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141
Ideal solution:
µ
1
−
µ
1
0
= −
RTV
1
0
c
2
(
1
M
+
V
1
0
2
M
2
2
c
2
+
...)
(
Eq
.10.56)
For real solutions the non-ideality is accounted for by introducing virial
coefficients (A
2
, A
3
, …):
Real (non-ideal) solution:
µ
1
−
µ
1
0
= −
RTV
1
0
c
2
1
M
+
A
2
c
2
+
A
3
c
2
3
+ ⋅ ⋅ ⋅
⎛
⎝⎜
⎞
⎠⎟
(Textbook Eq. 10.60)
It follows that:
0
1
2
2
2
0
1
2
2
2
(
)
2
(
)
2
V
A ideal solution
M
V
A real solution
M
=
≠
Next:
Δ
G
mix
=
G
solution
−
G
i
(pure compounds)
i
∑
=
n
i
µ
i
−
i
∑
n
i
µ
i
0
i
∑
µ
i
0
: standard state = pure compounds
=
n
i
(
µ
i
−
µ
i
0
)
i
∑
=
RT n
i
i
∑
X
i
(for ideal solutions)
For this equation to be valid independent of n
i
, μ
i
, μ
i
0
the following must be
true: