Commercial hydrogen is produced by a steam reforming reaction combined with a wa

Question

Commercial hydrogen is produced by a steam reforming reaction combined with a water-shift reaction to give the overall reaction, as shown below. CH_4 + H_2O rightarrow CO + 3H_2 Reforming reaction CO + H_2O rightarrow CO_2 + H_2 Water-shift reaction CH_4 + 2H_2O rightarrow CO_2 + 4H_2 Overall reaction The following free-energy data are valid at the reaction temperature. a) Calculate Delta G_f degree (in kJ/mole) at 727 degree C for the overall reaction. b) Give the numerical value of the equilibrium constant for the overall reaction at 1000K. c) The total pressure is the sum of the partial pressures (P=P_CH_4+P_H2O+P_CO+P_CO2 + P_H2). Given that P_CH4=8.93 times 10^-3 atm., P_CO=1.43 times 10^-1 atm., and P_CO2=5.14 times 10^-2 atm., calculate what percent of the overall volume of gas is H_2 under equilibrium conditions at atmospheric pressure.

Explanation / Answer

a) Required Reaction = CH4 + 2H2O ----- CO2 + 4H2

Reversing the first reaction we get

CH4 ---- C + 2H2

Reversing the second reaction and multiply it by 2 we get

2H2O-----2H2 + O2

adding the 4th reaction to it directly

C + O2----CO2

we will get the desired reaction

CH4 + 2H2O ----- CO2 + 4H2

Delta G (rxn) = -19572 + 2(192713) - 395810 = -29956 J/mol = -29.956 kJ/mol

b)

Delta G = -RTln(K)

-29956 = -(8.314)(1000)ln(K)

ln(K) = 3.6030

K = e^(3.6030) = 36.7081

c) The data for the pressure of H2O is missing in order to calculate the answer, since the equilibrium constant will contant the pressure of H2O in the expression

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