Question

Dihydrogen gas used in Habers process is produced by reacting methane from natural gas with high temperature steam. The first stage of two stage reaction involves the formation of $CO$ and $H_2$. In second stage, $CO$ formed in first stage is reacted with more steam in water gas shift reaction,
$CO\left(g\right)+H_{2}O\left(g\right)\rightleftharpoons {CO}_2\left(g\right)+H_2\left(g\right)$
If a reaction vessel at ${400}^{o}C$ is charged with an equimolar mixture of $CO$ and steam such that $P_{CO}=P_{H_{2}O}=4.0bar$, what will be the partial pressure of $H_2$ at equilibrium? $K_P=0.1$ at ${400}^{o}C$?

Answer 1

The initial partial pressures of CO and water are 4.0 bar and 4.0 bar respectively.
The equilibrium partial pressures (in bar) of $CO,H_{2}O,C{O}_2,H_2$ are $4-p,4-p,pandp$ respectively.
Let p bar be the equilibrium partial pressure of hydrogen.
The expression for the equilibrium constant is
$K_p=\frac{P_{C{O}_2}{P}_{H_2}}{P_{CO}{P}_{H_{2}O}}=\frac{p\times p}{(4-p)(4-p)}=0.1$
$p=1.264-0.316p$
$p=0.96$ bar.