# Thermodynamics

Thermodynamics
Introduction:
The branch of Science that study interrelationship between chemical reaction and
energy changes in physical and chemical processes is called Thermodynamics.

Thermodynamics terminology:
System:
A system is defined as a specified portion of universe which is under
thermodynamic observations or consideration.
Surrounding:
The remaining portion of the universe other than system is called surrounding.
Boundary:
The real surface or imaginary line that separates system from surrounding is
called boundary.
Homogeneous System:
When the system has the same chemical composition throughout, it is called
homogeneous system. For examples- Mixture of gases, true solution, etc.
Heterogeneous system:
When the system has different chemical composition throughout, it is called
heterogeneous system. For examples- ice in contact with water, ice with vapours
etc.

Types of system:
Open system:
A system which can exchange matter as well as energy with surrounding is called
open system. E.g Evaporation of water in an open beaker.

Closed system:
A system which can exchange energy but not matter with its surrounding is called
closed system. E.g. Evaporation of water in closed vessel.
Isolated system:
A system which can exchange neither energy nor matter with its surrounding is
called isolated system. E.g Hot water in thermo flask.

State Variable and State Function:
A system is said to be in certain thermodynamic state if all of its properties are
fixed. A state of a system depends upon the pressure, temperature, volume, mass
and composition. The state of a system is changed by changing the value of any of
these properties. So, these are called state variables.
A state function is a physical quantity and its value depends only on the state of
system and does not depend on the path by which this state has been reached.
For example- internal energy, enthalpy, entropy, free energy etc.
Extensive property:
The property of the system which value depends upon the amount of substance
or substance present in the system is called extensive properties. e.g . Mass,
Volume, surface area, enthalpy, entropy, free energy, etc.
Intensive property:
Intensive property of system is that which is independent of the amount of

substance present in the system. E.g. Temperature, Pressure, density,
concentration, Viscosity, refractive index, surface tension and specific heat.

Internal energy:
The constituent particles of a system contain different form of energy such as
kinetic energy, potential energy, chemical energy, rotational energy, vibrational
energy, etc. The sum of different form of energy associated with the molecules in
the system is called internal energy. It is denoted by symbol ‘E’.
E = Kinetic energy + potential energy + Rotational energy+ Vibrational energy +
Nuclear energy + electronic energy + Translation energy
Internal energy is an extensive and state function. Absolute value of internal
energy cannot be measured however; change in internal energy can be measured.

Thermodynamic process:
When thermodynamic system proceeds from one state to another states, such
type of operation is known as “thermodynamic process”. In other word, process
gives the path or operation by which a system changes from one state to another.
Some common types of process are:
Isothermal Process:
A process in which the temperature of the system remains constant is called
isothermal process. In such process, heat is neither supplied to the system nor
removed from it. For isothermal process, ∆T = 0.
A process in which the system does not exchange heat with surroundings i.e. no
heat leaves or enters the system is called adiabatic process. In such a process,
temperature of the system always changes. For adiabatic process, ∆q = 0.
Isobaric process:
A process in which the pressure of the system remains constant is called isobaric
process. For isobaric process, ∆H=0.

Isochoric Process:
A process in which the volume of the system remains constant is called isochoric
process. For this process, ∆V = 0.
Cyclic process:
A process in which the system undergoes a series of changes and ultimately
returns to the original state is called a cyclic process. For cyclic process, ∆E=0.

First law of Thermodynamics:
First law of thermodynamics is also known as law of conservation of energy. It
states that energy can neither be created nor be destroyed but can be
transformed from one form to another. Thus, whenever energy in one form
disappears, an equal amount of energy in some other form must appear.
The total energy of the universe remains constant.
Mathematically, Let E1 be the internal energy of a system in its state A and E2 the
internal energy in its state B. Suppose the system while undergoing change from
state A to state B absorbs heat q from surrounding and also performs some work
equal to w. The absorption of heat by the system tends to raise the energy of the
system. The performance of work by the system on the other hand tends to lower
the energy of the system. Hence the change of internal energy accompanying the
above process will be given by,
∆E= E2 – E1 = q-w
In general, if in a given process, the quantity of heat transferred from the
surrounding to the system is q and the work done is w then the change in internal
energy is
q = ∆E +w
This is mathematical form of 1st law of thermodynamics.

Special cases of the first law:
(a) For an isothermal expansion,
∆E = 0
q=0+w
q=w
It means the supplied heat energy is converted into work.
(b) For an isochoric process,
∆V = 0
q = ∆E
It means the supplied heat energy is converted into internal energy.
q=0
W = -∆E
It means work is done on the expense of internal energy.

Enthalpy:
It is defined as the total heat content at constant pressure. It is also an extensive
property and state function. It is represented by H. It is mathematically expressed
as,
H= E + PV
Let us consider a system is at initial state having internal Energy E1 , Enthalpy H1
under volume V1 at pressure P1. Let the system is brought to final state under
constant pressure where its internal energy is E2, Enthalpy H2 under volume V2.
Then, the change in enthalpy is determined as,
H2 – H1 = (E2 + PV2)-(E1+ PV1)
or, ∆H= E2-E1 + P (V2 – V1)
or, ∆H= ∆E+ P ∆V
Therefore, enthalpy change is defined as the sum of the internal energy change
and the pressure volume work done by the system.

Enthalpy of reaction:
Heat energy is generally evolved or absorbed as a result of chemical change. The
amount of heat evolved or absorbed in a chemical reaction is called heat of
reaction. The energy changes in chemical reactions are due to breaking of old
bonds and formation of new bonds between the atoms. The heat of reaction at
constant pressure (∆H) is given by:
∆H = ∆Hproduct – ∆Hreactant
The value of ∆H may be either zero, negative or positive. When ∆H is zero, heat is
neither evolved nor absorbed because the enthalpies of the product and the
reactants are the same.
When ∆H is negative, the net enthalpy of the product is less than that of the
reactants and the difference of enthalpy is given out in the form of heat. Such
reactions which are accompanied by the evolution of heat energy are called
exothermic reaction.
When ∆H is positive, the heat is absorbed by the reactants. Such reactions which
are accompanied by the absorption of heat energy are called endothermic
reaction.

Fig: Enthalpy change for exothermic reaction

Fig: Enthalpy change for endothermic reaction

Standard enthalpy of reaction:
The enthalpy of reaction at 298 K and 1 bar pressure when the reactants and
products are in their standard states is called standard enthalpy of reaction.

Enthalpy change during Phase transition:
Enthalpy of fusion:
The amount of heat absorbed for the conversion of one mole of a substance from
solid to liquid at same temperature or enthalpy change when one mole of solid is
melted at its melting point is called enthalpy of fusion.
Ice → Water ∆H0 fusion = 6.0KJ
Enthalpy of vaporization:
The enthalpy change when one mole of liquid is converted into vapors at its
boiling temperature is called enthalpy of vaporization.
E.g. H2O (l) → H2O(g) ∆H0 vaporization= 40.6 KJ
Enthalpy of formation:
The change in enthalpy when one mole a compound is formed from its
constituent element is called enthalpy of formation.
C(s) + O2(g) →CO2(g) ∆Hform= -393.5KJ
Enthalpy of Combustion:
The enthalpy change when one mole of the substance is completely burnt in
excess of air or oxygen at particular temperature is called enthalpy of
Combustion. Enthalpy of combustion is always have negative value
C(s) + O2(g) → CO2(g) ∆H= -393.5KJ
CH4(g) + 2O2(g) → CO2 (g) + 2H2O(l)
∆H= -890.4 KJ
Enthalpy of neutralization:
The enthalpy change when one gram equivalent of an acid is neutralized by a base
and vice-versa in dilute solutions is called enthalpy of neutralization.
HCl(aq) + NaOH(aq) → NaCl(aq) + H2O(l) ∆H = -13.7KCal or -57.32KJ
The enthalpy of neutralization of strong acid and strong base is always same .
This can be explained on the basis of theory of ionization. Strong acid and Strong

bases are assumed to be completely ionized in dilute solutions. Moreover, the
salts they form on mixing are also completely ionized. The reaction between a
strong acid like HCl and strong base NaOH can be written as:
H+ (aq) + Cl- (aq) + Na+ (aq) + OH- (aq) → Na+ (aq) + Cl- (aq) + H2O(l) ∆H=-13.7Kcal
H+ (aq) + OH- (aq) → H2O(l)
The neutralization is simply between the H+ and OH- given by the acid and bases
respectively. Hence the enthalpy of neutralization between acid and base is
always same.
Enthalpy of solution:
The enthalpy change when one mole of solute is completely dissolved in specified
quantity of a solvent at a given temperature is called enthalpy of solution.
KCl (s) + 200 H2O →KCl (aq) ∆H= + 18.6 KJ

Hess law of Constant Heat summation:
G.H Hess, a Russian chemist, in 1840 proposed the law of constant heat
summation based on his experimental observations regarding the enthalpies of
reaction. It states that “the enthalpy change (heat absorbed or evolved) in a
particular reaction is the same whether the reaction takes place in one step or in
a number of steps.” This means that the amount of heat absorbed or evolved in a
chemical reaction depends upon only upon the enthalpy of initial reactants and
the final products irrespective of the path or the manner by which the change has
taken place. In other words, the standard reaction enthalpies are the sum of the
standard enthalpies of the reactions into which the overall reaction may be
divided at the same temperature split up.
Suppose in a reaction, the reactant A changes to product B in one step and the
enthalpy change during this process is ∆H. Now suppose the same process is
carried out in two steps
The reactant A changes to C and the enthalpy change during the step is ∆H1
C changes to the product B and the enthalpy change during this step is ∆H2

Thus, according to Hess’s law, the enthalpy change for the reaction whether
reaction follows path I or Path II
∆H= ∆H1 + ∆H2

Theoretical justification Of Hess’ law:
The substance A can be converted into B by two paths. In path I, A is converted
directly into B and let heat evolved in this step is q. On the other hand, when Path
II is followed, let the heat evolved during the two steps A to C and C to B be q1
and q2 respectively. The total heat evolved in path II is q’ = q1 + q2. According to
Hess law q’ must be equal to q.
Let us suppose that q’ is greater than q. This means that by converting A to B
by path II and then converting B back to A by path I , the heat energy equal to q’-q
can be created which is against the first law of thermodynamics . Hence, q must
be equal to q’.
Illustrations of Hess law:
Let us illustrate the law by considering the formation of carbon dioxide from
carbon and oxygen. Carbon can be converted into CO2 by two ways:
Path I:C(s) + O2(g) → CO2 (g)
∆H0= -393.5 KJ
Path II : C(s) + 1/2O2 (g) → CO(g) ∆H10 = -110.5KJ
CO(s) + 1/2O2(g) → CO2(g) ∆H20 =-283.0KJ
C(s) + O2(g) → CO2(g)
∆H0 = -393.5 KJ
Hence, ∆H=∆H1 + ∆H2 .
Therefore, it may be concluded that according to Hess law thermochemical
equations can be added, subtracted or multiplied like algebraic equation to obtain
the desired equation.
Application of Hess’s law:
1. Determination of enthalpy of formation of substances
2. Determination of the enthalpy of transition.
3. Determination of enthalpy of hydration.

Q.N.1. Calculate the enthalpy of formation of ethane from the following data
i) C(S) + O2(g) → CO2(g)
∆H=-394.5 KJ
ii) H2(g) + 1/2O2(g) → H2O(l)
∆H= -285.8KJ
iii)C2H6(g) + 7/2O2(g) → 2CO2(g) + 3H2O(g) ∆H=-1560.0 KJ

Q.N. 2. Calculate the standard enthalpy of formation of CH3OH from the
following data
CH3OH(l) + 3/2O2(g) → CO2(g) + 2H2O(l)
C(s) + O2(g) → CO2(g)
H2(g) + 1/2O2(g) → H2O(l)

∆H0 = -726KJ/Mol
∆H0 = -393KJ /mol
∆H0 = -286KJ/mol

Bond dissociation Enthalpy and Bond enthalpy:
The amount of energy required to break one mole of bonds of a particular type
between the atoms in the gaseous state is called bond dissociation enthalpy. It is
generally expressed in terms of KJ/mol. For example, 435 Kj/mol of energy is
required to break H-H bonds in one mole of H2 molecules.
Bond enthalpy:
The average of the bond dissociation enthalpies required to dissociate a particular
type of bond in a substance is called bond enthalpy.
For example in water there are two O-H bonds. The bond dissociation enthalpies
of two O-H bonds in water are
H2O(g) → H(g) + OH(g) ∆H0= 497.8 KJ
OH(g) → H(g) + O(g) ∆H0 = 428.5 KJ
The bond energy is the average of these two bond dissociation enthalpies
Bond enthalpy of O-H bond= 497.8+428.5
= 463.15KJ
2
Similarly , in methane all the four C-H bonds are identical in bond length and
energy. But the energy required to break the individual C-H bonds in each
successive step differ. The overall thermochemical equation for atomization
reaction of methane is:
CH4(g) → C(g) + 4H(g)
∆H0 = 1665KJ/mol
The energy required to break the individual C-H bonds are :
CH4(g) → CH3(g) + H(g)
∆H0 = 427 KJmol-1
CH3(g) → CH2(g) + H(g)
∆H0 = 439 KJmol-1
CH2(g) → CH(g) + H(g)
∆H0 = 452KJmol-1
CH(g) → C(g) + H(g)
∆H0 = 347KJmol-1
CH4(g) → C(g) + 4H(g)
∆H0 = 1665 KJmolThe average bond enthalpy of C-H bond is
1

B.E= ∆H0 = 1665/4 = 416.25KJ mol-1
4

Note: The bond enthalpy data can be used to calculate the enthalpy change of the
many reactions also as,

Enthalpy of reaction = Sum of bond enthalpies of reactant- Sum of bond
enthalpies of product
∆H0rex = ∑ 𝐵. 𝐸𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡 − ∑ 𝐵. 𝐸𝑃𝑟𝑜𝑑𝑢𝑐𝑡
Spontaneous of process:
1st law of thermodynamics does not provide any information about the
spontaneity or feasibility of a process. For example, the first law of
thermodynamics do not indicates whether heat can flow from a cold body to a
hot body or from hot body to cold body. However, it is a common observations
that all processes have natural direction i.e. a direction in which they take place of
their own.
A process which can take place by itself under the given set of conditions
once it has been initiated if necessary is said to be spontaneous process. The
spontaneous process is also called feasible process.
For example:
a) Water keeps on evaporating from ponds, rivers, sea and open vessels.
b) Nitric oxide and Oxygen react to form nitrogen dioxide.
c) In domestic oven, coal keeps on burning once initiated.
On the other hand , the processes which do not take place by itself under the
given set of conditions and is only occur when external force is applied is called
non-spontaneous process.
E.g. A cup of tea can be made to hot by heating but this is not a spontaneous
process because an outside agency has to be used.
Similarly, a gas can be made to compress to a smaller volume by applying external
pressure.
Spontaneous changes proceed till equilibrium is achieved.
Driving force which makes a process spontaneous:
1. Minimum energy:
Systems having low energy are stable in nature. So that system tries to shift to
that direction which occurs with release of energy.
E.g when water flows from higher level to lower level, potential energy is
decreased.

To have minimum energy, system has to release the energy, so the physical and
chemical processes for which the enthalpy changes are negative tend to be
spontaneous. Therefore, all the exothermic processes are spontaneous.
However, there are many processes which are endothermic but spontaneous in
nature. For e.g. Evaporation of water in sea, Decomposition of calcium carbonate
by heating etc.
Therefore, energy factor alone cannot tell the spontaneous process.
Maximum randomness:
In order to find out some other factors which may be responsible for the
feasibility of a process, randomness of system is introduced. It may be concluded
that the process proceeds spontaneously in that direction in which the
randomness or disorder of the system increases.
E.g. when water is converted into vapor, disorder of water molecules get
increased. E.g. Conversions of solid into liquid and liquid in gas as the randomness
increases.
Entropy:
The property of the system which measures the degree of disorder or
randomness in the system is called entropy. It is generally expressed by the
symbol; S. Entropy is a state function and is an extensive property.
For a reversible process at equilibrium, the change in entropy may be represented
as:
∆S=

𝑞𝑟𝑒𝑣𝑒𝑟𝑠𝑖𝑏𝑙𝑒
𝑇

Where 𝑞𝑟𝑒𝑣𝑒𝑟𝑠𝑖𝑏𝑙𝑒 represents the heat absorbed when

the process is carried out reversibly and isothermally. Thus, entropy change
during a process may also be defined as the amount of heat absorbed
isothermally and reversibly divided by the absolute temperature at which heat is
absorbed.
The total entropy change of the system and surrounding of a spontaneous
process is given as,
∆S = ∆Ssystem + ∆Ssurrounding > 0
Since for isolated process, no energy and matter is exchanged , there is increase

in randomness that defines the increase in entropy of the system in isolated
system i.e ∆S >0 . But, if the system is not isolated , we have to take into the
account of both system and surrounding . Thus the total entropy change will be
the sum of the change in entropy of the system and surrounding
∆Stotal = ∆Ssystem + ∆Ssurrounding
But for spontaneous process , ∆Stotal must be positive i.e
∆Stotal = ∆Ssystem + ∆Ssurrounding > 0

Statement of second law of thermodynamics:
The second law of thermodynamics state that “The entropy of the universe
always increases in the course of spontaneous change.”

Entropy and spontaneity of a reaction:
1. If ∆Stotal is positive the process is spontaneous .
2. If ∆Stotal is negative the process is non-spontaneous .
3. If ∆Stotal is Zero the process is in equilibrium.

Entropy change during phase transition
1. Entropy of fusion:
It may be defined as the entropy change when 1 mole of solid substances
changes into liquid form at its melting point.
Water(s)

Water (l)
the change in entropy is given as,
∆S0fusion = q/T
During melting, q refers to the enthalpy of fusion of the substance (From first law
of thermodynamics ∆H= q)
∆S0fusion = ∆fusH0 /T
2. Entropy of Vaporization:
It may be defined as the entropy change when 1 mole of a liquid changes into
vapors at its boiling temperature.
Water (l)

Water (g)
the change in entropy is given as,
∆S0Vap = q/T

During melting, q refers to the enthalpy of Vaporization of the substance
∆S0Vap = ∆VapH0 / T
Entropy of sublimation:
It may be defined as the entropy change when 1 mole of a solid changes into
vapor at a particular temperature.
The change in entropy is given as ,
∆S0Sub = q/T
During melting, q refers to the enthalpy of sublimation of the substance
∆S0sub = ∆subH0 / T
Entropy change in a reaction (Entropy of a reaction) :
It is the difference between sum of the absolute entropy of the products and that
of the reactants.
∆Sreaction = ∑ ∆S𝑝𝑟𝑜𝑑𝑢𝑐𝑡 − ∑ ∆S𝑅𝑒𝑎𝑐𝑡𝑎𝑛𝑡
Standard Entropy:
The entropy value measured at 250C and 1 atm pressure is called the standard
value being the substance in the most stable and the purest form.
Gibb’s free energy Function:
As we have learnt previously, to tell the spontaneous of process both energy
factor and maximum entropy factor should be taken into consideration. It means
neither energy factor nor maximum entropy factor alone cannot predict the
spontaneous of a process. However, the quantity,
∆Stotal = ∆Ssystem + ∆Ssurrounding
can be used to predict the spontaneity of a process but in chemical reactions it is
not always possible to calculate ∆Ssurrounding as surrounding is very vast. Therefore,
a new thermodynamic function needs to be introduced to predict the direction of
spontaneity.
L. Willard Gibbs introduced a function Called Gibb’s energy function to
predict the direction of spontaneity. The function is denoted by symbol G.
Gibb’s energy of the system is defined as the “maximum amount of energy
available to a system during a process that can be converted into useful work.”

In other word, it is a thermodynamic function which is a measure of capacity of a
system to do useful work .It is given as,
G=H-TS
as we know, H= E+PV
So, G= E+PV-TS
Gibb’s energy change:
The change in Gibb’s energy of the system may be expressed as ,
∆GSys= ∆Hsys- ∆(TS)sys
∆Gsys =∆Hsys -T∆Ssys –Ssys ∆T
At constant temperature, ∆T=0 So that
∆Gsys =∆Hsys -T∆Ssys
The subscript “Sys” is dropped and we can write ,
∆G =∆H -T∆S`
This equation is called Gibb’s Helmholtz equation .
Gibb’s Energy change for predicting the feasibility of a reaction:
As we know ,
The total entropy change is given as,
∆Stotal = ∆Ssystem + ∆Ssurrounding ………………(1)
Since the reaction is carried out at constant temperature and pressure heat
evolved is equal to enthalpy change .i.e
qSys = ∆Hsys
Now, if a reaction is conducted at constant temperature and pressure and heat q
is given out to surrounding reversibly , then
(qp)Surr = -(qp)Sys = – ∆Hsys ……………………….. (2)
The entropy change of the surrounding is :
∆Ssurrounding =

(qp)Surr
𝑇

=-

(qp)S𝑦𝑠
𝑇

=-

∆Hsys
𝑇

…………………(3)

Substituting the value of Eq.(3) in eqn (1) we get
∆Stotal = ∆Ssys + (-

∆H𝑠𝑦𝑠
𝑇

) ………………………………….(4)

T∆Stotal = T∆Ssys – ∆H𝑠𝑦𝑠
– T∆Stotal = ∆H𝑠𝑦𝑠 – T∆Ssys ………………………………….(5)

As we know ,
∆Gsys =∆Hsys -T∆Ssys …………………………… (6)
So, from eqn (5) and (6)
– T∆Stotal = ∆Gsys
for spontaneous process, ∆Stotal is positive so that
∆G =-Ve for spontaneous chemical change.

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