Page 261 - Advanced Thermodynamics for Engineers, Second Edition

250 CHAPTER 12 CHEMICAL EQUILIBRIUM AND DISSOCIATION

Similarly it can be shown that

vU
i
m ¼
vm i
s;v; m jsi
(12.12)

vF
i
m ¼
vm i
T;v; m jsi
The following characteristics of chemical potential may be noted:
1. The chemical potential, m, is a function of properties and hence is itself a thermodynamic
property.
2. The numerical value of m is not dependent on the property from which it is derived. (All the
properties have the dimensions of energy and, hence, by the conservation of energy this is
reasonable.)
3. The numerical value of m is independent of the size of the system and is hence an intensive
property.
For example,

vU vðmuÞ vu
i (12.13)
¼ m ¼ ¼
vm i vðmx i Þ vx i
s;v;m jsi s;v;m jsi s;v;m jsi
Since m is an intensive property, it may be compared with the other intensive properties p, T etc. By
the two-property rule, this means that
(12.14)
p ¼ pðm; TÞ
and similarly
m ¼ mðp; TÞ: (12.15)
It can be shown that the chemical potential, m, for a pure phase is equal in magnitude to the specific
Gibbs energy at any given temperature and pressure
i.e.

m ¼ g: (12.16)
(Note: Although m ¼ g it is different from g inasmuch as it is an intensive property whereas g is a
specific property. Suppose there is a system of mass m, then the total Gibbs energy is G ¼ mg whereas
the chemical potential of the whole system is still m (cf. p or T ).)

12.3 STOICHIOMETRY
Consider the reaction

1
CO þ O 2 /CO 2 (12.17)
2