ChemBytes - Chapter 11

Answers

CHEMBytes: Additional Problems on Spontaneous Change and Equilibrium
  1. (a) One mole of an ideal gas expands reversibly from a volume of 2 to 20 liters. Calculate the entropy change of the system and of the surroundings. (b) The same isothermal expansion takes place irreversibly such that no work is done on or by the ideal gas, Calculate the entropy change of the system and of its surroundings. (c) Using the answers you have accumulated, show numerically that the spontaneous contraction of an ideal gas in an isolated system would violate the second law of thermodynamics.
    a) system: 9.14 J·K-1; surroundings: 9.14 J·K-1
    b) DSsys + DSsurr = -9.14 J·K-1
  2. When a mole of water supercooled to -10°C freezes isothermally, what is its entropy change? The process is described reversibly, so in order to calculate DS, a reversible path between initial and final states must be found. One such path is
    H2O(liq), -10°C <=> H2O(liq), 0°C
    H2O(liq), 0°C <=> H2O(s), 0°C
    H2O(s), 0°C <=> H2O(s), -10°C
    The molar enthalpy of fusion of ice at 0°C is 1440 cal, the molar heat capacity of ice is 9.0 cal/mol.K, and the molar heat capacity of water is 18.0 cal/mol.K. Use these data to compute DS for the water when it freezes at -10°C.
    The enthalpy of fusion of ice at -10°C is 1350 cal/mol. Find the entropy change of the surroundings when 1 mole of water freezes at -10°C. What is the total entropy change of the system and the surroundings for this process? Is the process irreversible according to the second law of thermodynamics?
    DS for water is -4.94 cal·K-1; DSsurr = 5.13 cal·K-1; DSsys + DSsurr = 1.19 cal·K-1; process is irreversible
  3. For the reaction
    SO2(g) + 1/2 O2(g) <=> SO3(g)
    calculate DG° and DH°. Compute the equilibrium constant at 298K and at 600K by assuming DH is independent of temperature.
    DG° and DH° at 298K are -70.89 kJ·mol-1 and -98.89 kJ·mol-1, respectively. Keq, at 298K and 600K, respectively: 2.67 X 1012 and 5.01 X 103
  4. The equilibrium vapor pressure of water over BaCl2.H20 is 2.5 torr at 25°C. What is DG for the process
    BaCl2.H2O(s) <=> BaCl2(s) + H2O(g)
    where the water vapor is imagined to be 1-atm pressure? What is DG for the process if the water vapor is produced at 2.5 torr?
    DG for 1 atm and 2.5 torr, respectively: 14.2 kJ·mol-1 and 0 kJ·mol-1