Page 49 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch05 Elementary Physical Chemistry

34 Elementary Physical Chemistry

Comment: It should be emphasized that G is a state function, because
B
H and S are state functions, meaning that the integral, ∆G= dG=
A
G(B) − G(A), depends only on the initial and final states A and B.

At constant temperature,
∆G =∆H − T ∆S (5.4)

or
−∆G/T =∆S − ∆H/T (5.5)

and, if the pressure is also constant, we can write, using Eq. (4.4),

−∆G/T =∆S sys +∆S surr =∆S tot (5.6)
Thus, instead of using entropy of the system and surroundings, we can use
the Gibbs free energy, which refers to the system only, and write

∆G T,P /T < 0 if process is spontaneous; (5.7a)
∆G T,P/T = 0 if process is reversible; (5.7b)
∆G T,P/T > 0 if process is impossible. (5.7c)
Or for short,

∆G T,P ≤ 0. (5.7d)
Thus, if there is only PV work, ∆G T,P =0 for a reversible change
(system in equilibrium) and negative for an irreversible change. This is a
powerful criterion for spontaneity.
The Gibbs energy discussed so far, although more convenient to work
with than entropy, is still not the most general. It is based on the assumption
that only PV work is present. If w other is also present, then at constant P
and T ,

∆H =∆U + P∆V (5.8a)
= q P − P∆V + w other + P∆V (5.8b)
= q P + w other (5.8c)
When the system exchanges heat with the surroundings, the heat lost
(gained) by the system is equal to the heat gained (lost) by the