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Using Equilibrium to Calculate Product

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At low to moderate pressures, the equilibrium state of the water gas shift
CO (g) + H2O (g) CO2 (g) + H2 (g)

reaction is approximately described by the relation

kp = (see attached file)

The feed to a continuous shift reactor contains 30 mol% CO, 10 mol% CO2, 40 mol% water and the balance an inert gas. The reaction proceeds to equilibrium.

(a) Calculate the moles of hydrogen produced per mole of water if the reaction is carried out at 1123 K.
(b) Calculate the temperature at which the reaction should be run to achieve a fractional CO conversion of 75 %.

Please see the attached file for the fully formatted problems.

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Solution Summary

This solution explains how to use an equilibrium equation at a specific temperature to calculate the moles of a product that are formed in a reaction. This solution also explains how to predict a temperature using the reverse of the method above.

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Part A

"Calculate the moles of hydrogen produced per mole of water if the reaction is carried out at 1123 K."

Dalton's Law of Partial Pressures states the volume of a mixture of gases is based on the mole fraction of the gases in the mixture. Because of this, we can replace the pressures in the equilibrium with mole percents:

0.0247 * e(4020/T) = (nCO2 * nH2) / (nCO * nH2O)

You can plug in the temperature to find the K:

0.0247 * e(4020/1123) = ...

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