CHEM 341. Fall 2000. Practice Problems (PS #8). NOT GRADED.
Note: In this problem set, unless stated otherwise, Yi = mole fraction of component i in the vapor phase, Xi = mole fraction of component i in the solution, P = total vapor pressure, Pi* = vapor pressure of pure substance i.
Raoult's Law
1. Name the three criteria for an ideal solution.
2. Show that if both components of a binary mixture obey Raoult's Law, the mole fraction of component #2 in the vapor phase is given by
3. At 100°C benzene has a vapor pressure of 180.9 kPa, and toluene has a vapor pressure of 74.4 kPa. Assuming that these substances form an ideal binary solution with each other, calculate the composition of the solution that will boil at 1 bar at 100°C and the vapor composition.
4. At 25°C the vapor pressures of chloroform and carbon tetrachloride are 26.54 and 15.27 kPa, respectively. If the liquids form an ideal solution, (a) what is the composition of the vapor in equilibrium with a solution containing 1 mol of each; (b) what is the total vapor pressure of the mixture?
DGmix, DSmix, DHmix, DVmix
5. Assuming ideal solution, calculate DG, DH, and DS of mixing 0.25 moles of benzene with 0.5 moles of toluene at 30°C.
Activities
6. At 39.9°C a solution of ethanol (X1 = 0.9006, P1* = 130.4 Torr) and isooctane (P2* = 43.9 Torr) forms a vapor phase with Y1 = 0.6667, P = 185.9 Torr.
(a) Calculate the activity and activity coefficient of each component.
(b) Calculate the vapor pressure of this solution using Raoult's Law.
Clausius-Clayperon
7. Aluminum has vapor pressure of 1.0 Torr at 1284°C and 10 Torr at 1487°C. Estimate the enthalpy of vaporization of this metal and the temperature at which the vapor pressure would be 5.0 Torr. (The actual temperature at 5 Torr is 1421°C.)
8. The vapor pressure of ethane between 100 and 200 K is given by
Calculate the enthalpy of vaporization at 125 K.
Chemical Equilibria
9. Explain how you could determine the values of DH and DS from a plot of ln K vs. 1/T.
10. The total pressure of the reaction
is 23.1 Torr at 30.1°C. The standard pressure is 750.069 Torr. Calculate the equilibrium constant for this reaction at 30.1°C.
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