Felder, Rousseau, Bullard, Elementary Principles of Chemical Processes, 4e ice A

Question

Felder, Rousseau, Bullard, Elementary Principles of Chemical Processes, 4e ice Assignment Gradebook Downloadable eTextbook nent At low to moderate pressures, the equilibrium state of the water-gas shift reaction CO + H20 CO2 H2 is approximately d by the relation yon.yin = K,.(T) = 0.0247 expl402UT(K where T is the reactor temperature, Keq is the reaction equilibrium constant, and y is the mole fraction of species i in the reactor contents at equilibrium. The feed to a batch shift reactor contains 30.0 mol% CO, 15.0 mol% CO2, so.0 mol% H20, and the balance an inert gas. The reactor is maintained at T-823 K. Degrees of Freedom For the batch reaction as specified above, carry out a degree-of-freedom analysis. How many elemental balances may be written? 3 Policy 1 2000-2018 &Sons; InG, All Rights

Explanation / Answer

The balanced reaction with ICE TABLE

CO + H2O + inert = CO2 + H2 + inert

I 0.30 0.50 0.05 0.15 0 0

C - x - x +x +x

E 0.30-x 0.50-x 0.15+x x 0.05

At equilibrium,

total moles = 0.30-x + 0.50-x + 0.15+x + x + 0.05

= 1

yCO2 = moles of CO2 /total moles = 0.15 + x

yH2 = x

yCO = 0.30 - x

yH2O = 0.50 - x

y inerts = 0.05

Equilibrium constant expression of the reaction

K = (0.15+x)(x)/(0.30-x)(0.50-x)

3.266 = (0.15x + x2) / (0.15 - 0.30x - 0.50x + x2)

(0.15x + x2) = 3.266(0.15 - 0.30x - 0.50x + x2)

0 = 0.4899 - 0.9798x - 1.633x -0.15x +3.266x2 - x2

2.266x2 2.7628x + 0.4899 = 0

x = 0.215

At equilibrium

yCO2 = 0.15 + 0.215 = 0.365

yH2 = 0.215

yCO = 0.30 - 0.215 = 0.085

yH2O = 0.50 - 0.215 = 0.285

yinerts = 0.05

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