes into gaseous state at a temperature below its melting point.

STANDARD ENTHALPY OF FORMATION

Enthalpy of formation is defined as the change in enthalpy in the formation of 1 mole of a substance from its constituting elements under standard conditions of temperature at 298K and 1 atm pressure.

ENTHALPY OF COMBUSTION

It is defined as the heat energy or change in enthalpy that accompanies the combustion of 1 mole of a substance in excess of air or oxygen.

THERMOCHEMICAL EQUATION

A balanced chemical equation together with the value of ΔrH and the physical state of reactants and products is known as thermochemical equation.

CONVENTIONS REGARDING THERMOCHEMICAL EQUATIONS

The coefficients in a balanced thermochemical equation refer to the number of moles of reactants and products involved in the reaction.

HESS'S LAW OF CONSTANT HEAT SUMMATION

The total amount of heat evolved or absorbed in a reaction is the same whether the reaction takes place in one step or in number of steps.

SPONTANEITY

SPONTANEOUS PROCESS

A process which can take place by itself or has a tendency to take place is called spontaneous process.
Spontaneous processes need not be instantaneous.
Its actual speed can vary from very slow to quite fast.
A few examples of spontaneous process are:
(i) Common salt dissolves in water of its own.
(ii) Carbon monoxide is oxidised to carbon dioxide of its own.

ENTROPY (S)

The entropy is a measure of the degree of randomness or disorder of a system.
Entropy of a substance is minimum in solid state while it is maximum in gaseous state.
The change in entropy in a spontaneous process is expressed as ΔS

GIBBS ENERGY AND SPONTANEITY

A new thermodynamic function, the Gibbs energy or Gibbs function G, can be defined as G = H-TS
ΔG = ΔH – TΔS
Gibbs energy change = enthalpy change – temperature x entropy
Change ΔG gives a criteria for spontaneity at constant pressure and temperature,
(i) If ΔG is negative (< 0) the process is spontaneous. (ii) If ΔG is positive (> 0) the process is non-spontaneous.

FREE ENERGY CHANGE IN REVERSIBLE REACTION

INTERMOLECULAR FORCES

Intermolecular forces are the forces of attraction and repulsion between interacting particles that have permanent dipole moments.
This interaction is stronger than the London forces but is weaker than ion-ion interaction because only partial charges are involved.
The attractive forces decrease with the increase of distance between dipoles.
The interaction energy is proportional to 1/r6 where r is the distance between polar molecules.

ION-DIPOLE INTERACTION

This is the force of attraction which exists between the ions (cations or anions) and polar molecules.
The ion is attracted towards the oppositely charged end of dipolar molecules.
The strength of attraction depends upon the charge and size of the ion and the dipole moment and the size of the polar molecule. For example: Solubility of common salt (NaCl) in water.

ION-INDUCED DIPOLAR INTERACTIONS

In this type of interaction permanent dipole of the polar molecule induced dipole on the electrically neutral molecule by deforming its electron cloud.
Interaction energy is proportional to 1/r6 where r is the distance between two molecules.

LONDON FORCES OR DISPERSION FORCES

As we know that in non-polar molecules, there is no dipole moment because of their electronics .
Charge cloud is symmetrically distributed.
But, it is believed that at any instant of time, the electron cloud of the molecule may be distorted so that an instantaneous dipole or momentary dipole is produced in which one part of the molecule is slightly more negative than the other part.
This momentary dipole induced dipoles in the neighbouring molecules.
Thus, the force of attraction exists between them and is exactly the same as between permanent dipoles.
This force of attraction is known as London forces or Dispersion forces.
These forces are always attractive and the interaction energy is inversely proportional to the sixth power of the distance between two interacting particles, (i.e. 1/r6 where r is the distance between two particles). This can be shown by fig. given below.

HYDROGEN BONDING

When a hydrogen atom is attached to a highly electronegative element by covalent bond, electrons are shifted towards the more electronegative atom.
Thus a partial positive charge develops on the hydrogen atom. Now, the positively charged hydrogen atom of one molecule may attract the negatively charged atom of some other molecule and the two molecules can be linked together through a weak force of attraction.

THERMAL ENERGY

The energy arising due to molecular motion of the body is known as thermal energy. Since motion of the molecules is directly related to kinetic energy and kinetic energy is directly proportional to the temperature.

THE GASEOUS STATE

Physical Properties of Gaseous State:
(i) gases have no definite volume and they do not have specific shape,
(ii) Gases mix evenly and completely in all proportions without any mechanical aid.
(iii) Their density is much lower than solids and liquids.
(iv) They are highly compressible and exert pressure equally in all directions.

BOYLE'S LAW (PRESSURE-VOLUME RELATIONSHIP)

At constant temperature, the volume of a given mass of gas is inversely proportional to its pressure.

CHARLE'S LAW

At constant pressure, the volume of a given mass of a gas is directly proportional to its absolute temperature.

GAY-LUSSAC'S LAW (PRESSURE-TEMPERATURE RELATIONSHIP)

At constant volume, pressure of a given mass of a gas is directly proportional to the temperature.

AVOGADRO LAW (VOLUME-AMOUNT RELATIONSHIP)

Avogadro’s law states that equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules.
V α n, Where n is the number of moles of the gas.
Avogadro constant: The number of molecules in one mole of a gas
= 6.022 x 1023

IDEAL GAS

A gas that strictly follows Boyle’s law, Charles’ law and Avogadro law, is called an ideal gas.
Real gases follow these laws only under certain specific conditions. When forces of interaction are practically negligible.

IDEAL GAS EQUATION

This is the combined gas equation of three laws and is known as the ideal gas equation.

DALTON'S LAW OF PARTIAL PRESSURE

When two or more non-reactive gases are enclosed in a vessel, the total pressure exerted by the gaseous mixture is equal to the sum of the partial pressure of individual gases.
Let P1 ,P2, and P3 be the pressure of three non reactive gases A, B, and C.
When enclosed separately in the same volume and under the same condition.
PTotal = P1+ P2 + P3
Where, PTotal = P is the total pressure exerted by the mixture of gases.

AQUEOUS TENSION

Pressure of non reacting gases are generally collected over water and therefore are moist.
Pressure of dry gas can be calculated by subtracting vapour pressure of water from total pressure of moist gas.
P2Dry gas = PTotal – Aqueous Tension

PARTIAL PRESSURE IN TERMS OF MOLE FRACTION

Let at the temperature T, three gases enclosed in the volume V, exert partial pressure P1 , P2 and P3 respectively, then

KINETIC MOLECULAR THEORY OF GASES

(i) Gases consist of large number of very small identical particles (atoms or molecules),
(ii) Actual volume occupied by the gas molecule is negligible in comparison to empty space between them.
(iii) Gases can occupy all the space available to them. This means they do not have any force of attraction between their particles.
(iv) Particles of a gas are always in constant random motion.
(v) When the particles of a gas are in random motion, pressure is exerted by the gas due to collision of the particles with the walls of the container.
(vi) Collisions of the gas molecules are perfectly elastic. This means there is no loss of energy after collision. There may be only an exchange of energy between colliding molecules.
(vii) At a particular temperature distribution of speed between gaseous particles remains constant.
(viii) Average kinetic energy of the gaseous molecule is directly proportional to the absolute temperature.

DEVIATION FROM IDEAL GAS BEHAVIOUR

REAL GAS

A gas which does not follow ideal gas behaviour under all conditions of temperature and pressure, is called real gas. Deviation with respect to pressure can be studied by plotting pressure Vs volume curve at a given temperature. (Boyle’s law)

COMPRESSIBILITY FACTOR (Z)

Deviation from ideal behaviour can be measured in terms of compressibility factor, Z.

VAN DER WAALS EQUATION

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Where V is a constant for molecular attraction while ‘V is a constant for molecular volume.
(a) There is no force of attraction between the molecules of a gas.
(b) Volume occupied by the gas molecule is negligible in comparison to the total volume of the gas.
Above two assumptions of the kinetic theory of gas was found to be wrong at very high pressure and low temperature.

LIQUIFACTION OF GASES

Liquifaction of gases can be achieved either by lowering the temperature or increasing the pressure of the gas simultaneously.
Thomas Andrews plotted isotherms of C02 at various temperatures shown in figure.

CRITICAL TEMPERATURE (Tc)

It is defined as that temperature above which a gas cannot be liquified however high pressure may be applied on the gas.
Tc = 8a/27bR, (Where a and b are van der Waals constants)

CRITICAL PRESSURE (Pc)

It is the pressure required to Liquify the gas at the critical temperature.
Pc = a/27b2
The volume occupied by one mole of the gas at the critical temperature and the critical pressure is called the critical volume (Vc).
For Example. For C02 to Liquify.
Tc = 30.98°C
Pc = 73,9 atm.
Vc = 95-6 cm3/mole
All the three are collectively called critical constants.

LIQUID STATE

Characteristics of Liquid State:
(i) In liquid, intermolecular forces are strong in comparison to gas.
(ii) They have definite volume but irregular shapes or we can say that they can take the shape of the container.
(iii) Molecules of liquids are held together by attractive intermolecular forces.

VAPOUR STATE

The pressure exerted by the vapour of a liquid, at a particular temperature in a state of dynamic equilibrium, is called the vapour pressure of that liquid at that temperature.
Vapour Pressure depends upon two factors:
(i) Nature of Liquid
(ii) Temperature

SURFACE TENSION

It is defined as the force acting per unit length perpendicular to the line drawn on the surface of liquid.
S.I. unit of Surface Tension = Nm-1
Surface Tension decreases with increase in temperature, because force acting per unit length decreases due to increase in kinetic energy of molecules.

VISCOSITY

It is defined as the internal resistance to flow possessed by a liquid.
The liquids which flow slowly have very high internal resistance, which is due to strong intermolecular forces and hence are said to be more viscous.

When liquid flows, the layer immediately below it tries to retard its flow while the one above tries to accelerate.
Thus, force is required to maintain the flow of layers.

EFFECT OF TEMP, ON VISCOSITY

Viscosity of liquids decreases as the temperature rises because at high temperature, molecules have high kinetic energy and can overcome the intermolecular forces to slip past one another.

BOYLE'S LAW

It states that, under isothermal conditions pressure of a given mass of a gas is inversely proportional to its volume.

CHEMICAL BOND

The force that holds different atoms in a molecule is called a chemical bond.

OCTET RULE

Atoms of different elements take part in chemical combinations in order to complete their octet or to attain the noble gas configuration.

VALENCE ELECTRONS

It is the outermost shell electron which takes part in a chemical combination.

FACTS STATED BY KOSSEL IN RELATION TO CHEMICAL BONDING

In the periodic table, the highly electronegative halogens and the highly electro-positive alkali metals are separated by noble gases.
Formation of an anion and cation by the halogens and alkali metals are formed by gain of electron and loss of electron respectively.
Both the negative and positive ions acquire the noble gas configuration.
The negative and positive ions are stabilized by electrostatic attraction Example,

MODES OF CHEMICAL COMBINATION

By the transfer of electrons: The chemical bond which is formed by the complete transfer of one or more electrons from one atom to another is termed as electrovalent bond or ionic bond.
By sharing of electrons: The bond which is formed by the equal sharing of electrons between one or two atoms is called covalent bond. In these bonds electrons are contributed by both.
Co-ordinate bond: When the electrons are contributed by one atom and shared by both, the bond is formed and it is known as dative bond or co-ordinate bond.

IONIC OR ELECTROVALENT BOND

Ionic or Electrovalent bond is formed by the complete transfer of electrons from one atom to another.
Generally, it is formed between metals and non-metals. We can say that it is the electrostatic force of attraction which holds the oppositely charged ions together.
The compound which is formed by ionic or electrovalent bonds is known as electrovalent compounds.
For Example, ,
(i) NaCl is an electrovalent compound. Formation of NaCl is given below:

Na+ ion has the configuration of Ne while Cl– ion represents the configuration of Ar.
(ii) Formation of magnesium oxide from magnesium and oxygen.

Electrovalency: Electrovalency is the number of electrons lost or gained during the formation of an ionic bond or electrovalent bond.

FACTORS AFFECTING THE FORMATION OF IONIC BOND

(i) Ionization enthalpy: As we know that ionization enthalpy of any element is the amount of energy required to remove an electron from the outermost shell of an isolated gaseous atom to convert it into cation. Hence, lesser the ionization enthalpy, easier will be the formation of a cation and have greater chance to form an ionic bond. Due to this reason alkali metals have more tendency to form an ionic bond. For example, in formation of Na+ ion I.E = 496 kJ/mol. While in case of magnesium, it is 743 kJ/mole. That’s why the formation of a positive ion for sodium is easier than that of magnesium.
Therefore, we can conclude that lower the ionization enthalpy, greater the chances of ionic bond formation.
(ii) Electron gain enthalpy (Electron affinities): It is defined as the energy released when an isolated gaseous atom takes up an electron to form anion. Greater the negative electron gain enthalpy, easier will be the formation of anion. Consequently, the probability of formation of ionic bonds increases.
For example, Halogens possess high electron affinity. So, the formation of anion is very common in halogens.

(iii) Lattice energy or enthalpy: It is defined as the amount of energy required to separate 1 mole of ionic compound into separate oppositely charged ions.

LATTICE ENERGY OF AN IONIC COMPOUND DEPENDS UPON FOLLOWING FACTORS:

(i) Size of the ions: Smaller the size, greater will be the lattice energy.
(ii) Charge on the ions: Greater the magnitude of charge, greater the interionic attraction and hence higher the lattice energy.

GENERAL CHARATERISTICS OF IONIC COMPOUNDS

(i) Physical State: They generally exist as crystalline solids, known as crystal lattice. Ionic compounds do not exist as single molecules like other gaseous molecules e.g., H2 , N2 , 02 , Cl2 etc.
(ii) Melting and boiling points: Since ionic compounds contain high interionic force between them, they generally have high melting and boiling points.
(iii) Solubility: They are soluble in polar solvents such as water but do not dissolve in organic solvents like benzene, CCl4etc.
(iv) Electrical conductivity: In solid state they are poor conductors of electricity but in molten state or when dissolved in water, they conduct electricity.
(v) Ionic reactions: Ionic compounds produce ions in the solution which gives a very fast reaction with oppositely charged ions. For example,

COVALENT BOND-LEWIS LANGMUIR CONCEPT

When the bond is formed between two or more atoms by mutual contribution and sharing of electrons, it is known as covalent bond.
If the combining atoms are the same , the covalent molecule is known as homoatomic.
If they are different, they are known as heteroatomic molecules.
For Example,

LEWIS REPRESENTATION OF SIMPLE MOLECULE (THE LEWIS STRUCTURES)

The Lewis dot Structure can be written through the following steps:
(i) Calculate the total number of valence electrons of the combining atoms.
(ii) Each anion means addition of one electron and each cation means removal of one electron. This gives the total number of electrons to be distributed.
(iii) By knowing the chemical symbols of the combining atoms.
(iv) After placing shared pairs of electrons for a single bond, the remaining electrons may account for either multiple bonds or as lone pairs. It is to be noted that the octet of each atom should be completed.

FORMAL CHARGE

In polyatomic ions, the net charge is the charge on the ion as a whole and not by particular atom. However, charges can be assigned to individual atoms or ions. These are called formal charges. It can be expressed as

LIMITATIONS OF THE OCTET RULE

(i) The incomplete octet of the central atoms: In some covalent compounds the central atom has less than eight electrons, i.e., it has an incomplete octet. For example,

Li, Be and B have 1, 2, and 3 valence electrons only.

(ii) Odd-electron molecules: There are certain molecules which have an odd number of electrons; the octet rule is not applied for all the atoms.

(iii) The expanded Octet: In many compounds there are more than eight valence electrons around the central atom. It is termed as an expanded octet. For Example,

OTHER DRAWBACKS OF OCTET THEORY

(i) Some noble gases also combine with oxygen and fluorine to form a number of compounds like XeF2 , XeOF2 etc.
(ii) This theory does not account for the shape of the molecule.
(iii) It does not give any idea about the energy of The molecule and relative stability.

BOND LENGTH

It is defined as the equilibrium distance between the centres of the nuclei of the two bonded atoms. It is expressed in terms of A. Experimentally, it can be defined by X-ray diffraction or electron diffraction method.

BOND ANGLE

It is defined as -the angle between the lines representing the orbitals containing the bonding – electrons.
It helps us in determining the shape. It can be expressed in degree. Bond angle can be experimentally determined by spectroscopic methods.

BOND ENTHALPY

It is defined as the amount of energy required to break one mole of bonds of a particular type to separate them into gaseous atoms.
Bond Enthalpy is also known as bond dissociation enthalpy or simple bond enthalpy. Unit of bond enthalpy = kJ mol-1
Greater the bond enthalpy, stronger is the bond. For e.g., the H—H bond enthalpy in hydrogen is 435.8 kJ mol-1.
The magnitude of bond enthalpy is also related to bond multiplicity.
Greater the bond multiplicity, more will be the bond enthalpy. For e.g., bond enthalpy of C —C bond is 347 kJ mol-1 while that of C = C bond is 610 kJ mol-1.
In polyatomic molecules, the term mean or average bond enthalpy is used.

BOND ORDER

According to Lewis, in a covalent bond, the bond order is given by the number of bonds between two atoms in a molecule. For example,
Bond order of H2 (H —H) =1
Bond order of 02 (O = O) =2
Bond order of N2 (N = N) =3
Isoelectronic molecules and ions have identical bond orders. For example, F2 and O22- have bond order = 1. N2, CO and NO+ have bond order = 3.
With the increase in bond order, bond enthalpy increases and bond length decreases. For example,

RESONANCE STRUCTURES

There are many molecules whose behaviour cannot be explained by a single-Lewis structure, Tor example, Lewis structure of Ozone represented as follows:

Thus, according to the concept of resonance, whenever a single Lewis structure cannot explain all the properties of the molecule, the molecule is then supposed to have many structures with similar energy.
Positions of nuclei, bonding and nonbonding pairs of electrons are taken as the canonical structure of the hybrid which describes the molecule accurately.
For 03, the two structures shown above are canonical structures and the III structure represents the structure of 03 more accurately. This is also called resonance hybrid.
Some resonating structures of some more molecules and ions are shown as follows:

POLARITY OF BONDS

Polar Covalent bonds
Non-Polar Covalent bonds

NON-POLAR COVALENT BONDS:

When the atoms joined by covalent bonds are the same like; H2, 02, Cl2, the shared pair of electrons is equally attracted by two atoms and thus the shared electron pair is equidistant to both of them.
Alternatively, we can say that it lies exactly in the centre of the bonding atoms. As a result, no poles are developed and the bond is called a non-polar covalent bond. The corresponding molecules are known as non-polar molecules.
For Example,

POLAR BONDS:

When covalent bonds formed between different atoms of different electronegativity, the shared electron pair between two atoms gets displaced towards highly electronegative atoms.
For Example, in HCl molecule, since electronegativity of chlorine is high as compared to hydrogen thus, electron pair is displaced more towards chlorine atom, thus chlorine will acquire a partial negative charge (δ–) and hydrogen atom have a partial positive charge (δ+) with the magnitude of charge same as on chlorination. Such a covalent bond is called polar covalent bond.

DIPOLE MOMENT

Due to polarity, polar molecules are also known as dipole molecules and they possess dipole moment. Dipole moment is defined as the product of magnitude of the positive or negative charge and the distance between the charges.

APPLICATIONS OF DIPOLE MOMENT

(i) For determining the polarity of the molecules.
(ii) In finding the shapes of the molecules. For example, the molecules with zero dipole moment will be linear or symmetrical. Those molecules which have asymmetrical shapes will be either bent or angular.
(e.g., NH3with μ = 1.47 D).
(iii) In calculating the percentage ionic character of polar bonds.

THE VALENCE SHELL ELECTRON PAIR REPULSION (VSEPR) THEORY

Sidgwick and Powell in 1940, proposed a simple theory based on the repulsive character of electron pairs in the valence shell of the atoms. It was further developed by Nyholm and Gillespie (1957).

MAIN POSTULATES ARE THE FOLLOWING:

(i) The exact shape of a molecule depends upon the number of electron pairs (bonded or non bonded) around the central atoms.
(ii) The electron pairs have a tendency to repel each other since they exist around the central atom and the electron clouds are negatively charged.
(iii) Electron pairs try to take such a position which can minimize the rupulsion between them.
(iv) The valence shell is taken as a sphere with the electron pairs placed at maximum distance.
(v) A multiple bond is treated as if it is a single electron pair and the electron pairs which constitute the bond as single pairs.

VALENCE BOND THEORY

Valence bond theory was introduced by Heitler and London (1927) and developed by Pauling and others. It is based on the concept of atomic orbitals and the electronic configuration of the atoms.
Let us consider the formation of hydrogen molecules based on valence-bond theory.
Let two hydrogen atoms A and B having their nuclei NA and NB and electrons present in them are eA and eB .
As these two atoms come closer new attractive and repulsive forces begin to operate.
(i) The nucleus of one atom is attracted towards its own electron and the electron of the other and vice versa.
(ii) Repulsive forces arise between the electrons of two atoms and nuclei of two atoms. Attractive forces tend to bring the two atoms closer whereas repulsive forces tend to push them apart.

ORBITAL OVERLAP CONCEPT

According to the orbital overlap concept, covalent bond formed between atoms results in the overlap of orbitals belonging to the atoms having opposite spins of electrons.
Formation of hydrogen molecule as a result of overlap of the two atomic orbitals of hydrogen atoms is shown in the figures that follows:

Stability of a Molecular orbital depends upon the extent of the overlap of the atomic orbitals.

TYPES OF ORBITAL OVERLAP

Depending upon the type of overlapping, the covalent bonds are of two types, known as sigma (σ ) and pi (π) bonds.

(i) Sigma (σ bond):

Sigma bond is formed by the end to end (head-on) overlap of bonding orbitals along the internuclear axis.
The axial overlap involving these orbitals is of three types:
s-s overlapping: In this case, there is overlap of two half-filled s-orbitals along the internuclear axis as shown below:

• s-p overlapping: This type of overlapping occurs between half-filled s-orbitals of one atom and half-filled p-orbitals of another atom.

• p-p overlapping: This type of overlapping takes place between half filled p-orbitals of the two approaching atoms.

(ii) pi (π bond):

π bond is formed by the atomic orbitals when they overlap in such a way that their axes remain parallel to each other and perpendicular to the internuclear axis.The orbital formed is due to lateral overlapping or side wise overlapping.

STRENGTH OF SIGMA AND PI BONDS

Sigma bond (σ bond) is formed by the axial overlapping of the atomic orbitals while the π-bond is formed by side-wise overlapping. Since axial overlapping is greater as compared to side wise. Thus, the sigma bond is said to be a stronger bond in comparison to a π-bond.

DISTINCTION BETWEEN SIGMA AND PI BOND

HYBRIDIZATION

Hybridisation is the process of intermixing of the orbitals of slightly different energies so as to redistribute their energies resulting in the formation of new sets of orbitals of equivalent energies and shape.

SALIENT FEATURES OF HYBRIDIZATION

(i) Orbitals with almost equal energy take part in the hybridisation.
(ii) Number of hybrid orbitals produced is equal to the number of atomic orbitals mixed,
(iii) Geometry of a covalent molecule can be indicated by the type of hybridisation.
(iv) The hybrid orbitals are more effective in forming stable bonds than the pure atomic orbitals.

CONDITIONS NECESSARY FOR HYBRIDIZATION

(i) Orbitals of valence shells take part in the hybridisation.
(ii) Orbitals involved in hybridisation should have almost equal energy.
(iii) Promotion of electrons is not a necessary condition prior to hybridisation.
(iv) In some cases filled orbitals of valence shells also take part in hybridisation.

TYPES OF HYBRIDIZATION

(i) sp hybridisation: When one s and one p-orbital hybridise to form two equivalent orbitals, the orbital is known as sp hybrid orbital, and the type of hybridisation is called sp hybridisation.
Each of the hybrid orbitals formed has 50% s-characer and 50%, p-character. This type of hybridisation is also known as diagonal hybridisation.

(ii) sp2 hybridisation: In this type, one s and two p-orbitals hybridise to form three equivalent sp2 hybridised orbitals.
All the three hybrid orbitals remain in the same plane making an angle of 120°. Example. A few compounds in which sp2 hybridisation takes place are BF3, BH3, BCl3 carbon compounds containing double bonds etc.

(iii) sp3 hybridisation: In this type, one s and three p-orbitals in the valence shell of an atom get hybridised to form four equivalent hybrid orbitals.
There is 25% s-character and 75% p-character in each sp3 hybrid orbital.
The four sp3 orbitals are directed towards four corners of the tetrahedron.
The structures of NH2 and H20 molecules can also be explained with the help of sp3 hybridisation.

The angle between sp3 hybrid orbitals is 109.5°. A compound in which sp3 hybridisation occurs is, (CH4).

FORMATION OF MOLECULAR ORBITALS

Linear Combination of Atomic Orbitals (LCAO)
The formation of molecular orbitals can be explained by the linear combination of atomic orbitals.
Combination takes place either by addition or by subtraction of wave function as shown below.

The molecular orbital formed by addition of atomic orbitals is called bonding molecular orbital while molecular orbital formed by subtraction of atomic orbitals is called antibonding molecular orbital.
Conditions for the combination of atomic orbitals:
(1) The combining atomic orbitals must have almost equal energy.
(2) The combining atomic orbitals must have the same symmetry about the molecular axis.
(3) The combining atomic orbitals must overlap to the maximum extent.

TYPES OF MOLECULAR ORBITALS

Sigma (σ) Molecular Orbitals: They are symmetrical around the bond-axis.
pi (π) Molecular Orbitals: They are not symmetrical, because of the presence of positive lobes above and negative lobes below the molecular plane.

ELECTRONIC CONFIGURATION AND MOLECULAR BEHAVIOUR

The distribution of electrons among various molecular orbitals is called electronic configuration of the molecule.

BOND ORDER

Bond order is defined as half of the difference between the number of electrons present in bonding and antibonding molecular orbitals.
Bond order (B.O.) = 1/2 [Nb-Na]
The bond order may be a whole number, a fraction or even zero.
It may also be positive or negative.
Nature of the bond: Integral bond order value for single double and triple bond will be 1, 2 and 3 respectively.

BOND LENGTH

Bond order is inversely proportional to bond-length. Thus, greater the bond order, smaller will be the bond-length.
Magnetic Nature: If all the molecular orbitals have paired electrons, the substance is diamagnetic. If one or more molecular orbitals have unpaired electrons, it is paramagnetic e.g., 02 molecule.

BONDING IN SOME HOMONUCLEAR (DIATOMIC) MOLECULES

(1) Hydrogen molecule (H2): It is formed by the combination of two hydrogen atoms. Each hydrogen atom has one electron in Is orbital, so, the electronic configuration of hydrogen molecule is

This indicates that two hydrogen atoms are bonded by a single covalent bond. Bond dissociation energy of hydrogen has been found = 438 kJ/mole. Bond-Length = 74 pm No unpaired electron is present therefore, it is diamagnetic.

(2) Helium molecule (He2): Each helium atom contains 2 electrons, thus in the He2 molecule there would be 4 electrons. The electrons will be accommodated in σ1s and σ*1s molecular orbitals:

HYDROGEN BONDING

When highly electronegative elements like nitrogen, oxygen, flourine are attached to hydrogen to form a covalent bond, the electrons of the covalent bond are shifted towards the more electronegative atom.
Thus, a partial positive charge develops on the hydrogen atom which forms a bond with the other electronegative atom. This bond is known as the hydrogen bond and it is weaker than the covalent bond. For example, in HF molecules, hydrogen bonds exist between the hydrogen atom of one molecule and fluorine atom of another molecule. It can be depicted as

TYPES OF H-BONDS:

Intermolecular hydrogen bond
Intramolecular hydrogen bond.

(i)Intermolecular hydrogen bond:

It is formed between two different molecules of the same or different compounds. For Example, in HF molecules, water molecules etc.

(ii) Intramolecular hydrogen bond:

In this type, hydrogen atom is in between the two highly electronegative F, N, O atoms present within the same molecule.
For example, in o-nitrophenol, the hydrogen is in between the two oxygen atoms.

GENESIS OF PERIODIC CLASSIFICATION

DOBEREINER'S TRIADS

In 1829, Dobereiner arranged certain elements with similar properties in groups of three in such a way that the atomic mass of the middle element was nearly the same as the average atomic masses of the first and the third elements.
A few triads proposed by him are listed.

LIMIATIONS OF DOBEREINER'S TRIADS

The triads given by Dobereiner were helpful in grouping some elements with similar characteristics together, but he could not arrange all the elements known at that time into triads.

NEWLAND'S LAW OF OCTAVES

John Newlands proposed the law of octaves by stating that when elements are arranged in order of increasing atomic masses, every eighth element has properties similar to the first.
Newlands called it the law of octaves because a similar relationship exists in the musical notes also.
This can be illustrated as:

LIMITATION OF NEWLAND'S LAW OF OCTAVES

(i) This classification was successful only up to the element calcium. After that, every eighth element did not possess the same properties as the element lying above it in the same group.
(ii) When noble gas elements were discovered at a later stage, their inclusion in the table disturbed the entire arrangement.

MENDELEEV'S PERIODIC TABLE

Mendeleev’s Periodic Law: The physical and chemical properties of the elements are a periodic function of their atomic masses.
Mendeleev arranged the elements known at that time in order of increasing atomic masses and this arrangement was called the periodic table.
Elements with similar characteristics were present in vertical rows called groups. The horizontal rows were known as periods.

DESCRIPTION OF MENDELEEV'S PERIODIC TABLE

(i) In the periodic table, the elements are arranged in vertical rows called groups and horizontal rows known as periods.
(ii) There are nine groups indicated by Roman Numerals as I, II, III, IV, V, VI, VII, VIII and zero. Group VIII consists of nine elements which are arranged in three triads. The zero group contains elements belonging to inert gases or noble gases and elements present have zero valency.
(iii) There are seven periods (numbered from 1 to 7) or, horizontal rows in the Mendeleev’s periodic table.

IMPORTANCE OF MENDELEEV'S PERIODIC TABLE

(i) This made the study of the elements quite systematic in the sense that if the properties of one element in a particular group are known, those of others can be predicted.
(ii) This helped to a great extent in the discovery of these elements at a later stage.
(iii) Mendeleev corrected the atomic masses of certain elements with the help of their expected positions and properties.

DEFECTS IN MENDELEEV'S PERIODIC TABLE

(i) Hydrogen has been placed in group IA along with alkali metals. But it also resembles halogens of group VII A in many properties.Thus, its position in Mendeleev’s periodic table is controversial.
(ii) Although the elements in Mendeleev’s periodic table have been arranged in order of their atomic masses, in some cases the element with higher atomic mass precedes the element with lower atomic mass.
(iii) We know that the isotopes of an element have different atomic masses but the same atomic number.
Since, periodic table has been framed on the basis of increasing atomic masses of the elements, different positions must have been allotted to all the isotopes of a particular element.
(iv) According to Mendeleev, the elements placed in the same group must resemble their properties. But there is no similarity among the elements in the two sub-groups of a particular group. (v) In some cases, elements with similar properties have been placed in different groups. (vi) Lanthanoids and actinoids were placed in two separate rows at the bottom of the periodic table without assigning a proper reason. (vii) No proper explanation has been offered for the fact that why the elements placed in group show resemblance in their properties.

MENDELEEV'S PERIODIC TABLE

Physical and chemical properties of the elements are the periodic function of their atomic numbers.
Present Form of the Periodic Table (Long form of Periodic Table)
The long form of periodic table, also called Modem Periodic Table, is based on Modern periodic law. In this table, the elements have been arranged in order of increasing atomic numbers.
Nomenclature of Elements with Atomic No. more than 100

STRUCTURAL FEATURES OF THE PERIODIC GROUPS

The long form of the periodic table also consists of the vertical rows called groups.
There are in all 18 groups in the periodic table.
Unlike the Mendeleev periodic table, each group is an independent group.

CHARACTERISTICS OF GROUPS

(i) All the elements present in a group have the same general electronic configuration of the atoms.
(ii) The elements in a group are separated by definite gaps of atomic numbers (2, 8, 8,18, 18,32).
(iii) The atomic sizes of the elements in the group increase down the group due to an increase in the number of shells.
(iv) The physical properties of the elements such as m.p., b.p. density, solubility etc., follow a systematic pattern.
(v) The elements in each group have generally similar chemical properties.

PERIODS

Horizontal rows in a periodic table are known as periods.
There are seven periods in the long form of the periodic table.
Characteristics of periods:
(i) In all the elements present in a period, the electrons are filled in the same valence shell.
(ii) The atomic sizes generally decrease from left to right.

s-BLOCK ELEMENTS

General electronic configuration: ns1-2 Characteristics of s-block elements:
(i) All the elements are soft metals.
(ii) They have low melting and boiling points.
(iii) They are highly reactive.
(iv) Most of them impart colours to the flame.
(v) They generally form ionic compounds.
(vi) They are good conductors of heat and electricity.

p-BLOCK ELEMENTS

General electronic configuration: ns2np1-6
Characteristics of p-block elements:
(i) The compounds of these elements are mostly covalent in nature.
(ii) They show variable oxidation states.
(iii) In moving from left to right in a period, the non-metallic character of the elements increases.
(iv) The reactivity of elements in a group generally decreases downwards.
(v) At the end of each period is a noble gas element with a closed valence shell ns2 np6 configuration.
(vi) Metallic character increases as we go down the group.

d-BLOCK ELEMENTS

General electronic configuration: (n -1) d1-10 ns0-2
The d-block elements are known as transition elements because they have incompletely filled d-orbitals in their ground state or in any of the oxidation states.
(i) They are all metals with high melting and boiling points. (ii) The compounds of the elements are generally paramagnetic in nature. (iii) They mostly form coloured ions, exhibit variable valence (oxidation states). (iv) They are oftenly used as catalysts.

f-BLOCK ELEMENTS

General electronic configuration: (n – 2) f1-14 (n -1) d0-1 ns2
They are known as inner transition elements because in the transition elements of d-block, the electrons are filled in (n – 1) d sub-shell while in the inner transition elements of f-block the filling of electrons takes place in (n – 2) f subshell, which happens to be one inner subshell.
(i) The two rows of elements at the bottom of the Periodic Table, called the Lanthanoids Ce (Z = 58) – Lu (Z = 71) and Actinoids Th (Z = 90) – Lr (Z = 103). (ii) These two series of elements are called Inner Transition Elements (f-Block Elements). (iii) They are all metals. Within each series, the properties of the elements are quite similar. (iv) Most of the elements pf the actinoid series are radio-active in nature.

METALS

(i) Metals comprise more than 78% of all known elements and appear on the left side of the Periodic Table.
(ii) Metals are solids at room temperature.
(iii) Metal usually has high melting and boiling points.
(iv) They are good conductors of heat and electricity.
(v) They are malleable and ductile.

NON-METALS

(i) Non-metals are located at the top right hand side of the Periodic Table.
(ii) Non-metals are usually solids or gases at low temperature with low melting and boiling points.
(iii) They are poor conductors of heat and electricity.
(iv) The non-metallic character increases as one goes from left to right across the Periodic Table.
(v) Most non-metallic solids are brittle and are neither malleable nor ductile.

METALLOIDS

The elements (e.g., silicon, germanium, arsenic, antimony and tellurium) show the characteristic of both metals and non-metals.
These elements are also called semimetals.

NOBLE GASES

These are the elements present in group 18.
Each period ends with a noble gas element.
All the members are of gaseous nature and because of the presence of all the occupied filled orbitals, they have very little tendency to take part in chemical combinations.
These are also called inert gases.

REPRESENTATIVE ELEMENTS

The elements of group 1 (alkali metals), group 2 (alkaline earth metals) and group 13 to 17 constitute the representative elements. They are elements of s-block and p-block.

TRANSITION ELEMENTS

The transition elements include all the d-block elements and they are present in the centre of the periodic table between s and p-block elements.

INNER TRANSITION ELEMENTS

Lanthanide (the fourteen elements after Lanthanum) and actinides (the fourteen elements after actinium) are called inner transition elements.
They are also called f-block elements.
The elements after uranium are also called transuranic elements.

PERIODIC TRENDS IN PROPERTIES OF ELEMENTS

TRENDS IN PHYSICAL PROPERTIES

Lanthanide (the fourteen elements after Lanthanum) and actinides (the fourteen elements after actinium) are called inner transition elements.
They are also called f-block elements.
The elements after uranium are also called transuranic elements.

Atomic Radii

It is defined as the distance from the centre of the nucleus to the outermost shell containing the electrons.
Depending upon whether an element is a non-metal or a metal, three different types of atomic radii are used.
These are:
(i) Covalent radius
(ii) Ionic Radius
(iii) van der Waals radius
(iv) Metallic radius.

(i) Covalent Radius

It is equal to half of the distance between the centres of the nuclei of two atoms held together by a purely covalent single bond.

(ii) Ionic Radius

It may be defined as the effictive distance from the nucleus of an ion upto which it has an influence in the ionic bond.

(iii) van der Waals radius

Atoms of Noble gases are held together by weak van der Waals forces of attraction. The van der Waals radius is half of the distance between the centre of nuclei of atoms of noble gases.

(iv) Metallic Radius

It is defined as half of the intemuclear distance between the two adjacent metal ions in the metallic lattice.

Variation of Atomic Radius in the Periodic Table

Variation in a Period: Along a period, the atomic radii of the elements generally decreases from left to right.

Variation in a group: The atomic radii of the elements in every group of the periodic table increases as we move downwards.

Ionic Radius

The ionic radii can be estimated by measuring the distances between cations and anions in ionic crystals. In general, the ionic radii of elements exhibit the same trend as the atomic radii.

Cation

The removal of an electron from an atom results in the formation of a cation. The radius of cation is always smaller than that of the atom.

Anion

Gain of an electron leads to an anion. The radius of the anion is always larger than that of the atom.

Isoelectronic Species

Some atoms and ions which contain the same number of electrons, we call them isoelectronic species. For example, O2-, F–, Na+ and Mg2+ have the same number of electrons (10). Their radii would be different because of their different nuclear charges.

Ionization Enthalpy

It is the energy required to remove an electron from an isolated gaseous atom in its ground state.
M (g) + I.E ——->M+ (g) + e–
The unit of ionization enthalpy is kJ mol-1 and the unit of ionization potential is electron volt per atom.
Successive Ionization Enthalpies:
If a gaseous atom is to lose more than one electron, they can be removed one after the other i.e., in succession and not simultaneously. This is known as successive ionization enthalpy (or potential).

Variation of Ionization Enthalpies in the Periodic Table

Variation of Ionization Enthalpy Along a Period

Along a period ionization enthalpies are expected to increase in moving across from left to the right, because the nuclear charge increases and the atomic size decreases.

Variation of Ionization Enthalpy in a Group

The ionization enthalpies of the elements decrease on moving from top to the bottom in any group.
The decrease in ionization enthalpies down any group is because of the following factors.
(i) There is an increase in the number of the main energy shells (n) in moving from one element to the other.
(ii) There is also an increase in the magnitude of the screening effect due to the gradual increase in the number of inner electrons.

Electron Gain Enthalpy

Electron Gain Enthalpy is the energy released when an electron is added to an isolated gaseous atom so as to convert it into a negative ion. The process is represented as:

For the majority of the elements the electron gain enthalpy is negative.
For example, the electron gain enthalpy for halogens is highly negative because they can acquire the nearest noble gas configuration by accepting an extra electron.
In contrast, noble gases have large positive electron gain enthalpies because the extra electron has to be placed in the next higher principal quantum energy level thereby producing a highly unstable electronic configuration.

Successive Electron Gain Enthalpies:

We have studied that electrons from gaseous atoms are lost in succession (i.e., one after the other).
Similarly, these are also accepted one after the other, i.e., in succession.
After the addition of one electron, the atom becomes negatively charged and the second electron is to be added to a negatively charged ion.
But the addition of a second electron is opposed by electrostatic repulsion and hence the energy has to be supplied for the addition of the second electron.
Thus the second electron gain enthalpy of an element is positive.
For example, when an electron is added to an oxygen atom to form A– ion, energy is released.
But when another electron is added to 0- ion to form O2- ion, energy is absorbed to overcome the strong electrostatic repulsion between the negatively charged 0– ion and the second electron being added. Thus, the first electron gain enthalpy:

Factors on which Electron Gain Enthalpy Depends:

(i) Atomic size: As the size of an atom increases, the distance between its nucleus and the incoming electron also increases and electron gain enthalpy becomes less negative,
(ii) Nuclear charge: With the increase in nuclear charge, force of attraction between the nucleus and the incoming electron increases and thus electron gain enthalpy becomes more negative.
(iii) Symmetry of the Electronic Configuration: The atoms with symmetrical configuration (having fully filled or half filled orbitals in the same sub-shell) do not have any urge to take up extra electrons because their configuration will become unstable. In that case the energy will be needed and electron gain enthalpy (Δ eg H) will be positive. For example, noble gas elements have positive electron gain enthalpies.

Variation of Electron Gain Enthalpy Across a Period:

Electron gain enthalpy becomes more negative with an increase in the atomic number across a period.
Variation of Electron Gain Enthalpy in a Group:
Electron gain enthalpy becomes less negative as we go down a group.

Electronegativity

A qualitative measure of the ability of an atom in a chemical compound to attract shared electrons to itself is called electronegativity.
Unlike ionization enthalpy and electron gain enthalpy, it is not a measurable quantity.
However, a number of numerical scales of electronegativity of elements viz, Pauling scale, Milliken- Jaffe scale, Allred Kochow scale have been developed.
The electronegativity of any given element is not constant; it varies depending on the element to which it is bound.
Across a Period:
Electronegativity generally increases across a period from left to right.
In a Group:
It decreases down a group.

Periodic Trends in Chemical Properties along a Period

(i) Metallic character: Decrease across a period maximum on the extreme left (alkali metals).
(ii) Non-metallic character: Increasess along a period. (From left to right).
(iii) Basic nature of oxides: Decreases from left to right in a period.
(iv) Acidic nature of oxides: Increases from left to right in a period.

Variation from Top to Bottom on Moving Down a Group

(i) Metallic character. Generally increases because of increase in atomic size and hence decrease in the ionizatiort energy of the elements in a group from top to bottom.
(ii) Non-metallic character. Generally decreases down a group. As electronegativity of elements decreases from top to bottom in a group,
(iii) Basic nature of oxides. Since the metallic character or electropositivity of elements increases when going from top to bottom in a group, the basic nature of oxidation naturally increases.
(iv) Acidic character of oxides. Generally decreases as the non-metallic character of elements decreases in going from top to bottom in a group.
(v) Reactivity of metals. Generally increases down a group. Since the tendency to lose electrons increases.
(vi) Reactivity of non-metals. Generally decreases down the group, Higher the electro-negativity of non-metals, greater is their reactivity. Since electronegativity of non-metals in a group decreases from top to bottom, their reactivity also decreases.

Anomalous Properties of Second Period Elements

The first element of each of the group 1 (lithium) and 2 (beryllium) and group 13-17 (boron to fluorine) differs in many respects from the other members of their respective groups.
For example, lithium unlike other alkali metals, and beryllium unlike other alkaline earth metals form compounds which have significant covalent character; the other members of these groups, pre-dominatly form ionic compounds.
It has been observed that some elements of the second period show similarities with the elements of the third period placed diagonally to each other, though belonging to different groups.
For example,

This similarity in properties of elements placed diagonally to each other is called a diagonal relationship.

DISCOVERY OF ELECTRON-DISCHARGE TUBE EXPERIMENT

In 1879, William Crooks studied the conduction of electricity through gases at low pressure. He performed the experiment in a discharge tube which is a cylindrical hard glass tube about 60 cm in length. It is sealed at both the ends and fitted with two metal electrodes as shown in Fig. 2.1.

The electrical discharge through the gases could be observed only at very low pressures and at very high voltages. The pressure of different gases could be adjusted by evacuation. When sufficiently high voltage is applied across the electrodes, current starts flowing through a stream of particles moving in the tube from the negative electrode (cathode) to the positive electrode (anode). These were called cathode rays or cathode ray particles.

PROPERTIES OF CATHODE RAYS

(i) Cathode rays travel in a straight line.
(ii) Cathode rays start from cathode and move towards the anode.
(iii) These rays themselves are not visible but their behaviour can be observed with the help of certain kinds of materials (fluorescent or phosphorescent) which glow when hit by them.
(iv) Cathode rays consist of negatively charged particles. When an electric field is applied on the cathode rays with the help of a pair of metal plates, these are found to be deflected towards the positive plate indicating the presence of negative charge.
(v) The characteristics of cathode rays do not depend upon the material of electrodes and the nature of gas present in the cathode ray’tube.

DETERMINATION OF CHARGE/MASS RATIO (e/m) RATIO FOR ELECTRONS

J. J. Thomson for the first time experimentally determined charge/mass ratio called elm ratio for the electrons.
For this, he subjected the beam of electrons released in the discharge tube as cathode rays to influence the electric and magnetic fields.
These were acting perpendicular to one another as well as to the path followed by electrons.
According to Thomson, the amount of deviation of the particles from their path in presence of electrical and magnetic field depends upon following factors:
(i) Greater the magnitude of the charge on the particle, greater is the interaction with the electric or magnetic field and thus greater is the deflection.
(ii) The mass of the particle — lighter the particle, greater the deflection.
(iii) The deflection of electrons from their original path increases with the increase in the voltage across the electrodes or strength of the magnetic field.
By carrying out accurate measurements on the amount of deflections observed by the electrons on the electric field strength or magnetic field strength, Thomson was able to determine the value of e/me = 1.758820 x 1011 C kg-1, where me = Mass of the electron in kg and e = magnitude of charge on the electron in coulomb (C).

CHARGE ON THE ELECTRON

R.A. Millikan devised a method known as oil drop experiment to determine the charge on the electrons.

DISCOVERY OF PROTON-ANODE RAYS

In 1886, Goldstein modified the discharge tube by using a perforated cathode. On reducing the pressure, he observed a new type of luminous rays passing through the holes or perforations of the cathode and moving in a direction opposite to the cathode rays. These rays were named as positive rays or anode rays or as canal rays. Anode rays are not emitted from the anode but from a space between anode and cathode.

PROPERTIES OF ANODE RAYS

(i) The value of positive charge (e) on the particles constituting anode rays depends upon the nature of the gas in the discharge tube.
(ii) The charge to mass ratio of the particles is found to depend on the gas from which these originate.
(iii) Some of the positively charged particles carry a multiple of the fundamental unit of electrical charge.
(iv) The behaviour of these particles in the magnetic or electric field is opposite to that observed for electron or cathode rays.

PROTON

The smallest and lightest positive ion was obtained from hydrogen and was called proton.
Mass of proton = 1.676 x 10-27 kg
Charge on a proton = (+) 1.602 x 10-19 C

NEUTRON

It is a neutral particle.
It was discovered by Chadwick (1932).
By the bombardment of thin sheets of beryllium with fast moving a-particles he observed that highly penetrating rays consist of neutral particles which were named neutrons.

THOMSON MODEL OF ATOM

(i) J. J. Thomson proposed that an atom may be regarded as a sphere of approximate radius 1CT8 cm carrying positive charge due to protons and in which negatively charged electrons are embedded.
(ii) In this model, the atom is visualized as a pudding or cake of positive charge with electrons embedded into it.
(iii) The mass of the atom is considered to be evenly spread over the atom according to this model.

DRAWBACK OF THOMSON MODEL OF ATOM

This model was able to explain the overall neutrality of the atom, but it could not satisfactorily explain the results of scattering experiments carried out by Rutherford in 1911.

RUTHERFORD'S ALPHA PARTICLE SCATTERING EXPERIMENT

Rutherford in 1911, performed some scattering experiments in which he bombarded thin foils of metals like gold, silver, platinum or copper with a beam of fast moving a-particles.
The thin gold foil had a circular fluorescent zinc sulphide screen around it.
Whenever a-particles struck the screen, a tiny flash of light was produced at that point.
From these experiments, he made the following observations:
(i) Most of the a-particles passed through the foil without undergoing any deflection,
(ii) A few a-particles underwent deflection through small angles.
(iii) Very few are deflected back i.e., through an angle of nearly 180°.
From these observations, Rutherford drew the following conclusions:
(i) Since most of the a-particles passed through the foil without undergoing any deflection, there must be sufficient empty space within the atom.
(ii) A small fraction of a-particles was deflected by small angles. The positive charge has to be concentrated in a very small volume that repelled and deflected a few positively charged a-particles. This very small portion of the atom was called the nucleus.
(iii) The volume of the nucleus is very small as compared to the total volume of the atom.

RUTHERFORD'S NUCLEAR MODEL OF AN ATOM

(i) The positive charge and most of the mass of the atom was densely concentrated in an extremely small region. This very small portion of the atom was called the nucleus by Rutherford.
(ii) The nucleus is surrounded by electrons that move around the nucleus with a very high speed in circular paths called orbits.
(iii) Electrons and nucleus are held together by electrostatic forces of attraction.

ATOMIC NUMBER

The number of protons present in the nucleus is equal to the atomic number (z).
For example, the number of protons in the hydrogen nucleus is 1, in the sodium atom it is 11, therefore, their atomic numbers are 1 and 11.
In order to keep the electrical neutrality, the number of electrons in an atom is equal to the number of protons (atomic number, z).
For example, the number of electrons in hydrogen atom and sodium atom are 1 and 11 respectively.
Atomic Number (z) = Number of protons in the nucleus of an atom = Number of electrons in a neutral atom.

MASS NUMBER

Number of protons and neutrons present in the nucleus are collectively known as nucleons.
The total number of nucleons is termed as mass number (A) of the atom.
Mass Number (A) = Number of protons (p) + Number of neutrons (n).

ISOTOPES

Atoms with identical atomic numbers but different atomic mass numbers are known as Isotopes.

CHARACTERISTICS OF ISOTOPES

(i) Since the isotopes of an element have the same atomic number, but different mass number, the nuclei of isotopes contain the same number of protons, but different number of neutrons.
(ii) Since, the isotopes differ in their atomic masses, all the properties of the isotopes depending upon the mass are different.
(iii) Since, the chemical properties are mainly determined by the number of protons in the nucleus, and the number of electrons in the atom, the different isotopes of an element exhibit similar chemical properties. For example, all the isotopes of carbon on burning give carbon dioxide.

ISOBARS

DRAWBACKS OF RUTHERFORD'S MODEL

(i) When a body is moving in an orbit, it achieves acceleration. Thus, an electron moving around a nucleus in an orbit is under acceleration. According to Maxwell’s electromagnetic theory, charged particles when accelerated must emit electromagnetic radiation. Therefore, an electron in an orbit will emit radiation, the energy carried by radiation comes from electronic motion.
Its path will become closer to the nucleus and ultimately should spiral into the nucleus within . 10-8 s. But actually this does not happen. Thus, Rutherford’s model cannot explain the stability of an atom if the motion of electrons is described on the basis of classical mechanics and electromagnetic theory.
(ii) Rutherford’s model does not give any idea about distribution of electrons around the nucleus and about their energies.

DEVELOPMENTS LEADING TO BOHR'S MODEL OF ATOM

Two developments played a major role in the formulation of Bohr’s model of atom. These were:
(i) Dual character of the electromagnetic radiation which means that radiations possess both wave like and particle like properties.
(ii) Experimental results regarding atomic spectra which can be explained only by assuming quantized electronic energy levels in atoms.

NATURE OF ELECTROMAGNETIC RADIATION (ELECTROMAGNETIC WAVE THEORY)

This theory was put forward by James Clark Maxwell in 1864. The main points of this theory are as follows:
(i) The energy is emitted from any source (like the heated rod or the filament of a bulb through which electric current is passed) continuously in the form of radiations and is called the radiant energy.
(ii) The radiation consists of electric and magnetic fields oscillating perpendicular to each other and both perpendicular to the direction of propagation of the radiation.
(iii) The radiations possess wave character and travel with the velocity of light 3 x 108 m/sec.
(iv) These waves do not require any material medium for propagation. For example, rays from the sun reach us through space which is a non-material medium

CHARACTERISTICS OF A WAVE

WAVELENGTH

It is defined as the distance between any two consecutive crests or troughs. It is represented by X and its S.I. unit is metre.

FREQUENCY

Frequency of a wave is defined as the number of waves passing through a point in one second. It is represented by v (nu) and is expressed in Hertz (Hz). 1 Hz = 1 cycle/sec.

VELOCITY

Velocity of a wave is defined as the linear distance travelled by the wave in one second.
It is represented by c and is expressed in cm/sec or m/sec.

AMPLITUDE

Amplitude of a wave is the height of the crest or the depth of the through. It is represented by V and is expressed in the units of length.

WAVE NUMBER

It is defined as the number of waves present in 1 metre length. Evidently it will be equal to the reciprocal of the wavelength. It is represented by bar v (read as nu bar).

ELECTROMAGNETIC SPECTRUM

When electromagnetic radiations are arranged in order of their increasing wavelengths or decreasing frequencies, the complete spectrum obtained is called electromagnetic spectrum.

LIMITATIONS OF ELECTROMAGNETIC WAVE THEORY

Electromagnetic wave theory was successful in explaining properties of light such as interference, diffraction etc; but it could not explain the following:
(i) The phenomenon of black body radiation.
(ii) The photoelectric effect.
(iii) The variation of heat capacity of solids as a function of temperature.
(iv) The line spectra of atoms with reference to hydrogen.

BLACK BODY RADIATION

The ideal body, which emits and absorbs all frequencies is called a black body and the radiation emitted by such a body is called black body radiation. The exact frequency distribution of the emitted radiation from a black body depends only on its temperature.

At a given temperature, intensity of radiation emitted increases with decrease of wavelength, reaches a maximum value at a given wavelength and then starts decreasing with further decrease of wavelength as shown in Fig 2.6.

PLANCK'S QUANTUM THEORY

To explain the phenomenon of ‘Black body radiation’ and photoelectric effect, Max Planck in 1900, put forward a theory known as Planck’s Quantum Theory.
This theory was further extended by Einstein in 1905. The main points of this theory was as follows:
(i) The radiant energy emitted or absorbed in the form of small packets of energy. Each such packet of energy is called a quantum.
(ii) The energy of each quantum is directly proportional to the frequency of the radiation.

where h is a proportionality constant, called Planck’s constant. Its value is equal to 6.626 x 10-34 Jsec.

PHOTOELECTRRIC EFFECT

Hertz, in 1887, discovered that when a beam of light of a certain frequency strikes the surface of some metals, electrons are emitted or ejected from the metal surface. The phenomenon is called the photoelectric effect.

OBSERVATIONS IN PHOTOELECTRRIC EFFECT

(i) Only photons of light of a certain minimum frequency called threshold frequency (v0) can cause the photoelectric effect. The value of v0 is different for different metals.
(ii) The kinetic energy of the electrons which are emitted is directly proportional to the frequency of the striking photons and is quite independent of their intensity.
(iii) The number of electrons that are ejected per second from the metal surface depends upon the intensity of the striking photons or radiations and not upon their frequency.

EXPLANATION OF PHOTOELECTRRIC EFFECT

Einstein in (1905) was able to give an explanation of the different points of the photoelectric effect using Planck’s quantum theory as under:
(i) Photoelectrons are ejected only when the incident light has a certain minimum frequency (threshold frequency v0)
(ii) If the frequency of the incident light (v) is more than the threshold frequency (v0), the excess energy (hv – hv0) is imparted to the electron as kinetic energy. (iii) On increasing the intensity of light, more electrons are ejected but the energies of the electrons are not altered.

DUAL BEHAVIOUR OF ELECTROMAGNETIC RADIATION

From the study of behaviour of light, scientists came to the conclusion that light and other electromagnetic radiations have dual nature. These are wave nature as well as particle nature. Whenever radiation interacts with matter, it displays particle-like properties in contrast to the wavelike properties (interference and diffraction) which it exhibits when it propagates. Some microscopic particles, like electrons, also exhibit this wave-particle duality.

SPECTRUM

AWhen a ray of white light is passed through a prism the wave with shorter wavelength bends more than the one with a longer wavelength. Since ordinary white light consists of waves with all the wavelengths in the visible range, an array of white light is spread out into a series of coloured bands called spectrum. The light of red colour which has the longest wavelength is deviated the least while the violet light, which has the shortest wavelength is deviated the most.

CONTINUOUS SPECTRUM

When a ray of white light is analysed by passing through a prism it is observed that it splits up into seven different wide bands of colours from violet to red (like rainbow). These colours are so continuous that each of them merges into the next. Hence, the spectrum is called the continuous spectrum.

EMISSION SPECTRA

Emission Spectra is noticed when the radiations emitted from a source are passed through a prism and then received on the photographic plate. Radiations can be emitted in a number of ways such as:
(i) from the sun or glowing electric bulb.
(ii) by passing electric discharge through a gas at low pressure.
(iii) by heating a substance to high temperature.

LINE SPECTRA

When the vapours of some volatile substance are allowed to fall on the flame of a Bunsen burner and then analysed with the help of a spectroscope. Some specific coloured lines appear on the photographic plate which are different for different substances. For example, sodium or its salts emit yellow light while potassium or its salts give out violet light.

ABSORPTION SPECTRA

When white light is passed through the vapours of a substance and the transmitted light is then allowed to strike a prism, dark lines appear in the otherwise continuous spectrum. The dark lines indicate that the radiations corresponding to them were absorbed by the substance from the white light. This spectrum is called the absorption spectrum.Dark lines appear exactly at the same positions where the lines in the emission spectra appear.

LINE SPECTRUM OF HYDROGEN

When electric discharge is passed through hydrogen gas enclosed in a discharge tube under low pressure and the emitted light is analysed by a spectroscope, the spectrum consists of a large number of lines which are grouped into different series. The complete spectrum is known as the hydrogen spectrum. On the basis of experimental observations, Johannes Rydberg noted that all series of lines in the hydrogen spectrum could be described by the following expression:

Rydberg in 1890, and has given a simple theoretical equation for the calculation of wavelengths and wave numbers of the spectral lines in different series of hydrogen spectrum. The equation is known as the Rydberg formula (or equation).

This relation is valid for hydrogen atoms only. For other species,

where Z is the atomic number of the species.
Here RH = constant, called Rydberg constant for hydrogen and n1 , n2 are integers (n2 > n1)
For any particular series, the value of n1 is constant while that of n2 changes.
For example,
For Lyman series, n1= 1, n2= 2, 3, 4, 5………..
For Balmer series, n1 = 2, n2 = 3, 4, 5, 6………..
For Paschen series, n1= 3, n2 = 4, 5, 6, 7………..
For Brackett series,n1 = 4, n2 = 5, 6, 7, 8………..
For Pjund series, n1 =5, n2 = 6, 7, 8, 9………..
Thus, by substituting the values of n1 and n2 in the above equation, wavelengths and wave number of different spectral lines can be calculated. When n1 = 2, the expression given above is called Balmer’s formula.

BOHR'S MODEL OF ATOM

Niels Bohr in 1913, proposed a new model of atoms on the basis of Planck’s Quantum Theory. The main points of this model are as follows:
(i) In an atom, the electrons revolve around the nucleus in certain definite circular paths called orbits.
(ii) Each orbit is associated with definite energy and therefore these are known as energy levels or energy shells. These are numbered as 1, 2, 3, 4……….. or K, L, M, N………..
(iii) Only those energy orbits are permitted for the electron in which angular momentum of the electron is a whole number multiple of h/2π. Angular momentum of electron (mvr) = nh/2π (n = 1, 2, 3, 4 etc).
m = mass of the electron.
v = tangential velocity of the revolving electron.
r = radius of the orbit.
h = Planck’s constant.
n is an integer.
(iv) As long as an electron is present in a particular orbit, it neither absorbs nor loses energy and its energy, therefore, remains constant.
(v) When energy is supplied to an electron, it absorbs energy only in fixed amounts as quanta and jumps to higher energy state away from the nucleus known as excited state. The excited state is unstable, the electron may jump back to the lower energy state and in doing so, it emits the same amount of energy. (∆E = E2 – E1).

ACHIEVEMENTS OF BOHR'S THEORY

1. Bohr’s theory has explained the stability of an atom.
2. Bohr’s theory has helped in calculating the energy of electrons in hydrogen atoms and one electron species. The mathematical expression for the energy in the nth orbit is,

3. Bohr’s theory has explained the atomic spectrum of hydrogen atoms.

LIMITATIONS OF BOHR'S MODEL

(i) The theory could not explain the atomic spectra of the atoms containing more than one electron or multielectron atoms.
(ii) Bohr7s theory failed to explain the fine structure of the spectral lines.
(iii) Bohr’s theory could not offer any satisfactory explanation of Zeeman effect and Stark effect.
(iv) Bohr’s theory failed to explain the ability of atoms to form molecules formed by chemical bonds.
(v) It was not in accordance with Heisenberg’s uncertainty principle.

DUAL BEHAVIOUR OF MATTER (de Broglie Equation)

de Broglie in 1924, proposed that matter, like radiation, should also exhibit dual behaviour i.e., both particle like and wave like properties. This means that like photons, electrons also have momentum as well as wavelength. From this analogy, de Broglie gave the following relation between wavelength (λ) and momentum (p) of a material particle.

HEISENBERG'S UNCERTAINITY PRINCIPLE

It states that, “It is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron”.

SIGNIFICANCE OF UNCERTAINITY PRINCIPLE

(i) It rules out the existence of definite paths or trajectories of electrons and other similar particles.
(ii) The effect of Heisenberg’s uncertainty principle is significant only for microscopic objects and is negligible for macroscopic objects.

REASONS FOR THE FAILURE OF BOHR'S MODEL

(i) The wave character of the electron is not considered in the Bohr Model.
(ii) According to the Bohr Model an orbit is a clearly defined path and this path can completely be defined only if both the position and the velocity of the electron are known exactly at the same time. This is not possible according to Heisenberg’s uncertainty principle.

QUANTUM MECHANICAL MODEL OF ATOM

Quantum mechanics: Quantum mechanics is a theoretical science that deals with the study of the motions of microscopic objects that have both observable wave-like and particle-like properties.
Important Features of Quantum Mechanical Model of Atom
(i) The energy of electrons in an atom is quantized i.e., can only have certain values.
(ii) The existence of a quantized electronic energy level is a direct result of the wave-like properties of electrons.
(iii) Both the exact position and exact velocity of an electron in an atom cannot be determined simultaneously.
(iv) An atomic orbital has a wave function φ. There are many orbitals in an atom. Electrons occupy an atomic orbital which has definite energy. An orbital cannot have more than two electrons. The orbitals are filled in increasing order of energy. All the information about the electron in an atom is stored in orbital wave function φ.
(v) The probability of finding electron at a point within an atom is proportional to square of orbital wave function i.e., |φ2|at that point. It is known as probability density and is always positive.
From the value of φ2 at different points within an atom, it is possible to predict the region around the nucleus where electron most probably will be found.

QUANTUM NUMBERS

Atomic orbitals can be specified by giving their corresponding energies and angular momentums which are quantized (i.e., they have specific values). The quantized values can be expressed in terms of quantum number. These are used to get complete information about an electron i.e., its location, energy, spin etc.
Principal Quantum Number (n)
It is the most important quantum number since it tells the principal energy level or shell to which the electron belongs.
It is denoted by the letter V and can have any integral value except zero, i.e., n = 1, 2, 3, 4……….. etc.
The various principal energy shells are also designated by the letters, K, L, M, N, O, P ….. etc. Starting from the nucleus.
The principal quantum number gives us the following information:
(i) It gives the average distance of the electron from the nucleus.
(ii) It completely determines the energy of the electron in hydrogen atoms and hydrogen like particles.
(iii) The maximum number of electrons present in any principal shell is given by 2n2 where n is the number of the principal shell.

(i) Azimuthal or Subsidiary or Orbital Angular Quantum Number (l)

It is found that the spectra of the elements contain not only the main lines but there are many fine lines also present. This number helps to explain the fine lines of the spectrum.
The azimuthal quantum number gives the following information:
(i) The number of subshells present in the main shell.
(ii) The angular momentum of the electron present in any subshell.
(in) The relative energies of various subshells.
(iv) The shapes of the various subshells present within the same principal shell.
This quantum number is denoted by the letter T. For a given value of n, it can have any value ranging from 0 to n – 1. For example,
For the 1st shell (k), n = 1, l can have only one value i.e., l = 0 For n = 2, the possible values of l can be 0 and 1.
Subshells corresponding to different values of l are represented by the following symbols:
value of l 0 1 2 3 4 5 ……………..
Notation for subshell s p d f g h ………………..

(ii) Magnetic Orbital Quantum Number (m or m1)

The magnetic orbital quantum number determines the number of preferred orientations of the electrons present in a subshell.
Since each orientation corresponds to an orbital, therefore, the magnetic orbital quantum number determines the number of orbitals present in any subshell.
The magnetic quantum number is denoted by letter m or ml and for a given value of l, it can have all the values ranging from – l to + l including zero.
Thus, for the energy value of l, m has 2l + 1 values.
For example,
For l = 0 (s-subshell), ml can have only one value i.e., m1 = 0.
This means that the s-subshell has only one orientation in space.
In other words, the s-subshell has only one orbital called s-orbital.

(iii) Spin Quantum Number (S or ms)

This quantum number helps to explain the magnetic properties of the substances.
A spinning electron behaves like a micromagnet with a definite magnetic moment.
If an orbital contains two electrons, the two magnetic moments oppose and cancel each other.

SHAPES OF s-ORIBITALS

s-orbital is present in the s-subshell. For this subshell, l = 0 and ml = 0.
Thus, an s-orbital with only one orientation has a spherical shape with uniform electron density along all the three axes.
The probability of Is electron is found to be maximum near the nucleus and decreases with the increase in the distance from the nucleus.
In 2s electrons, the probability is also maximum near the nucleus and decreases to zero probability.
The spherical empty shell for 2s electrons is called nodal surface or simply node.

SHAPES OF p-ORIBITALS

p-orbitals are present in the p-subshell for which l = 1 and m1 can have three possible orientations – 1, 0, + 1.
Thus, there are three orbitals in the p-subshell which are designated as px, py and pz orbitals depending upon the axis along which they are directed.
The general shape of a p-orbital is dumb-bell consisting of two portions known as lobes.
Moreover, there is a plane passing through the nucleus along which finding of the electron density is almost nil.
This is known as the nodal plane as shown in the fig.

From the dumb-bell pictures, it is quite obvious that unlike s-orbital, a p-orbital is directional in nature and hence it influences the shapes of the molecules in the formation of which it participates.

SHAPES OF d-ORIBITALS

d-orbitals are present in the d-subshell for which l = 2 and m[ = -2, -1, 0, +1 and +2.
This means that there are five orientations leading to five different orbitals.

AUFBAU PRINCIPLE

The principle states: In the ground state of the atoms, the orbitals are filled in order of their increasing energies.
In other words, electrons first occupy the lowest energy orbital available to them and enter into higher energy orbitals only after the lower energy orbitals are filled.
The order in which the energies of the orbitals increase and hence the order in which the orbitals are filled is as follows:
Is, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, id, 5p, 6s, if, 3d, 6p, 7s, 5f 6d, 7p
The order may be remembered by using the method given in fig.2.11.

PAULI EXCLUSION PRINCIPLE

According to this principle, no two electrons in an atom can have the same set of four quantum numbers.
Pauli exclusion principle can also be stated as: Only two electrons may exist in the same orbital and these electrons must have opposite spins.

HUND'S RULE OF MAXIMUM MULTIPLICITY

It states that: pairing of electrons in the orbitals belonging to the same subshell (p, d or f) does not take place until each orbital belonging to that subshell has got one electron each i.e., it is singly occupied.

ELECTRONIC CONFIGURATION OF ATOMS

The distribution of electrons into orbitals of an atom is called its electronic configuration.
The electronic configuration of different atoms can be represented in two ways.
For example:

CAUSES OF STABILITY OF COMPLETELY FILLED AND HALF-FILLED SUBSHELLS

The completely filled and half filled subshells are stable due to the following reasons:
1. Symmetrical distribution of electrons: The completely filled or half filled subshells have symmetrical distribution of electrons in them and are therefore more stable.
2. The stabilizing effect arises whenever two or more electrons with the same spin are present in the degenrate orbitals of a subshell.
These electrons tend to exchange their positions and the energy released due to their exchange is called exchange energy.
The number of exchanges that can take place is maximum when the subshell is either half filled or completely filled.
As a result the exchange energy is maximum and so is the stability.

IMPORTANT TABLES

IMPORTANCE IN CHEMISTRY

Chemistry has a direct impact on our lives and has a wide range of applications in different fields. These are given below:

A. IN AGRICULTURE AND FOOD:

(i) It has provided chemical fertilizers such as urea, calcium phosphate, sodium nitrate, ammonium phosphate etc.
(ii) It has helped to protect the crops from insects and harmful bacteria, by the use of certain effective insecticides, fungicides and pesticides.
(iii) The use of preservatives has helped to preserve food products like jam, butter, squashes etc. for longer periods.

B. IN HEALTH AND SANITATION:

(i) It has provided mankind with a large number of life-saving drugs. Today, dysentery and pneumonia are curable due to the discovery of sulfa drugs and penicillin life-saving drugs. Cisplatin and taxol have been found to be very effective for cancer therapy and AZT (Azidothymidine) is used for AIDS victims.
(ii) Disinfectants such as phenol are used to kill the micro-organisms present in drains, toilets, floors etc.
(iii) A low concentration of chlorine i.e., 0.2 to 0.4 parts per million (ppm) is used for sterilization of water to make it fit for drinking purposes.

C. SAVING THE ENVIRONMENT:

The rapid industrialisation all over the world has resulted in a lot of pollution. Poisonous gases and chemicals are being constantly released in the atmosphere. They are polluting the environment at an alarming rate. Scientists are working day and night to develop substitutes which may cause lower pollution. For example, CNG (Compressed Natural Gas), a substitute of petrol, is very effective in checking pollution caused by automobiles.

D. APPLICATION IN INDUSTRY:

Chemistry has played an important role in developing many industrially manufactured fertilizers, alkalis, acids, salts, dyes, polymers, drugs, soaps,
detergents, metal alloys and other inorganic and organic chemicals including new materials contribute in a big way to the national economy.

MATTER

Anything which has mass and occupies space is called matter. For example, books, pencils, water, air are composed of matter as we know that they have mass and they occupy space.

CLASSIFICATION OF MATTER

There are two ways of classifying the matter:
(A) Physical classification
(B) Chemical classification

(A) PHYSICAL EXAMINATION

Matter can exist in three physical states:
1. Solids 2. Liquids 3. Gases
1. Solids: The particles are held very close to each other in an orderly fashion and there is not much freedom of movement. Characteristics of solids: Solids have definite volume and definite shape.
2. Liquids: In liquids, the particles are close to each other but can move around. Characteristics of liquids: Liquids have definite volume but not definite shape.
3. Gases: In gases, the particles are far apart as compared to those present in solid or liquid states. Their movement is easy and fast.
Characteristics of Gases: Gases have neither definite volume nor definite shape. They completely occupy the container in which they are placed.

(B) CHEMICAL CLASSIFICATION

1. Pure substances:

A pure substance may be defined as a single substance (or matter) which cannot be separated by simple physical methods.
Pure substances can be further classified as (i) Elements (ii) Compounds

(i) Elements:

An element consists of only one type of particle. These particles may be atoms or molecules.
For example, sodium, copper, silver, hydrogen, oxygen etc. are some examples of elements.
They all contain atoms of one type.
However, atoms of different elements are different in nature.
Some elements such as sodium . or copper contain single atoms held together as their constituent particles whereas in some others two or more atoms combine to give molecules of the element.
Thus, hydrogen, nitrogen and oxygen gases consist of molecules in which two atoms combine to give the respective molecules of the element.

(ii) Compounds:

It may be defined as a pure substance containing two or more elements combined together in a fixed proportion by weight and can be decomposed into these elements by suitable chemical methods.
Moreover, the properties of a compound are altogether different from the constituting elements.
The compounds have been classified into two types. These are:

(a) Inorganic Compounds:

These are compounds which are obtained from non-living sources such as rocks and minerals. A few examples are: Common salt, marble, gypsum, washing soda etc.

(b) Organic Compounds:

These are the compounds which are present in plants and animals. All the organic compounds have been found to contain carbon as their essential constituent. For example, carbohydrates, proteins, oils, fats etc.

2. Mixtures

The combination of two or more elements or compounds which are not chemically combined together and may also be present in any proportion, is called mixture. A few examples of mixtures are: milk, sea water, petrol, lime water, paint glass, cement, wood etc.

Types of Mixtures:

(i) Homogeneous mixtures: A mixture is said to be homogeneous if it has a uniform composition throughout and there are no visible boundaries of separation between the constituents. For example: A mixture of sugar solution in water has the same sugar water composition throughout and all portions have the same sweetness.
(ii) Heterogeneous mixtures: A mixture is said to be heterogeneous if it does not have uniform composition throughout and has visible boundaries of separation between the various constituents. The different constituents of a heterogeneous mixture can be seen even with naked eye. For example: When iron filings and sulphur powder are mixed together, the mixture formed is heterogeneous. It has a greyish-yellow appearance and the two constituents, iron and sulphur, can be easily identified with naked eye.

DIFFERENCES BETWEEN COMPOUNDS AND MIXTURES

Compounds:

1. In a compound, two or more elements are combined chemically.
2. In a compound, the elements are present in the fixed ratio by mass. This ratio cannot change.
3. Compounds are always homogeneous, i.e., they have the same composition throughout.
4. In a compound, constituents cannot be separated by physical methods.
5. In a compound, the constituents lose their identities i.e., i compound does not show the characteristics of the constituting elements.

Mixtures:

1. In a mixture, more elements or compounds are simply mixed and not combined chemically.
2. In a mixture the constituents are not present in a fixed ratio. It can vary.
3. Mixtures may be either homogeneous or heterogeneous in nature.
4. Constituents of mixtures can be separated by physical methods.
5, In a mixture, the constituents do not lose their identities i.e., a mixture shows the characteristics of all the constituents .
We have discussed the physical and chemical classification of matter.

PROPERTIES OF MATTER AND THEIR MEASUREMENTS

PHYSICAL PROPERTIES

Those properties which can be measured or observed without changing the identity or the composition of the substance. Some examples of physical properties are colour, odour, melting point, boiling point etc.

CHEMICAL PROPERTIES

It requires a chemical change to occur. The examples of chemical properties are characteristic reactions of different substances. These include acidity, basicity, combustibility etc.

UNITS OF MEASUREMENT

Fundamental Units: The quantities mass, length and time are called fundamental quantities and their units are known as fundamental units. There are seven basic units of measurement for the quantities: length, mass, time, temperature, amount of substance, electric current and luminous intensity.

SI-SYSTEM

This system of measurement is the most common system employed throughout the world. It has given units of all the seven basic quantities listed above.

DEFINITELY OF BASIC SI UNITS

1. Metre: It is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second.
2. Kilogram: It is the unit of mass. It is equal to the mass of the international prototype of the kilogram.
3. Second: It is the duration of 9192631, 770 periods of radiation which correspond to the transition between the two hyperfine levels of the ground state of caesium- 133 atoms.
4. Kelvin: It is the unit of thermodynamic temperature and is equal to 1/273.16 of the thermodynamic temperature of the triple point of water.
5. Ampere: The ampere is that constant current which if maintained in two straight parallel conductors of infinite length, of negligible circular cross section and placed, 1 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 N per metre of length.
6. Candela: It may be defined as the luminous intensity in a given direction, from a source which emits monochromatic radiation of frequency 540 x 1012 Hz and that has a radiant intensity in that direction of 1/ 683 watt per steradian.
7. Mole: It is the amount of substance which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon -12. Its symbol is ‘mol’.

MASS AND WEIGHT

MASS

Mass of a substance is the amount of matter present in it.
The mass of a substance is constant.
The mass of a substance can be determined accurately in the laboratory by using an analytical balance.
The SI unit of mass is kilogram.

WEIGHT

It is the force exerted by gravity on an object. Weight of a substance may vary from one place to another due to change in gravity.

VOLUME

Volume means the space occupied by matter.
It has the units of (length)3.
In SI units, volume is expressed in metre3 (m3).
However, a popular unit of measuring volume, particularly in liquids is litre (L) but it is not in SI units or an S.I. unit.
Mathematically,
1L = 1000 mL = 1000 cm3 = 1dm3.
Volume of liquids can be measured by different devices like a burette, pipette, cylinder, measuring flask etc. All of them have been calibrated.

TEMPERATURE

There are three scales in which temperature can be measured. These are known as Celsius scale (°C), Fahrenheit scale (°F) and Kelvin scale (K).

-> Thermometers with Celsius scale are calibrated from 0°C to 100°C.
-> Thermometers with Fahrenheit scale are calibrated from 32°F to 212°F.
-> Kelvin Scale of temperature is S.I. scale and is very common these days. Temperature on this scale is shown by the sign K. The temperature on two scales are related to each other by the relationship.

DENSITY

Density of a substance is its amount of mass per unit volume. So, SI units of density can be obtained as follows:

This unit is quite large and a chemist often expresses density in g cm3 where mass is expressed in grams and volume is expressed in cm3.

UNCERTAINTY IN MEASUREMENTS

All scientific measurements involve a certain degree of error or uncertainty.
The errors which arise depend upon two factors.
(i) Skill and accuracy of the worker
(ii) Limitations of measuring instruments.

LAWS OF CHEMICAL COMBINATIONS

The combination of elements to form compounds is governed by the following five basic laws.
(i) Law of Conservation of Mass
(ii) Law of Definite Proportions
(iii) Law of Multiple Proportions
(iv) Law of Gaseous Volume (Gay Lussac’s Law)
(v) Avogadro’s Law

(i) LAW OF CONSERVATION OF MASS

The law was established by a French chemist, A. Lavoisier.
The law states:
In all physical and chemical changes, the total mass of the reactants is equal to that of the products.
In other words, matter can neither be created nor destroyed.
The following experiments illustrate the truth of this law.
(a) When matter undergoes a physical change.

It is found that there is no change in weight though a physical change has taken place.
(b) When matter undergoes a chemical change.
For example, decomposition of mercuric oxide.

During the above decomposition reaction, matter is neither gained nor lost.

(ii) LAW OF DEFINITE PROPORTIONS

According to this law:
A pure chemical compound always consists of the same elements combined together in a fixed proportion by weight.
For example, Carbon dioxide may be formed in a number of ways i.e.,

(iii) LAW OF MULTIPLE PROPORTIONS

If two elements combine to form two or more compounds, the weight of one of the elements which combines with a fixed weight of the other in these compounds, bears a simple whole number ratio by weight.
For example,

(iv) GAY LUSSAC'S LAW OF GASEOUS VOLUMES

The law states that, under similar conditions of temperature and pressure, whenever gases combine, they do so in volumes which bear simple whole number ratios with each other and also with the gaseous products. The law may be illustrated by the following examples. (a) Combination between hydrogen and chlorine:

(b) Combination between nitrogen and hydrogen: The two gases lead to the formation of ammonia gas under suitable conditions. The chemical equation is

(v) AVOGADRO'S LAW

Avogadro proposed that equal volumes of gases at the same temperature and pressure should contain an equal number of molecules.
For example,
If we consider the reaction of hydrogen and oxygen to produce water, we see that two volumes of hydrogen combine with one volume of oxygen to give two volumes of water without leaving any unreacted oxygen.

DALTON'S ATOMIC THEORY

In 1808, Dalton published ‘A New System of Chemical Philosophy’ in which he proposed the following:
1. Matter consists of indivisible atoms.
2. All the atoms of a given element have identical properties including identical mass. Atoms of different elements differ in mass.
3. Compounds are formed when atoms of different elements combine in a fixed ratio.
4. Chemical reactions involve reorganisation of atoms. These are neither created nor destroyed in a chemical reaction.

ATOMIC MASS

The atomic mass of an element is the number of times an atom of that element is heavier than an atom of carbon taken as 12. It may be noted that the atomic masses as obtained above are the relative atomic masses and not the actual masses of the atoms. One atomic mass unit (amu) is equal to l/12th of the mass of an atom of carbon-12 isotope. It is also known as a unified mass.

AVERAGE ATOMIC MASS

Most of the elements exist as isotopes which are different atoms of the same element with different mass numbers and the same atomic number. Therefore, the atomic mass of an element must be its average atomic mass and it may be defined as the average relative mass of an atom of an element as compared to the mass of carbon atoms (C-12) taken as 12w.

MOLECULAR MASS

Molecular mass is the sum of atomic masses of the elements present in a molecule. It is obtained by multiplying the atomic mass of each element by the number of its atoms and adding them together.
For example,
Molecular mass of methane (CH4)
= 12.011 u + 4 (1.008 u)
= 16.043 u

FORMULA MASS

Ionic compounds such as NaCl, KNO3, Na2C03 etc. do not consist of molecules i.e., single entities but exist “as ions closely packed together in a three dimensional space as shown in -Fig. 1.5.

In such cases, the formula is used to calculate the formula mass instead of molecular mass. Thus, formula mass of NaCl = Atomic mass of sodium + atomic mass of chlorine = 23.0 u + 35.5 u = 58.5 u.

MOLE CONCEPT

It is found that one gram atom of any element contains the same number of atoms and one gram molecule of any substance contains the same number of molecules.
This number has been experimentally determined and found to be equal to 6.022137 x 1023 The value is generally called Avogadro’s number or Avogadro’s constant.
It is usually represented by NA:
Avogadro’s Number, NA = 6.022 × 1023

PERCENTAGE COMPOSITION

One can check the purity of a given sample by analysing this data. Let us understand by taking the example of water (H20). Since water contains hydrogen and oxygen, the percentage composition of both these elements can be calculated as follows:

EMPIRICAL FORMULA

The formula of the compound which gives the simplest whole number ratio of the atoms of yarious elements present in one molecule of the compound.
For example, the formula of hydrogen peroxide is H202.
In order to express its empirical formula, we have to take out a common factor 2.
The simplest whole number ratio of the atoms is 1:1 and the empirical formula is HO. Similarly, the formula of glucose is C6H1206.
In order to get the simplest whole number of the atoms,
(i) Common factor = 6
(ii) The ratio is = 1 : 2 : 1 The empirical formula of glucose = CH20

MOLECULAR FORMULA

The formula of a compound which gives the actual ratio of the atoms of various elements present in one molecule of the compound. For example, molecular formula of hydrogen peroxide = H202and Glucose = C6H1206
Molecular formula = n x Empirical formula
Where n is the common factor and also called the multiplying factor.
The value of n may be 1, 2, 3, 4, 5, 6 etc.
In case n is 1, Molecular formula of a compound = Empirical formula of the compound.

STOICHIOMETRY AND STOICHIOMETRIC CALCULATIONS

The word ‘stoichiometry’ is derived from two Greek words—Stoicheion (meaning element) and metron (meaning measure). Stoichiometry deals with the calculation of masses (sometimes volume also) of the reactants and the products involved in a chemical reaction.
Let us consider the combustion of methane. A balanced equation for this reaction is as given below:

LIMITING REACTANT/REAGENT

Sometimes, in alchemical equations, the reactants present are not the amount as required according to the balanced equation. The amount of products formed then depends upon the reactant which has reacted completely. This reactant which reacts completely in the reaction is called the limiting reactant or limiting reagent. The reactant which is not consumed completely in the reaction is called an excess reactant.

REACTIONS IN SOLUTIONS

When the reactions are carried out in solutions, the amount of substance present in its given volume can be expressed in any of the following ways:
1. Mass percent or weight percent (w/w%)
2. Mole fraction
3. Molarity
4. Molality

1. Mass percent:

It is obtained by using the following relation:

2. Mole fraction:

It is the ratio of the number of moles of a particular component to the total number of moles of the solution. For a solution containing n2 moles of the solute dissolved in n1 moles of the solvent,

3. Molarity:

It is defined as the number of moles of solute in 1 litre of the solution.

4. Molality:

It is defined as the number of moles of solute present in 1 kg of solvent. It is denoted by m.

WAVES

Wave is a form of disturbance which travels through a material medium due to the repeated f periodic motion of the particles of the medium about their mean positions without any actual transportation of matter.

CHARACTERISTICS OF WAVE

The characteristics of waves are as follows:
(i) The particles of the medium traversed by a wave execute relatively small vibrations about their mean positions but the particles are not permanently displaced in the direction of propagation of the wave.
(ii) Each successive particle of the medium executes a motion quite similar to its predecessors along/perpendicular to the line of travel of the wave.
(iii) During wave motion only transfer of energy takes place but not that of a portion of the medium.

TYPES OF WAVE

Waves are mainly of three types:
(a) mechanical or elastic waves,
(b) electromagnetic waves and
(c) matter waves.

(a) Mechanical waves

Mechanical waves can be produced or propagated only in a material medium. These waves are governed by Newton’s laws of motion. For example, waves on water surface, waves on strings, sound waves etc.

Types of Mechanical waves :

Mechanical waves are of two types:
(i) Transverse wave motion, (ii) Longitudinal wave motion

(i) Transverse wave motion

In transverse waves the particles of the medium vibrate at right angles to the direction in which the wave propagates.
Waves on strings, surface water waves and electromagnetic waves are transverse waves.
In electromagnetic waves (which include light waves) the disturbance that travels is not a result of vibrations of particles but it is the oscillation of electric and magnetic fields which takes place at right angles to the direction in which the wave travels.

(ii) Longitudinal wave motion

In these types of waves, particles of the medium vibrate to and fro about their mean position along the direction of propagation of energy.
These are also called pressure waves.
Sound waves are longitudinal mechanical waves.

b) Electromagnetic waves

These are the waves which require no material medium for their production and propagation, i.e., they can pass through vacuum and any other material medium.
Common examples of electromagnetic waves are visible light; ultra–violet light; radiowaves, microwaves etc.

(c) Matter waves

These waves are associated with moving particles of matter, like electrons, protons, neutrons etc.

WAVELENGTH

The distance travelled by the disturbance during the time of one vibration by a medium particle is called the wavelength (λ). In case of a transverse wave the wavelength may also be defined as the distance between two successive crests or troughs. In case of a longitudinal wave, the wavelength (λ) is equal to distance from the centre of one compression (or refraction) to another.

WAVE VELOCITY

Wave velocity is the time rate of propagation of wave motion in the given medium. It is different from particle velocity.
Wave velocity depends upon the nature of the medium.
Wave velocity (υ) = frequency (v) x wavelength (λ)

AMPLITUDE

The amplitude of a wave is the maximum displacement of the particles of the medium from their mean position.

FREQUENCY

The number of vibrations made by a particle in one second is called Frequency. It is represented by v. Its unit is hertz (Hz) v =1/T

TIME PERIOD

The time taken by a particle to complete one vibration is called time period. T = 1/v, it is expressed in seconds.

THE VELOCITY OF TRANSVERSE WAVES IN A STRETCHED STRING IS GIVEN BY:

where T is the tension in the string and μ is the mass per unit length of the string, μ is also called linear mass density of the string. The SI unit of μ is kg m-1.

THE VELOCITY OF LONGITUDINAL WAVES IN AN ELASTIC MEDIUM IS GIVEN BY:

where E is the modulus of elasticity of the medium and ρ is the density of the medium. In case of solids, E is Young’s modulus of elasticity (Y), then

NEWTON'S FORMULA FOR THE VELOCITY OF SOUND IN AIR

According to Newton, when sound waves travel in air or in a gaseous media, the change is taking place isothermally and hence, it is found that

Speed of sound in air at STP conditions, calculated on the basis of Newton’s formula is 280 ms-1.
However, the experimentally determined value is 332 ms-1.
According to Laplace, during propagation of sound waves, the change takes place under adiabatic conditions because gases are thermal insulators and compressions and refractions are alternately taking place with a high frequency.

FACTORS INFLUENCING VELOCITY OF SOUND

The velocity of sound in any gaseous medium is affected by a large number of factors like density, pressure, temperature, humidity, wind velocity etc.
(i) The velocity of sound in a gas is inversely proportional to the square root of density of the gas.
(ii) The velocity of sound is independent of the change in pressure of the gas, provided temperature remains constant.
(iii) The velocity of sound in a gas is directly proportional to the square root of its absolute temperature.
(iv) The velocity of sound in moist air is greater than the velocity of sound in dry air.
(v) If wind flows at an angle θ to the direction of propagation of sound, the velocity of sound is v + w cos θ, where w is the velocity of wind.

GENERAL EQUATION OF PROGRESSIVE WAVES

“A progressive wave is one which travels in a given direction with constant amplitude, i.e., without attenuation.”
As in wave motion, the displacement is a function of space as well as time, hence displacement relation is expressed as a combined function of position and time as:
y (x,t) = A sin (kx — ωt + Ф)
We may also choose a cosine function instead of a sine function. Here A, K, ω and Ф are four constant for a given wave and are known as amplitude, angular wave number, angular frequency and initial phase angle of given wave.

RELATION BETWEEN PHASE AND PATH DIFFERENCE

A wave motion can be reflected from a rigid as well as from a free boundary. A travelling wave, at a rigid boundary or a closed end, is reflected with a phase reversal but the reflection at an open boundary takes place without any phase change.

THE PRINCIPLE OF SUPERPOSITION OF WAVE

When any number of waves meet simultaneously at a point in a medium, the net displacement at a given time is the algebraic sum of the displacements due to each wave at that time.

STANDING WAVES OR STATIONARY WAVES

When two sets of progressive wave trains of the same type (i.e., both longitudinal or both transverse) having the same amplitude and time period/frequency/ wavelength travelling with same speed along the same straight line in opposite directions superimpose, a new set of waves are formed. These are called stationary waves or standing waves.

PROGRESSIVE WAVES

1. The disturbance progresses onwards; it is being handed over from particle to particle. Each particle executes the same type of vibration as the preceding one, though at a different time.
2. The waves are in the form of crests and troughs, i.e., sine/cosine functions, which move on wards with a definite velocity.
3. Every particle has the same amplitude; which it attains in its own time depending upon the progress of the wave.
4. The phase of every particle varies continuously from 0 to 2π .
5. No particle remains permanently at rest. Twice during each vibration, the particles are momentarily at rest. Different particles attain this position at different times.
6. All the particles have the same maximum velocity which they attain one after another, as the wave advances.
7. There is a regular flow of energy across every plane along the direction of propagation of the wave. The average energy in a wave is half potential and half kinetic.

STATIONARY WAVES

1. The disturbance is stationary, there being no forward or backward movement of the wave. Each particle has its own vibration characteristics.
2. The waves have the appearance of a sine/cosine function, which shrinks to a straight line, twice in each vibration. It never advances.
3. Every particle has a fixed allotted amplitude. Some have zero amplitude (nodes) ,some have maximum amplitude (antinodes) always. Each particle attains this at the same given moment.
4. All the particles in one-half of the waves have a fixed phase and all the particles in the other half of the wave have the same phase in the opposite direction simultaneously.
5. There are particles which are permanently at rest (nodes) and all other particles have their own allotted maximum displacement, which they attain simultaneously. These particles are momentarily at rest twice in each vibration, all at the same time.
6. All the particles attain their individual allotted velocities depending upon their positions, simultaneously. Two particles (nodes) in one wave form have zero velocities all the time.
7. There is no flow of energy at all, across any plane. Each particle has its own allotted individual energy.

FREQUENCY OF THE STRETCHED STRING

In general, if the string vibrates in P loops, the frequency of the string under that mode is given by

Based on this relation three laws of transverse vibrations of stretched strings arise. They are law of length, law of tension and law of mass.

LAW OF LENGTH

The fundamental frequency v is inversely proportional to the length L of the stretched string.

LAW OF TENSION

The fundamental frequency is directly proportional to the square root of the tension in the string.

LAW OF MASS

The fundamental frequency is inversely proportional to the square root of mass per unit length of the given string when L and T are kept constants.

BEATS

The phenomenon of regular rise and fall in the intensity of sound, when two waves of nearly equal frequencies travelling along the same line and in the same direction superimpose each other is called beats.
One rise and one fall in the intensity of sound constitutes one beat and the number of beats per second is called beat frequency.
It is given as: vb = (v1-v2)
where v1 and v2 are the frequencies of the two interfering waves; v1 being greater than v2.

DOPPLER EFFECT

According to Doppler’s effect, whenever there is a relative motion between a source of sound and listener, the apparent frequencies of sound heard by the listener is different from the actual frequency of sound emitted by the source. For sound the observed frequency v’ is given by

Here v = true frequency of wave emitted by the source, v = speed of sound through the medium, v0 the velocity of observer relative to the medium and vs the velocity of source relative to the medium. In using this formula, velocities in the direction OS (i.e., from the observer towards the source) are treated as positive and those opposite to it are taken as negative.

IMPORTANT TABLES

PERIODIC MOTION

Motions, processes or phenomena, which repeat themselves at regular intervals, are called periodic.

OSCILLATORY MOTION

The motion of a body is said to be oscillatory motion if it moves to and fro about a fixed point after regular intervals of time. The fixed point about which the body oscillates is called mean position or equilibrium position.

SIMPLE HARMONIC MOTION

Simple harmonic motion is a special type of periodic oscillatory motion in which
(i) The particle oscillates on a straight line
(ii) The acceleration of the particle is always directed towards a fixed point on the line.
(iii) The magnitude of acceleration is proportional to the displacement of the particle from the fixed point.

CHARACTERISTICS OF SHM

The displacement x in SHM at time t is given by
x = A sin (ωt+ Ф ), where the three constants A, ω and Ф characterize the SHM, i.e., they distinguish one SHM from another. A SHM can also be described by a cosine function as follows:
x = A cos (ωt + δ)
The displacement of an oscillating particle at any instant is equal to the change in its position vector during that time. The maximum value of displacement in an oscillatory motion on either side of its mean position is called “displacement amplitude” or “simple amplitude”.
Thus, amplitude A = x max.
The time taken by an oscillating particle to complete one full oscillation to and fro about its mean (equilibrium) position is called the “time period” of SHM. It is given by

FREQUENCY

The number of oscillations in one second is called frequency. It is expressed in sec-1 or Hertz. Frequency and time period are independent of amplitude.

PHASE

The quantity (ωt+ Ф) is called the phase of SHM at time t; it describes the state of motion at that instant.
The quantity Ф is the phase at time f = 0 and is called the phase constant or initial phase or epoch of the SHM.
The phase constant is the time-independent term in the cosine or sine function.

The force responsible for maintaining the S.H.M. is called restoring force.
If the displacement (x) from the equilibrium position is small, the restoring force (F) acting on the body is given by
F = -kx, where k is a force constant.

ENERGY IN SHM

When a body executes SHM, its energy changes between kinetic and potential, but the total energy is always constant. At any displacement x from the equilibrium position:

SPRINGS IN SERIES

If two springs, having spring constant k1 and k2, are joined in series, the spring constant of the combination is given by

SPRINGS IN PARALLEL

If two springs, having spring constants k1 and k2, are joined in parallel, the spring constant of the combination is given by
k = k1 + k2
When one spring is attached to two masses m1 and m2, then

SIMPLE PENDULUM

A simple pendulum is the most common example of bodies executing S.H.M. An ideal simple pendulum consists of a heavy point mass body suspended by a weightless in extensible and perfectly flexible string from a rigid support about which it is free to oscillate.
The time period of simple pendulum of length ‘l’ is given by

The time period of a simple pendulum depends on
(i) length of the pendulum and
(ii) the acceleration due to gravity (g).
A second’s pendulum is a pendulum whose time period is. 2s. At a place where g = 9.8 ms-2, the length of a second’s pendulum is found to be 99.3 cm (= 1 m).
If a liquid of density p oscillates in a vertical U-tube of uniform cross sectional area A, then the time period of oscillation is given by

If a cylinder of mass m, length L, density of material p and uniform area of cross section A, oscillates vertically in a liquid of density o, then the time period of oscillation is given by

UNDAMPED AND DAMPED SIMPLE HARMONIC OSCILLATIONS

(i) UNDAMPED SIMPLE HARMONIC OSCILLATIONS

When a simple harmonic system oscillates with a constant amplitude which does not change with time, its oscillations are called undamped simple harmonic oscillations.

(ii) DAMPED SIMPLE HARMONIC OSCILLATIONS

When a simple harmonic system oscillates with a decreasing amplitude with time, its oscillations are called damped simple harmonic oscillations. The angular frequency of the damped oscillator is given by

A system is said to execute free oscillations, if on being displaced or disturbed from its position of equilibrium, it oscillates itself without outside interference.
When a system is compelled to oscillate with a frequency other than its natural frequency, it is said to execute forced oscillations.
The external force which causes forced oscillation, is of sinusoidal nature. It is given as

Resonance is the phenomenon of setting a body into oscillations with large amplitudes under the influence of some external periodic force whose frequency is exactly equal to the natural frequency of the given body. Such oscillations are called the “resonant oscillations”.
The two or more oscillations linked together in such a way that the exchange of energy takes place between them are called coupled oscillators. The oscillations produced by coupled oscillators are known as coupled oscillations.
The speed of a mechanical wave depends upon the properties of the medium in which it is travelling. If E is the elastic constant and ρ is the density of the medium then the speed of the wave is given by

In the case of electromagnetic waves, we know that they are the combinations of the oscillation of electric and magnetic fields in perpendicular directions.
Their speed of propagation depends upon the permitivity and the permeability of the medium. If μ0 is permeability and ε0 is the permitivity of the medium in vaccum, then

IMPORTANT TABLES

The kinetic theory was developed in the nineteenth century by Maxwell, Boltzman and others.
Kinetic theory explains the behaviour of gases based on the idea that the gas consists of rapidly moving atoms or molecules.

IDEAL GAS

An ideal gas or a perfect gas is that gas which strictly obeys gas laws such as Boyle’s law, Charle’s law, Gay Lussac’s law etc.
An ideal gas has following characteristics:
(i) The Molecule of an ideal gas is a point mass with no geometrical dimensions.
(ii) There is no force of attraction or repulsion amongst the molecules of the gas.

KINETIC THEORY AND GAS PRESSURE

The pressure of a gas is the result of continuous bombardment of the gas molecules against the walls of the container. According to the kinetic theory, the pressure P exerted by an ideal gas is given by

BOYLE'S LAW

According to this law, the volume (V) of a fixed mass of a gas is inversely proportional to the pressure (P) of the gas, provided the temperature of the gas is kept constant.

CHARLE'S LAW

According to this law, the volume (V) of a given mass of a gas is directly proportional to the temperature of the gas, provided pressure of the gas remains constant.

GAY LUSSAC'S LAW (OR PRESSURE LAW )

According to this law, the pressure P of a given mass of a gas is directly proportional to its absolute temperature T, provided the volume V of the gas remains constant.

EQUATION OF STATE OF AN IDEAL GAS

The relationship between pressure P, volume V and absolute temperature T of a gas is called its equation of state.
The equation of state of an ideal gas: PV = nRT,
where n is the number of moles of the enclosed gas and R is the molar gas constant which is the same for all gases and its value is R = 8.315 JK-1 mob-1

AVOGADRO'S LAW

Equal volumes of all gases under S.T.P. contain the same number of molecules equalling 6.023 x 1023.

GRAHAM'S LAW OF DIFFUSION OF GASES

It states that the rate of diffusion of a gas is inversely proportional to the square root of the density of the gas. Hence, denser the gas, the slower is the rate of diffusion.

DALTON'S LAW OF PARTIAL PRESSURES

According to this law, the resultant pressure exerted by a mixture of non-interacting gases is equal to the sum of their individual pressures.
i-e., P = P1 + P2 + ————-Pn
Mean (or average) speed of molecules of a gas is defined as the arithmetic mean of the speeds of gas molecules.

Root mean square speed of gas molecules is defined as the square root of the mean of the squares of the speeds of gas molecules.

Most probable speed of gas molecules is defined as the speed which is possessed by maximum number of molecules in a gas

KINETIC INTERPRETATION OF TEMPERATURE

The total average kinetic energy of all the molecules of a gas is proportional to its absolute temperature (T).
Thus, the temperature of a gas is a measure of the average kinetic energy ‘IT of the molecules of the gas.
U = 3/2 RT
According to this interpretation of temperature, the average kinetic energy U is zero at T = 0, i.e., the motion of molecules ceases altogether at absolute zero.

DEGREE OF FREEDOM

The total number of independent co-ordinates required to specify the position of a molecule or the number of independent modes of motion possible with any molecule is called degree of freedom. Mono-, di-, and polyatomic (N) molecules have, 3,5 or (3 N-K) number of degrees of freedom where K is the number of constraints [restrictions associated with the structure].

LAW OF EQUIPARTITION OF ENERGY

For a dynamic system in thermal equilibrium, the energy of the system is equally distributed amongst the various degrees of freedom and the energy associated with each degree of freedom per molecule is 1/2 kT, where k is Boltzman constant.

MEAN FREE PATH

Mean free path of a molecule in a gas is the average distance travelled by the molecule between two successive collisions

(i) Smaller the number of molecules per unit volume of the gas, larger is the mean free path.
(ii) Smaller the diameter, larger is the mean free path.
(iii) Smaller the density, larger is the mean free path. In the case of vacuum, ρ = 0, λ —>∞
(iv) Smaller the pressure of a gas, larger is the mean free path.
(v) Higher the temperature of a gas, larger is the mean free path.