Engineering Chemistry S Datta

THERMODYNAMICS 79
So, for isochoric process
Free energy (G)
A = E – TS or dA = dE – TdS – SdT = dE – dq – SdT
= – PdV – SdT.
F δAI HG
δT
K J
v
= – S, and for an isothermal process
F δAI HG
δ K J = – P.
Two thermodynamic functions, which are very useful for physicochemical studies are:
• Gibb’s free energy (G) and
V T
• Helmholtz free energy or work function (A).
Gibb’s free energy is related to enthalpy and entropy as,
∴
Free energy and useful work
G = H – TS.
∆G = ∆H – T∆S. (at constant temperature).
Suppose a reversible change takes place at constant temperature T and at constant
pressure P. The work of expansion of volume is expressed by P∆V and suppose the system does
an additional amount of work which is denoted by useful work. Therefore, from the first law of
thermodynamics, we have,
q = ∆E + P∆V + W useful
Now, since
∴
= ∆H + W useful
q = T∆S,
T∆S = ∆H + W useful
∆H – T∆S = – W useful
= (∆G) P, T.
or, – (∆G) P, T
= W
.
useful
Hence, decrease in Gibb’s free energy is a measure of the ‘useful work’ obtainable from
the process.
Standard free energy change
G is a state function. To assign numerical values to free energy change of a system, it is
necessary to assign a standard value for the free energy of a system at a specified state. The
standard state is defined at constant pressure of 1 atmosphere and constant temperature i.e.,
25°C or 298 K.
Therefore, standard free energy change (∆G°) is defined as the free energy change for a
process taking place at standard state for the reactants and the products obtained are also in
their standard states.
∴
∆G° = ∑G° (products)
– ∑G° (reactants)
Relations of ∆G
(i) ∆G = W useful
(at constant T and P).
= – nFE (n = number of electrons, F = Faraday and E = emf of a cell. This relation
correlates free energy change to cell potential)
(ii) ∆G = ∆H – T∆S (at constant T)