9.7 Gaseous Mixtures and Their Properties
The treatment of mixtures was introduced in Sect. 1.6 in terms of Dalton’s laws
p i
p
¼
N i
N
¼ x i
ð8Þ
Properties of mixtures were considered in Sect. 5.9
U T
ð Þ ¼
X n
i¼1
N i u i ¼ N
X n
i¼1
x i u i T
ð Þ
ð76Þ
H T
ð Þ ¼
X n
i¼1
N i h i ¼ N
X n
i¼1
x i h i T
ð Þ
ð77Þ
S T; p
ð
Þ ¼ N
X n
i¼1
x i s i T; p
ð
ÞþNR
X
i
x i Àlnx i
ð
Þ
ð80AÞ
9.7.1 Specific Gibbs Function of Mixture in Terms of T-p
We are now in a position to consider the Gibbs function of a mixture of ideal gases:
G T; p
ð
Þ ¼ H T
ð Þ À TS T; p
ð
Þ
¼
X
i
N i h i T
ð Þ À T
X
i
N i F i T
ð Þ þ NRTln
p
p 0
À TR
X
i
N i Àlnx i
ð
Þ ð178Þ
where F i (T), which is a function of T, represents the value of the first two terms on
RHS of Eq. (80). One can define another function(s) of T as follows:
u i T
ð Þ
h i T
ð Þ
RT
À
F i T
ð Þ
R
With that definition, Eq. (178) can be written as
G T; p
ð
Þ ¼ RT
X
i
N i u i T
ð Þ þ
X
i
N i ln
p
p 0
þ
X
i
N i lnx i
"
#
¼ RT
X
i
N i u i T
ð Þ þ ln
p
p 0
þ lnx i
ð178AÞ
9.7 Gaseous Mixtures and Their Properties
259