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SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 165
�e excess Gibbs energy is de�ne in [5B.5–156] as GE = ∆mixG − ∆mixG ideal.
As explained in Section 5F.3 on page 185, the Gibbs energy of mixing is given
in terms of the activities as ∆mixG = nRT (xA ln aA + xB ln aB), whereas the
ideal Gibbs energy of mixing is ∆mixG ideal = nRT (xA ln xA + xB ln xB). �e
activities are written as aA = γAxA and hence
GE = ∆mixG − ∆mixG ideal
= nRT (xA ln aA + xB ln aB) − nRT (xA ln xA + xB ln xB)
= nRT (xA ln γAxA + xB ln γBxB) − nRT (xA ln xA + xB ln xB)
= nRT (xA ln γA + xB ln γB)
Using the �nal expression GE/n is computed from the given data and using
the activity coe�cients (based on Raoult’s law) already derived.�e computed
values are given in the table.
I5.4 On the basis of Raoult’s law, the activity in terms of the vapour pressure pJ is
given by [5F.2–183], aJ = pJ/p∗J , where p∗J is the vapour pressure of the pure
substance. �e activity coe�cient is de�ned through [5F.4–183], aJ = γJxJ,
therefore γJ = pJ/p∗J xJ. �e partial pressure in the gas phase is determined
from the mole fraction in the gas phase, yJ, pJ = yJptot, so the �nal calculation
is γJ = yJptot/p∗J xJ.
�e total pressure is given in kPa, whereas the vapour pressure over pure oxy-
gen is given in Torr.�e conversion is
(p kPa) = (p′ Torr) × (101.325 kPa)/(1 atm)
(760 Torr)/(1 atm)
�e temperature-composition phase diagram is shown in Fig. 5.36 and the
computed values of the activity coe�cient are given in the table below. �e
fact that the activity coe�cient is close to 1 indicates near-ideal behaviour.
0.0 0.2 0.4 0.6 0.8 1.0
75
80
85
90
95
xO2 or yO2
T
/K
vapour
liquid
Figure 5.36