Thermodynamics of mixtures continued
For a mixture, we have learned:
dG = VdPSdT +
ii
dn
μ
∑
and
G(P, T, n
1
, n
2
, …) =
n
∑
where
i
(
P
,
T
,
n
1
,
n
2
,...)
is the chemical potential of a component in the mixture. The last
expression is deceptively simple because chemical potentials are, generally speaking,
complex functions of the composition of the mixture.
Ideal mixtures
Instead of the numbers of moles n
1
, n
2
, … we can use the mole fractions x
1
=n
1
/n, x
2
=
n
2
/n … as variables. Here n = n
1
+ n
2
+ … is the total number of moles in the system.
Because chemical potentials are intensive quantities, they do not depend on
n
, only on the
mole fractions. A mixture is said to behave like an ideal solution (mixture)
if:
μ
i
(P,T, x
1
, x
2
, …) =
μ
i
0
(P,T) + RT ln x
i
(3)
where
μ
i
0
(P,T) is the chemical potential of the pure compound.
Consider, for instance, a mixture of gases at a low pressure such that they can be
considered to be ideal. The distances between molecules are large so we can neglect their
interactions. In this case each gas behaves is if it occupies the entire volume alone. The
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 Spring '11
 Makarov
 Thermodynamics, ln xi, RT ln xi

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