## Transcribed Text

Problem 1:
In a monolayer of gas adsorbed onto a solid surface, a two-dimensional assumption is
approximately valid. Derive the partition function for a system of N monatomic, non-interacting
molecules confined to a two-dimensional region of area A at fixed temperature T. (For non-
interacting particles, the interaction potential is everywhere zero.) What is the expression for
two-dimensional pressure in this system?
How would your expressions for the partition function and the 2D pressure change if the
molecules were nonspherical?
Problem 2:
Assume argon, xenon, water, and n-octane all obey the same 2-parameter corresponding states
relation, based on the usual reduced pressure and reduced temperature. Estimate the saturation
pressure of xenon at the temperature corresponding to argon at 86.302 K. Repeat for water and
n-octane. Comment on the accuracy of each estimate and explain why simple CST succeeds or
fails in each case. Reference data are given in Table 1.
Table 1. Experimental vapor pressure data for various substances.
T (K)
Psal (atm)
Tc (K)
Pc (bar)
argon
86.302
0.9
150.8
48.7
xenon
165.9
1.05
289.7
58.4
water
370.7
0.898
647.3
221.2
n-octane
325.82
0.075
568.8
24.9
Problem 3:
Consider the following PT projection of a phase diagram typical of H2O/CO2 systems. Plot T-xj-
y1 and P-x1-y1 diagrams for the indicated pressures and temperatures. Clearly indicate any
three-phase lines, azeotropes, critical end points, and lines for coexisting vapor and liquid
phases on your diagrams.
P.
P3
P,
,
vP)
P.
vp2
T,
,
T3
T4
4
T5
Figure 1. A P-T projection showing class III behavior
Problem 4:
Starting from the canonical (T, V,NI, N2) ensemble for a binary mixture, for which the
thermodynamic potential is A (Helmholtz free energy), use the Legendre transform method to
derive expressions in the osmotic ensemble, with independent variables (T, P, N1, 122) for: (a)
thermodynamic potential; (b) partition function; (c) probability distribution law.

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