(2)1In the System A-B, Activity Coefficients Can Be Expressed By

CHE 303 (Winter 2009) ______

LAST NAME, FIRST

Problem set #9

(1)[1]At 80oC compounds A and B each have vapor pressures of 700 mmHg. At 80oC this system forms an azeotrope containing 50 mol % A and exerts a pressure of 960 mmHg. Using Van Laar model, calculate the equilibrium pressure and vapor composition at 80oC over a liquid solution containing 25 mol % A.

Ans:yA = 0.385, P = 924 mmHg

(2)1In the system A-B, activity coefficients can be expressed by

ln A = 0.5xB2 and ln B = 0.5xA2

The vapor pressures of A and B at 80oC are PAsat = 900 mmHg and PBsat = 600 mmHg. Is there an azeotrope in this system at 80oC, and if so, what is the azeotrope pressure and composition?

Ans:xA = 0.90547, P = 904 mmHg

(3)1 At 80oC compounds A and B each have vapor pressures of 800 mmHg. At this temperature the A-B system forms an azeotrope containing 50 mol % A at a pressure of 1050 mmHg. Compound A has a heat of vaporization of 8000 cal/mol and B has a heat of vaporization of 10,000 cal/mol. Estimate the azeotrope composition and pressure at 60oC. The activity coefficients can be expressed by

ln A = CxB2 and ln B = CxA2

Ans:xA = 0.57865, P = 489.5 mmHg

(4)1A stream contains 30 mol % toluene, 40 mol % ethylbenzene, and 30 mol % water. Assuming that mixtures of ethylbenzene and toluene obey Raoult’s law and that the hydrocarbons are completely immiscible in water, calculate the temperature and compositions at the bubble point and at the dew point. The total pressure is 1 atm.

Ans:Bubble point, T(K) = 361.62, T(C) = 88.47

yw = 0.65287, yt = 0.21751, ye = 0.03241

Dew point, T(K) = 388.06, T(C) = 114.91

xt = 0.26565, xe = 0.73435

(5)1At 100oC nitrobenzene and water are only partially miscible with saturated with saturated liquid compositions at 0.147 mol % nitrobenzene and 91.7 mol % nitrobenzene. At this temperature the vapor pressure of nitrobenzene is 21 mmHg.

(a) Estimate the total pressure and the vapor composition when two liquid phases and a vapor phase are in equilibrium.

(b) To design a stripping column to remove nitrobenzene from dilute aqueous solutions, it is necessary to have vapor-liquid equilibrium data. Estimate the vapor composition in equilibrium with an aqueous solution containing 0.0100 mol % nitrobenzene at a temperature of 100oC. Also estimate the total pressure.

Ans:a)yNB = 0.0247, P = 778 mmHg

b) yNB = 0.0017, P = 761 mmHg

(6)n-Hexane (1) and ethyl alcohol (2) are put into an evacuated, isothermal container. After equilibrium is established at 75oC, it is observed that two liquid phases and a vapor phase are in equilibrium. One of the liquid phases contains 9.02 mol % n-hexane. Activity coefficients for this system can be represented by the following equation:

RTln i = 8.163xj2

(a) Calculate the equilibrium composition of the coexisting liquid phase.

(b) Calculate the equilibrium pressure and vapor-phase mole fractions.

Data: Vapor pressure equations (T in oK and P in bar)

ln P1sat=  4728.98/T + 13.4643

ln P2sat=  3570.58/T + 10.4575

Ans:a)x1II = 0.9098, P = 778 mmHg

b) y1 = 0.4206, P = 1.9656 bar

(7)1 At equilibrium the following data were taken for the reaction

A(g) = B(g) + C(g)

Use these data to determine equilibrium mol fraction of A, B, and C that results when A decomposes at 250oC and 10 atm. Assume ideal gas behavior and = constant.

Ans:yA = 0.11487

yB = yc = 0.44256

(8)1For the following gas-phase reaction in equilibrium at 500oK it is found that A is 10% dissociated at 10 atm pressure

A(g) = B(g) + C(g)

Assume ideal gas behavior and calculate the percent dissociation of A at 500oK and 1 atm pressure.

Ans:30.3%

[1] Kyle, B.G., Chemical and Process Thermodynamics, Prentice Hall, 1999