Name                                                                                  

 

 

Short Answer Questions

Answer any four of the following five questions (10 pts each)

 

1.      Phase Equilibria

True or false?

  1. At equilibrium, a substance that occurs in two phases will have the same concentration in both phases.
  2. Two phases at equilibrium must have the same pressure.
  3. The Clapeyron equation applies only to a phase transition involving a vapor phase.
  4. The Clapeyron equation is an exact thermodynamic equation.
  5. The Clausius-Clapeyron equation is an exact thermodynamic equation.
  6. It is impossible for four phases of a single substance to coexist at equilibrium.
  7. The Clausius-Clapeyron equation can be used for a solid-liquid phase transition.
  8. The Clapeyron equation cannot be used for a liquid-vapor phase transition.

2.            Clapeyron Equation
Two phases of a liquid crystalline compound, a and b, are in equilibrium. The density of a is less than that of b, and the conversion of a to b is an exothermic process. If we wish to shift the equilibrium towards form b, should we use high or low temperature and high or low pressure? Explain.






3.            Chemical Potential
The following diagram illustrates the temperature dependence of chemical potentials of the solid, liquid, and vapor phases of pure substance A. Indicate on the diagram how the curves will be affected by the addition of nonvolatile compound B which dissolves in the liquid phase, but not in the solid phase. Indicate the effect, if any, on the melting and boiling points of A.










Ehrenfest Classification of Transition Order
The isothermal compressibility coefficient k of a pure substance describes the rate of change of its volume with pressure. Sketch the appearance of the isothermal compressibility coefficient of a pure substance near the phase transition pressure for a first-order and for a second-order transition according to the Ehrenfest classification.

4.            Thermodynamic Activity and Vapor Pressure
The Henry’s Law constant for ethanol in diethyl ether at 20°C is 160 torr. The partial pressure of ethanol is 12.45 torr when its mole fraction in the liquid is 0.100, and the vapor pressure of pure ethanol is 44.40 torr at this temperature. Find
(a) the Raoult’s Law activity and activity coefficient of ethanol
(b) the Henry’s Law activity and activity coefficient of ethanol

Problems

Do any three of the following four problems. Be sure to show your work! Partial credit will be awarded for the correct approach even if your answer is not completely correct. Use the back of these sheets if necessary.

1.      Partial Molar Quantities
At 18°C, the total volume of an aqueous solution of MgSO4 in 1.000 kg of H2O fits the expression
V / cm3 = 1001.21 + 34.69(m-0.070)2
where m is understood to be m / mo (i.e., m is unitless with the numerical value of the molality of MgSO4). Calculate the partial molar volume of the components in a solution of molality 0.100.


















2.      Vapor Pressure and Free Energy
The DfG of Br2(g) at 25°C is 82.40 kJ mol-1. Estimate the vapor pressure of Br2(l) at this temperature (the standard state of Br2 at this temperature and a pressure of 1 bar is the liquid form.)

3.      Triple Point
The vapor pressure of solid benzene (C6H6) is 299 Pa at -30°C and 3270 Pa at 0°C. The vapor pressure of liquid C6H6 is 6170 Pa at 10°C and 15800 Pa at 30°C. From these data, calculate (a) the triple point of C6H6 and (b) the enthalpy of fusion of C6H6.





















4.      Trouton’s Rule
The boiling point of n-hexane at 1 bar is 68.6°C. Estimate (a) its enthalpy of vaporization, and (b) its vapor pressure at 60°C.


Useful Information

Physical Constants:

L = 6.022´1023 mol-1;   R = 8.315 J-1 K-1 mol-1 = 0.08206 atm dm3 K-1 mol-1

1 torr = 1 mm Hg = 133.322 Pa;  1 atm = 1.01325´105 Pa = 760 torr

Partial Molar Quantities

;    for Y = G, V, H, A, U, S...

Gibbs-Duhem Equation

for Y = G, V, H, A, U, S,...

Molality:

Ideal Gas

mA = mA°+RT ln P/P°

xA,vap = PA/Ptot

P°= 1 bar

Ideal Solution

mA = mA*+RT ln xA,soln

xA,soln = PA/PA*

pure substance

Ideal-Dilute Solution

mB = mB°+RT ln xB,soln

xB,soln = PB/KB*

behavior at xB®0
extrapolated to xB=1

 

Nonideal Solution

 

mA = mA°+RT ln aA,soln

 

aA,soln = PA/PA* OR
aB,soln = PB/KB

pure substance, OR
behavior at xB®0
extrapolated to xB=1

Derivative Relations

Chemical Potential

Condition for Phase Equilibrium

  for substance i between phases a and b

Clapeyron Equation

Clausius-Clapeyron Equation

 

Trouton’s Focus
DvapS = 88 kJ K-1 mol-1 for a variety of liquids (given by intercept of Clausius-Clapeyron plot)