## Problems for Chap

9.1 The gas-phase reaction CO + %O2 = CO2 is in equilibrium at a total pressure of 1 atm in a closed container. The thermochemical properties are given on p. 12 of the notes for balancing numbers twice those of the reaction as written above.

(a) For a stoichiometric initial mixture of reactants (i.e. CO/O2 =2), calculate and tabulate the equilibrium constant and gas composition for temperatures from 2000 K to 2800 K at 200 K intervals.

(b) A stoichiometric mixture with 0.10 moles CO and 0.05 moles O2 initially at 300 K reacts to equilibrium in an adiabatic container. Determine the final temperature, composition, and fraction of the initial CO that has reacted. The heat capacity of the gas plus the container (which heats up along with the gas) is 11 J/K. Note: A graphical solution utilizing the results of part(a) is required.

9.2 A mixture of H2 and CH4 establishes a "carbon activity", defined as the ratio of the carbon partial pressure generated by the reaction C(g) + 2H2(g) = CH4(g) to the vapor pressure of solid carbon (graphite). The standard free energy change for the above reaction is AGo(g). For the reaction with solid carbon, C(s) + 2H2(g) = CH4(g), the standard free energy change is AGo(s). For graphite sublimation, C(s) = C(g) the free energy change is AGo(sub).

(a) What is the relationship between AGo(g), AGo(s), and AGo(sub)?

(b) At 1000 K and 1 atm total pressure, what hydrogen pressure gives a carbon activity of unity? At this temperature, AGo(s) = 19.2 kJ/mole.

(c) What happens if the H2 pressure is lower than the value in part (b)?

9.3 Consider the gas phase reaction: PCl3(g) + Cl2(g) = PCl5(g) at equilibrium at 400 K and 1 atm total pressure. The closed system is initially charged with 1 mole of PCl3 and 2 moles of Cl2. The standard free energy change of this reaction is -3.53 kJ/mole. What is the mole fraction of PCl5 at equilibrium?

9.4 Uranium metal is produced commercially by reduction of the fluoride salt with magnesium. A stoichiometric initial charge of the reactants at room temperature (i.e., 1 mole UF4 and 2 moles Mg) are placed in a reaction vessel and heated slightly to initiate the reaction. The reaction proceeds and the heat of the reaction raises the temperature to 1263oC, at which temperature the system consists of a molten fluoride salt and a liquid U-Mg alloy. These two liquids are immiscible. The overall reaction is:

where "salt " means the molten fluoride salt phase and "melt" means the liquid alloy.

(a) Assuming ideal solution behavior in both phases, what is the fractional conversion of UF4 to uranium metal (this is the "reaction progress variable"). The equilibrium constant is to be calculated from the thermochemical data given in the tables below, in which H and G are in kcal/mole. Note: because all species are in the liquid state at equilibrium, the thermochemical data for each must pertain to pure liquids, even though the stable state is not liquid at the reaction temperature.

(b) repeat part (a) but using the "element-conservation method" instead of the reaction-progress-variable method.

magnesium

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