CHEMICAL THERMODYNAMICS
The branch of science which deals with the study of different forms of energy and the
relationships between them is known as thermodynamics.
If we study to chemical changes and chemical substances only, the restricted branch of
thermodynamics is known as Chemical Thermodynamics.
The complete study of thermodynamics is based upon three generalizations called First,
Second and Third laws of thermodynamics.
Some basic terms and concepts
1. System and Surroundings
The part of the universe chosen for thermodynamic consideration is called a system.
The remaining portion of the universe, excluding the system, is called surroundings.
2. Open, closed and isolated systems
(a) Open system. A system is said to be an open system if it can exchange both the
matter and energy with the surroundings. For example: Tea placed in an open cup.
(b) Closed system. If a system can exchange only energy with the surroundings but not
matter, it is called a closed system. For example: Tea placed in closed steel tea-pot.
(c) Isolated system. If a system can neither exchange matter nor energy with the
surroundings, it is called an isolated system. For example: Tea placed in thermos
flask.
3. State of the system and system variables
The state of the system means the condition of the system which is described in terms of
temperature (T), pressure (P), volume (V) etc. of the system.
If any of these properties of the system change, the state of the system changes. That is why
these properties of a system are called state variables.
4. State function
A physical quantity is said to be state function if its value depends only upon the state of the
system and does not depend upon the path by which this state has been attained.
5. Macroscopic system and Macroscopic Properties
If a system contains a large number of chemical species i.e. atoms, ions or molecules, it is
called a macroscopic system. The word macroscopic means large quantities. Thermodynamic
does not deal with the properties of the individual atoms and molecules but deals with the
matter of in bulk. Such properties of the macroscopic systems like temperature, pressure,
volume, density, melting point, boiling point etc. are called macroscopic properties or
thermodynamic properties. These are of two types:
(i)
Extensive properties. These are those properties which depend upon the quantity
of the matter contained in the system. The common examples are mass, volume
and heat capacity.
(ii)
Intensive properties. These are those properties which depend upon the nature of
the substance and are independent of the amount of the substance present in the
system. The common examples are temperature, pressure, freezing point, boiling
point etc.
6. Thermodynamic processes. A thermodynamic process is said to occur when the system
changes from initial state to final state. These are as follows:
(i)
Isothermal process. When a process is carried out in such a manner that the
temperature remains constant throughout the process, it is called an isothermal
process.
(ii)
Adiabatic process. When a process is carried out in such a manner that no heat
can flow from the system to the surroundings it is called an adiabatic process.
(iii)
Isochoric process. It is a process during which volume of the system is kept
constant.
(iv)
Isobaric process. It is a process during which the pressure of the system is kept
constant.
7. Reversible and Irreversible Process.
A reversible process is a process which is carried out slowly so that all changes occurring
in the direct process can be exactly reversed. It takes infinite time for completion and it is
only imaginary.
On the other hand, irreversible process is defined as that process which is not carried out
slowly so that successive steps of the direct process cannot be reversed. It takes a finite
time for completion and actually occurs in nature.
8. Some thermodynamic quantities
(a) Internal energy. It is the sum of different types of energies of atoms or molecules
such as electronic energy, nuclear energy, chemical bond energy, potential energy and
kinetic energy. Thus
E= Ee + En + Ec + Ep + Ek
“The energy thus stored within a substance is called its internal energy” and is usually
denoted by E.
Internal energy is a state function (depends only upon the state of the system) and is
independent of the method by which this state has been attained.
∆E= E2-E1
Sign of ∆E.
∆E is negative if energy is evolved
and ∆E is positive if energy is absorbed.
Units of ∆E. The units of energy are joules or erg.
(b) Work. Work is said to be done when the point of application of a force is displaced in
the direction of the force.
w=F×dl
F is the magnitude of the force and dl is the displacement of the point of application.
Work of expansion or pressure-volume work.
w= P∆V
Sign of w.
w is negative if work done by the system and work is positive if work is done on the system.
Units of w. The units of work are same as those of energy. Joules or erg
(1J=1kgm2s-2).
Work done in isothermal reversible expansion of an ideal gas.
w= - 2.303 nRT log V2/V1
= -2.303 nRT log P1/P2.
Heat. Heat is another mode of energy exchanged between the system and the surroundings as
a result of the difference of temperature between them. It is usually represented by the letter
‘q’.
Sign of ‘q’. When heat is given by the system to the surroundings, it is given a negative sign.
When heat is absorbed by the system from the surroundings, it is given a positive sign.
Units of q. Heat is measured in terms of calories.
1 calorie= 4.184 joules
I joules= 0.2390 calories
First Law of Thermodynamics
“Energy can neither be created nor destroyed although it may be converted from one form to
another.” Or
“The total energy of the universe (i.e. system and surroundings) remains constant, although it
may transfer from one form to the other.”
Justification for the First Law of Thermodynamics
(i)
Whenever a certain quantity of some form of energy disappears, an exactly
equivalent amount of some other form of energy must be prodeuced. For example,
(a) In the operation of electric fan, the electrical energy which is consumed is
converted into mechanical work which moves the blades.
(b) The electrical energy supplied to a heater is converted into heat whereas
electrical energy passing through the filament of a bulb is converted onto light.
(ii)
It is impossible to construct a machine which would produce work continuously
without consuming energy.
Mathematical formulation of the first law of thermodynamics
The internal energy of the system can be increased in two ways:
(i)
(ii)
By supplying heat to the system
By doing work on the system
Suppose the initial internal energy of a system = E1
If it absorbs heat q, its internal energy will become E1 + q
If further work w is done on the system, the internal energy will further increase and
become= E1 + q+ w. Let us call this final internal energy as E2. Then,
E2= E1+q+w
or E2-E1= q+w
or ∆E= q+w
(i)
This equation is the mathematical formulation of the first law of thermodynamics.
If the work done is the work of expansion, then w= -P∆V, where ∆V is the change in volume
and P is the external pressure. Equation (i) can then be written as
∆E= q - P∆V
Or q = ∆E + P∆V
(ii)
For an ideal gas undergoing an isothermal change, ∆E=0, Hence
q= -w
According to first law of thermodynamics ∆E = q+w
q, ∆E and w are in joules
Heat absorbed by the system, q is +ve
Heat given out by the system, q is –ve.
Energy absorbed by the system, ∆E is +ve
Energy given out by the system, ∆E is –ve.
Work done on the system, w is +ve
Work done by the system, w is –ve.
Example 1. Calculate the internal energy change in each of the following cases:(i)
(ii)
A system absorbs 5 kJ of heat and does 1 kJ of work.
5 kJ of work is done on the system and 1 kJ of heat is given out by the system.
Solution. (i) Here q= + 5 kJ
w= - 1 kJ
According to the first law of thermodynamics,
∆E= q + w = 5+ (-1) = 4 kJ.
(ii) Here w = + 5 kJ, q = -1 kJ
∆ E = q +w = -1 + (+5) = 4 kJ.
Example 2. One mole of gas is allowed to expand from a volume of 1 litre to a volume of 5
litres against the constant external pressure of 1 atm (1 atm= 101.3 J). Calculate the amount
of work done.
Solution. ∆V = V2-V1 = 5-1= 4 litres.
P = 1 atm
W = -P∆V
= -1×4 litre atm = - 4 litre atm
= - 4 × 101.3 J = - 405.2 J.
Example 3. Calculate the maximum work obtained when 0.75 mol of an ideal gas expands
isothermally and reversibly at 270C from a volume of 15 L to 25 L.
Solution. For isothermal and reversible expansion of an ideal gas.
w = -nRT ln V2/V1
or w = -2.303 nRT log V2/V1
Putting, n = 0.75 mol, V1 = 15 L, V2 = 25 L, T = 27+273= 300 K and R= 8.314 K-1mol-1,
w = - 2.303 × 0.75 × 8.314 × 300 log 25/15
= - 955.5 J.
Spontaneous and non spontaneous process
A process which may take place by itself or by initiation is called a spontaneous process.
On the other hand, a process which can neither take place by itself nor by initiation is called a
non-spontaneous process.
Examples of spontaneous process
(i)
(ii)
Dissolution of salt in water.
Flow of heat from hot body to cold body e.g cooling down a cup of tea.
Examples of non spontaneous process
(i)
(ii)
Dissolution of sand in water.
Flow of heat from cold body to hot body.
Entropy
“Entropy is the measure of the randomness or disorder of the system.”
Entropy is denoted by ‘S’ and is a state function. The greater the randomness, the higher is
the entropy. The gaseous state has higher entropy, the liquid state has the entropy in between
and the solid has least entropy. The change in the value of entropy called the entropy change
and is given by
∆S= S final – S initial or ∆S = S1-S2 or ∆S = q/T
When the randomness of a system increases, ∆S has a positive value, when randomness
decreases ∆S is negative. The spontaneous change is always determined by the sign of the
total entropy change.
(i)
(ii)
(iii)
If ∆S is positive, the process is spontaneous.
If ∆S is negative, the direct process is non-spontaneous; the reverse process may
be spontaneous.
If ∆S is zero, the process is in equilibrium.
Q. Predict the sign of ∆S in the system for the following processes:
(a) CO2 (s)
CO2 (g)
∆S is positive because randomness increases when it move in the gaseous state.
Second law of thermodynamics
In any spontaneous process, the total entropy of a system and its surroundings always
increases.
Or
The total entropy of the universe is continuously increasing.
Or
For all the spontaneous process, the total entropy change is positive.
Or
All spontaneous process is thermodynamic irreversible.
Thus the main ideas of the first and the second law of thermodynamic may be summed as
“The energy of the universe is constant whereas the entropy of the universe is continuously
increasing.”
Gibbs Free Energy
This is another thermodynamic quantity that helps in predicting the spontaneity of a process.
It is usually denoted by ‘G’ and is defined mathematically by the following equation
G=H-TS
where H is the heat content, T is the absolute temperature and S is the entropy of the system.
Change in Gibbs free energy of the system is∆G = ∆H - T∆S and this equation is known as Gibbs Helmoholtz equation.
where ∆H is enthalpy change, ∆S is entropy change.
Spontaneity in terms of free energy change
(i)
(ii)
(iii)
If ∆G is negative, the process will be spontaneous.
If ∆G is zero, the process is in equilibrium.
If ∆G is positive, the direct process is non-spontaneous; the reverse process may
be spontaneous.
Entropy is associated with temperature also because as the temperature of the substance
increases, random molecular motion (randomness) increases and therefore the entropy
increases with the increasing temperature.
An endothermic reaction which may be non-spontaneous at low temperature may become
spontaneous at high temperature and also an exothermic reaction may be non-spontaneous at
high temperature may become spontaneous at low temperature.
Third Law of Thermodynamics
Nernst in 1906 made an important observation about the entropies of perfectly crystalline
substances at absolute zero and put the following generalisation known as third law of
thermodynamics:
The entropy of a perfectly crystalline solid approaches zero as the temperature approaches
absolute zero.
Or
The entropy of all perfectly crystalline solids may be taken as zero at the absolute zero of
temperature.