Chemistry Reference
In-Depth Information
0.5
0.5
p
= 1
T
= 1
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
T
= 3
T
= 5
p
= 3
p
= 5
0.0
0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
x
A
x
A
FIGURE 2.4
The isothermal compressibility of the same system as in Figure 2.3.
Next, we calculate the KBI from the inversion of the KB theory. The results are
2
G
=
ρσ
−
2
σ
AA
AA
2
G
=
ρσ
−
2
σ
(2.67)
BB
BB
2
G
=
ρσ
−
σσ
−
AB
AA
BB
and
(
)
2
2
2
σ
=
x
σ
+
1
−
x
σ
BB
(2.68)
AAA
A
In the limit, ρ
B
→ 0 (or
x
A
→ 1), these quantities reduce to (ρ → ρ
A
),
2
G
=
ρσ
−
2
σ
AA
AAA
AA
2
G
=
ρσ
−
2
σ
(2.69)
BB
AAA
BB
2
G
=
ρσ
−
σ
−σ
AB
AAAA
AABB
and similar equations for the limit ρ
A
→ 0 (or
x
A
→ 0).
Two other limiting cases are of interest. At very low densities ρ → 0, we have
G
=−
2
σ
AA
AA
G
=−
2
σ
(2.70)
BB
BB
G
=−
σσ
−
AB
AA
BB
