# HW11 by xuyuzhu

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```									                                        Ch E 3322
Chemical Engineering Thermodynamics

HW 11          Due Monday November 21, 2011

1. The coal gasification process involves treating solid coal with air (or oxygen) to form a
mixture of hydrogen, carbon monoxide, carbon dioxide, water, and nitrogen. There are two
independent reactions, which can be written:

C + H2O       H2 + CO

C + CO2       2 CO

a) Write the expressions for Kj(1, 2).
b) Find expressions for K1(T) and K2(T); calculate K1 and K2 at both 1100 and 1500 K for
pressures of 1, 20, and 50 bar. (At 1100 K and 20 bar, K1 = 11.2, K2 = 11.4)
c) Find the compositions at the temperatures and pressures of part b assuming ideal gas.
Assume that the feed is 1 mol steam to 2.38 mol air and that the coal is a pure solid.
(At 1100 K and 20 bar, yCO2 = 0.093, yCO = 0.222, yW = 0.068, yH2 = 0.170, yN2 = 0.447)
d) In the above calculation, we implicitly assumed that the mole fraction of oxygen in the
final composition was zero (by not including oxygen in the reactions). Calculate whether
this is a valid assumption using the reaction below. Hint: Find K(T) for this reaction and
then use the values from part c to calculate yO2; do not redo the entire problem.

2 C + O2            2 CO

2. An important high temperature reaction is that of nitrogen and hydrogen to form ammonia.
Assume that the reaction is carried out using iron catalyst at 800 K and 200 bar with a
stoichiometric feed.
a) Find the equilibrium composition assuming ideal gas.
b) Find the equilibrium composition assuming that the gas is not ideal, but that the gas is an
ideal solution. (yNH3 = 0.144, yH2 = 0.642, yN2 = 0.214)
c) Find the equilibrium composition assuming that the gas is not ideal nor an ideal solution.
d) Is it important to assume non-ideal gas?

3. Zinc metal is produced from ZnO at high temperature (1000 - 1500 K) by reduction with
carbon. Zinc is a gas in this temperature regime and its vapor pressure is given below, as is
the change in Gibbs' free energy reaction 1 (in J/mol) as a function of temperature; T is in K
in both equations. Assume that the reaction occurs in a closed vessel, initially purged of all
gases. Only solid carbon and zinc oxide are added to the vessel. Find the minimum
temperature and equilibrium composition when the products reach 1 atm total pressure.

ZnO (s) + CO (g)           Zn (g) + CO2 (g)

C (s) + CO2 (g)            2 CO (g)

ln (P°zinc/atm) = 11.734 - 13838/T

      G°1(T) = 40,608 - 24.96 T - 2.98 T ln T + 3.484 x 10-3 T2 - 0.259 x 10-6 T3 - 58,450 T-1
(T = 1172 K; yZn = 0.503, yCO = 0.491, yCO2 = 0.006)

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