Page 55 - Bruno Linder Elementary Physical Chemistry

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

40 Elementary Physical Chemistry

Comment: It should be emphasized that the chemical potential is
an intensive property, which depends on T and P as well as on the
composition but not on the amount.

We have shown in the last section that for one mole of a one-component
system at pressure P,

G = G o∗ + RT ln P f /P o (5.30)
∗
In terms of activities [Eq. (5.27)]

G = G o∗ + RT ln a (5.31)
∗
or
o
µ = µ + RT ln a (5.32)
In a mixture, we can write for component i,

o
µ i = µ + RT ln a i (5.33)
i
5.7. Relation of ∆G o to the Equilibrium Constant, K
¯
Consider the reaction,

aA + bB cC + dD (5.34)

Denoting the molar quantities of A as m and of B as m , we can express
∗
∗
A B
the free energy change of the reaction as
o o o o
∆ rG = {cG +dG − aG − bG
C D A B
+RT [c lna C +d ln a D − aln a A − bln a B ]} (5.35a)
c
o
d
b
a
=∆G + RT ln(a a /a a ) (5.35b)
A B
C D
o
=∆G + RT ln K (5.35c)
At equilibrium, ∆G =0 and so
ln K = −∆G o (5.36a)