88 Handbook of Chemistry

State of System

7
When microscopic properties have definite value, the conditions of
existence of the system is known as state of system.
State functions (State variables) When values of a system are
independent of path followed and depend only on initial and final
state, it is known as state function, e.g. ∆U , ∆H , ∆G etc.

Thermodynamics
Path functions These depend upon the path followed, e.g. work,
heat, etc.

Thermodynamic Properties
The branch of science which deals with the quantitative relationship Intensive Properties
between heat and other forms of energies is called thermodynamics. Properties of the system which depend only on the nature of matter
but not on the quantity of matter are called intensive properties, e.g.
Thermodynamic Terms pressure, temperature, specific heat, etc.
(i) System It refers to the part of universe in which observations Extensive Properties
are carried out. Properties of the system which are dependent on the quantity of
(ii) Surroundings The part of universe other than the system is matter are called extensive properties, e.g. internal energy, volume,
known as surroundings. enthalpy, etc.
(iii) Boundary The wall that separates the system from the
Thermodynamic Process
surroundings is called boundary.
It is the operation which brings change in the state of the system.
(iv) Thermodynamic equilibrium A system in which the Thermodynamic processes are
macroscopic properties do not undergo any change with time is
(i) Isothermal process In which temperature remains
called thermodynamic equilibrium.
constant, i.e. ( dT = 0, ∆U = 0).
(v) Thermal equilibrium If there is no flow of heat from one (ii) Isochoric process In which volume remains constant,
portion of the system to another, the system is said to be in i.e. ( ∆V = 0).
thermal equilibrium.
(iii) Isobaric process In which pressure remains constant,
(vi) Mechanical equilibrium If no mechanical work is done by i.e. ( ∆p = 0).
one part of the system on another part of the system, it is said to
(iv) Adiabatic process In which heat is not exchanged by system
be in mechanical equilibrium. Such a condition exists when with the surroundings, i.e. ( ∆q = 0).
pressure remains constant.
(v) Cyclic process It is a process in which system returns to
its original state after undergoing a series of change,
Types of Systems i.e. ∆U cyclic = 0 ; ∆H cyclic = 0.
(i) Open system The system in which energy and matter both (iv ) Reversible process A process that follows the reversible
can be exchanged with the surroundings.
path, i.e. the process which occurs in infinite number of steps in a
(ii) Closed system The system in which only energy can be way that the equilibrium conditions are maintained at each step,
exchanged with the surroundings. and the process can be reversed by infinitesimal change in the
(iii) Isolated system The system in which neither energy nor state of functions.
matter can be exchanged with the surroundings.
 Thermodynamics 89 90 Handbook of Chemistry

(vii) Irreversible process The process which cannot be reversed Modes of Transference of Energy
and amount of energy increases. All natural processes are
irreversible. Work (W )
If the system involves gaseous substances and there is a difference of
Internal Energy (E or U) pressure between system and surroundings, work is referred as
It is the total energy within the substance. It is the sum of many types pressure-volume work (W pV ).
of energies like vibrational energy, translational energy, etc. It is an
extensive property and state function. Expression for Pressure-Volume Work
Its absolute value cannot be determined but experimentally change in (i) Work done in irreversible expansion against constant pressure
internal energy ( ∆U ) can be determined by p under isothermal conditions
∆U = U 2 − U 1 or ΣU P − ΣU R q = − W pV = pext ∆V
For exothermic process, ∆U = − ve, whereas for endothermic process (ii) Work done in reversible expansion under isothermal conditions
∆U = +ve. V 
q = − W rev = 2.303 nRT log  2 
U depends on temperature, pressure, volume and quantity of matter  V1 
and is independent of the method by which state has been attained.
p1
or q = − W rev = 2.303 nRT log
p2
Zeroth Law of Thermodynamics or Law of
Thermal Equilibrium (iii) Work done in reversible expansion under adiabatic conditions
nR
The law states that if the two systems are in thermal equilibrium with W rev = (T2 − T1 )
a third system then they are also in thermal equilibrium with each γ −1
other. Temperature is used here to know whether the system is in where, γ = Poisson’s ratio
thermal equilibrium or not.
(Under adiabatic conditions T V γ −1
= constant)
First Law of Thermodynamics (iv) Work done in irreversible expansion under adiabatic conditions
Energy can neither be created nor destroyed although it can be  p T − p2T1 
converted from one form to the other. W irrev = − pext × nR  1 2 
 p1 p2 
Mathematically, ∆U = q + W
where, ∆U = internal energy change (v) When an ideal gas expands in vacuum then
q = heat added to system pext = 0
W = work added to system Work done is maximum in reversible conditions.
Units CGS system – erg
Sign convention
SI system – joule
(i) q is + ve = heat is supplied to the system
(ii) q is – ve = heat is lost by the system Work and heat both appear only at the boundary of the system
(iii) W is +ve = work done on the system during a change in state.
(iv) W is –ve = work done by the system
Heat (q)
It occurs when there is a difference of temperature between system
and surroundings. It is a random form of energy and path dependent.
Its units are joule or calorie.
 Thermodynamics 91 92 Handbook of Chemistry

Heat Capacity of a System Enthalpy (H )

Heat capacity (C) of a system is defined as the amount of heat required It is the sum of internal energy and pV -energy of the system. It is a
to raise the temperature of a system by 1°C. state function and extensive property. Mathematically,
Molar Heat Capacity H = U + pV
It is the heat capacity of 1 mole of substance of the system. Like U , absolute value of H also cannot be known, ∆H is determined
experimentally.
Specific Heat Capacity ∆H = H 2 − H 1 or ∆H = ΣH P − ΣH R
It is the heat capacity of 1 g of substance of the system. For exothermic reaction (the reaction in which heat is evolved),
q = mc ∆T , ∆H = −ve, whereas for endothermic reaction (the reaction in which
heat is absorbed), ∆H = +ve.
where, m = mass of substance, c = specific heat or specific heat capacity
Relationship between ∆H and ∆U
Molar heat capacity, at constant pressure, C p = c p × M
∆H = ∆U + p ∆V or ∆H = ∆U + ∆n ( g ) RT
Molar heat capacity, at constant volume, CV = cV × M
Here, ∆n g = change in the number of gas moles.
(c p and cV are specific heats at constant pressure and constant volume
respectively and M is molecular weight of gas) Enthalpy Change or Reaction Enthalpy ( ∆r H)
c p − cV = R (R = Molar gas constant) It is the change in enthalpy that accompanies a chemical reaction
R represented by a balanced chemical equation.
C p − CV =
M ∆ r H = ΣH ( P ) − ΣH ( R )
 3 Enthalpy of reaction expressed at the standard state conditions is
The molar heat capacity at constant volume, CV =   R
 2 called standard enthalpy of reaction ( ∆H s ).
The molar heat capacity at constant pressure, Factors affecting enthalpy of reaction are
(i) Physical state of reactants and products.
 3  5
Cp =   R + R =   R (ii) Allotropic forms of elements involved.
 2  2
(iii) Chemical composition of reactants and products.
Cp  5
Poisson’s ratio, γ= =   = 1.66 (iv) Amount of reactants.
CV  3
(v) Temperature.
γ = 1.66 for monoatomic gas
γ = 1.40 for diatomic gas Various Forms of Enthalpy of Reaction
γ = 1.33 for triatomic gas Enthalpy of Formation (∆ f H° )
It is the heat change when one mole of compound is obtained from its
Measurement of ∆H and ∆U : Calorimetry
constituent elements. Enthalpy of formation at standard state is
(a) For gaseous reactions Reactions involving gases are carried known as standard enthalpy of formation ( ∆ f H ° ) and is taken as
out in a bomb calorimeter at constant volume. zero by convention.
∆U = − (Heat absorbed by bomb calorimeter)
(b) For reaction in solution Reactions involving solution are
Enthalpy of Combustion (∆ CH° )
carried out at constant pressure inside a coffee-cup calorimeter. It is the enthalpy change taking place when one mole of a compound
undergoes complete combustion in the presence of oxygen (∆C H ).
∆ r H = ( mc ∆T )calorimeter + ( mc ∆T )solution .
∆C H is always negative, because process of combustion is exothermic.
 Thermodynamics 93 94 Handbook of Chemistry

Enthalpy of Solution (∆ sol H° ) Enthalpy of Dilution

It is the enthalpy change when one mole of a substance is dissolved in It is the enthalpy change, when one mole of a substance is diluted from
large excess of solvent, so that on further dilution no appreciable heat one concentration to another.
change occur.
So, ∆sol H ° = ∆ lattice H ° + ∆ hyd H °
Enthalpy of Sublimation ( ∆ sub H° )
It is the enthalpy change, when one mole of a solid substance sublimes.
Enthalpy of Hydration ( ∆ hyd H° )
It is the enthalpy change when one mole of anhydrous or partially
Lattice Enthalpy
hydrated salt combines with required number of moles of water to form It is the enthalpy change, when one mole of an ionic compound
a specific hydrate undergoes complete combustion. It is an exothermic dissociates into its ions in gaseous state.
process.
Bond Enthalpy ( ∆ bond H° )
Enthalpy of Fusion ( ∆ fus H° ) Enthalpy is required to break a bond and energy is released when
It is the enthalpy change that accompanies melting of one mole of solid bond is formed. For this, two different terms are used in
substance. thermodynamics.
(a) Bond dissociation enthalpy The enthalpy change is the
Enthalpy of Vaporisation ( ∆ vap H° ) change in enthalpy when one mole of covalent bonds of a gaseous
It is the enthalpy change that accompanies conversion of one mole of covalent compound is broken to form product in the gas phase.
liquid substance completely into vapours. (b) Mean bond enthalpy The average value of dissociation
energies of polyatomic molecule.
Enthalpy of Neutralisation ( ∆ n H° )
Some factors affecting the bond enthalpy:
It is the enthalpy change that takes place when 1 g-equivalent of an
acid (or base) is neutralised by 1 g-equivalent of a base (or acid) in (i) Size of atoms (ii) Electronegativity
dilute solution. (iii) Bond length (iv) Number of bonding electrons
Enthalpy of neutralisation of strong acid and strong base is always
constant, i.e. 57.1 kJ. Joule-Thomson Effect
The phenomenon of cooling of a gas when it is made to expand
Enthalpy of neutralisation of strong acid and weak base or weak acid adiabatically from a region of high pressure to a region of extremely
and strong base is not constant and numerically less than 57.1 kJ due low pressure is known as Joule-Thomson effect. This effect is zero
to the fact that here the heat is used up in ionisation of weak acid or when an ideal gas expands in vacuum.
weak base. This is known as enthalpy of ionisation of weak acid/or
When an ideal gas undergoes expansion under adiabatic condition in
base.
 ∂E 
vacuum, no change takes place in its internal energy, i.e.   = 0
Enthalpy of Transition ( ∆ t H° )  ∂V  T
It is the enthalpy change when one mole of the substance undergoes  ∂E 
where,   is called the internal pressure.
transition from one allotropic form to another.  ∂V  T

Enthalpy of Atomisation ( ∆ a H° ) Joule-Thomson Coefficient

It is the enthalpy change occurring when one mole of the molecule The number of degrees of temperature change produced per
breaks into its atoms. atmospheric drop in pressure at constant enthalpy when a gas is
allowed to expand through a porous plug is called Joule-Thomson
coefficient. It is given as
 Thermodynamics 95 96 Handbook of Chemistry

dT Dulong and Petit Law

µ=
dp This law states “The product of specific heat and molar mass of any
where, µ = Joule-Thomson coefficient, dT = change in temperature metallic element is equal to 6.4 cal/mol/°C, i.e.
dp = change in pressure. Specific heat × molar mass = 6.4 cal/mol/°C

Inversion Temperature Kirchhoff’s Equation

The temperature below which a gas becomes cooler on expansion is ∆H 2 − ∆H 1 ∆E2 − ∆E1
∆C p = and ∆CV =
known as the inversion temperature. It is given as T2 − T1 T2 − T1
2a
Ti = Clausius-Clapeyron Equation
Rb
where, a and b = van der Waals’ constant. p2 ∆H V  T2 − T1 
− 2.303 log =  
At inversion temperature Ti , the Joule Thomson coefficient µ = 0, i.e. p1 R  T1T2 
the gas is neither heated nor cooled. where, ∆H V = molar heat of vaporisation.

Laws of Thermochemistry Spontaneous Process

Lavoisier Laplace Law The physical or chemical process which proceeds by its own in a
The enthalpy change during a reaction is equal in magnitude to the particular direction under given set of conditions without outside help
enthalpy change in the reverse process but it is opposite in sign. is called spontaneous process. It cannot be reversed.
All natural processes are spontaneous process.
Hess’s Law of Constant Heat Summation Spontaneous process where no initiation is needed
The standard enthalpy of a reaction, which takes place in several steps, (i) Sugar dissolves in water.
is the sum of the standard enthalpies of the intermediate reactions into
(ii) Evaporation of water.
which the overall reactions may be divided at the same temperature.
(iii) Nitric oxide (NO) reacts with oxygen.
According to Hess’s law
Spontaneous process where some initiation is required
∆H = ∆H 1 + ∆H 2 + ∆H 3
(i) Coal keeps on burning once initiated.
Applications of Hess’s law are
(ii) Heating of CaCO3 to give calcium oxide and CO2 is initiated by
(a) In determination of heat of formation.
heat.
(b) In determination of heat of transition.
∆
(c) In determination of heat of hydration. CaCO3 ( s) → CaO( s) + CO2( g)
(d) To calculate bond energies.
Entropy (S)
Trouton’s Rule It is the measure of degree of randomness or disorder of the molecules.
According to this rule, “The ratio of enthalpy of vaporisation and It is a state function and extensive property.
normal boiling point of a liquid is approximately equal to 88 J per mol Units : JK −1 mol−1
per kelvin, i.e.
∆H vap The change in entropy during a process is mathematically given as
≈ 88 J/mol/K q ∆H
T ∆ r S ° = Σ S ° ( products) − ΣS ° ( reactants) = rev =
T T
where, qrev = heat absorbed by the system in reversible manner
T = temperature
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∆S > 0, Increase in randomness, heat is absorbed. Second Law of Thermodynamics

∆S < 0, Decrease in randomness, heat is evolved. The entropy of the universe is always increasing in the course of every
Entropy of even elementary substances are not zero. spontaneous or natural change.
Entropy change of an ideal gas is given by Or
T  V  All spontaneous processes or natural changes are thermodynamically
∆S = nCV ln  2  + nR ln  2  irreversible without the help of an external work, i.e., heat cannot flow
 T1   V1 
itself from a colder to hotter body.
Entropy Change During Phase Transition Gibbs Energy or Gibbs Free Energy
The change of matter from one state to another state is called phase It is the energy available for a system at some conditions and by which
transition. useful work can be done. It is a state function and extensive property.
The entropy changes at the time of phase transition: Mathematically, G = H − TS
∆H fusion
∆S melting = Change in Gibbs energy during the process is given by Gibbs
Tm Helmholtz equation.
Tm = melting point of substance ( ∆G = G2 − G1 = ∆H − T∆S )
∆H vaporisation where, ∆G = Gibbs free energy, H = enthalpy of system
∆S vaporisation =
Tb TS = random energy,
Tb = boiling point of substance ∆Gsystem = − T∆S total [In hypothetical system where ∆H = 0]
∆H sublimation
∆Ssublimation = The Gibbs energy criterion of spontaneity
Tsub
∆G > 0, process is non-spontaneous
Tsub = sublimation temperature ∆G < 0, process is spontaneous
Enthalpy Criterion of Spontaneous Process ∆G = 0, process is in equilibrium state.
All the processes which are accompanied by decrease of energy Effect of Temperature on Spontaneity
(exothermic reactions, having negative value of ∆H ) occur
spontaneously. It fails when some endothermic reactions occur S.No. Sign of ∆H Sign of ∆S ∆ G = ∆ H − T∆ S Remarks
spontaneously. 1. Negative Positive Always negative Spontaneous at all
temperatures
Entropy Criterion of Spontaneous Process
2. Positive Negative Always positive Non-spontaneous
A process is spontaneous if and only if the entropy of the universe at all temperatures
increases. 3. Positive Positive Positive at low Non-spontaneous
For a process to be spontaneous temperature at low temperature
(∆S universe > 0 or ∆Ssyst + ∆Ssurr > 0) Negative at high Spontaneous at high
temperature temperature
At equilibrium state, ∆S = 0.
4. Negative Negative Negative at low Spontaneous at low
Limitations of ∆S criterion and need for another term We temperature temperature
cannot find entropy change of surroundings during chemical changes. Positive at high Non-spontaneous
So we need another parameter for spontaneity viz Gibbs’ energy of temperature at high
system (G). temperatures
 Thermodynamics 99 100 Handbook of Chemistry

Now an exothermic reaction which is non-spontaneous at high We can find absolute entropies of pure substances at different
temperature may become spontaneous at low temperature. Similarly, temperature.
endothermic reactions which are non-spontaneous at low temperature
T T
may become spontaneous at high temperature. ∆S = ∫0 C pd ln T = 2.303 ∫
0
CP d log T
Standard Free Energy Change ( ∆G° )
where, C p = heat capacities
It is the change in free energy which takes places when the reactants
are converted into products at the standard states, i.e. (1 atm and T = temperature between 0 K and T K.
298 K) This law is only applicable for perfectly crystalline substances. If there
∆ G ° = ∆ H ° − T∆ S ° is imperfection at 0 K, the entropy will be larger than zero.
∆G ° = Σ∆G ° – Σ∆G °
f (Products) f (Reactant)
Carnot Cycle
where, ∆G °f = standard energy of formation It is an imaginary cycle which demonstrates the maximum conversion
of heat into work. It involves four processes
Standard energy of formation of all free elements is zero.
(i) isothermal reversible expansion;
Gibbs Energy Change and Equilibrium (ii) adiabatic reversible expansion;
Criterion for equilibrium, (iii) isothermal reversible compression;
A+ B (iv) adiabatic reversible compression.
º C+D The efficiency of a heat engine in a Carnot cycle,
∆G = 0
T2 − T1 q2 − q1 w
Now, relation ∆G = ∆G ° + RT ln Q η= = =
T2 q2 q2
0 = ∆G ° + RT ln K
or ∆G ° = − RT ln K
or ∆G ° = − 2.303 RT log K
⇒ We also know that
∆G ° = ∆H ° − T∆S ° = − RT ln K

Relation between ∆G° and EMF of the Cell

°
∆G ° = − nFEcell
where, n = number of electrons lost or gained
F = Faraday or 96500 C
° = standard electrode potential
Ecell

Third Law of Thermodynamics

This law was formulated by Nernst in 1906. According to this law,
‘‘The entropy of a perfectly crystalline substance at zero K or absolute
zero is taken to be zero’’.