(30 pts.) Consider a liquid solution of species

A

and

B

at equilibrium with its vapor phase. The vapor is an ideal-gas mixture. The liquid phase, however, is non-ideal. The convention I activity coefficient of species

A

in the liquid is given by the following expression

ln(\\\\gamma _(A))=C*x_(B)^(2)

with

C=1.20

at

T=300K

. At

T=300K

, the vapor pressures of the pure species are

p_(A)^(**)=35kPa

and

p_(B)^(**)=20kPa

. Pressure effects on the activity coefficients can be neglected.\ (a) (8 pts.) Use the Duhem-Margules equations to derive an expression for the convention I activity coefficient of species B in the liquid,

\\\\gamma _(B)

, in terms of composition at

T=300K

.\ (b) (8 pts.) Consider a liquid solution of composition

x_(A)=0.25

at

T=300K

at equilibrium with its vapor phase. Find the vapor pressure of the liquid solution,

p

, and the composition of the vapor phase.\ (c) (8 pts.) The binary system has an azeotrope at

T=300K

. Calculate the vapor pressure,

p

, at the azeotrope and the composition.\ (d) (6 pts.) Sketch the

pxy

diagram of the binary at

T=300K

.

1. (30 pts.) Consider a liquid solution of species A and B at equilibrium with its vapor phase. The vapor is an ideal-gas mixture. The liquid phase, however, is non-ideal. The convention I activity coefficient of species A in the liquid is given by the following expression ln(A)=CxB2 with C=1.20 at T=300K. At T=300K, the vapor pressures of the pure species are pA=35kPa and pB=20kPa. Pressure effects on the activity coefficients can be neglected. (a) (8 pts.) Use the Duhem-Margules equations to derive an expression for the convention I activity coefficient of species B in the liquid, B, in terms of composition at T=300K. (b) (8 pts.) Consider a liquid solution of composition xA=0.25 at T=300K at equilibrium with its vapor phase. Find the vapor pressure of the liquid solution, p, and the composition of the vapor phase. (c) (8 pts.) The binary system has an azeotrope at T=300K. Calculate the vapor pressure, p, at the azeotrope and the composition. (d) (6 pts.) Sketch the pxy diagram of the binary at T=300K