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,
$CO (g) + H_{2} O (g) ⇌ CO_{2} (g) + H_{2} (g)$
If a reaction vessel at $400^{o} C$ is charged with an equimolar mixture of $CO$ and steam such that $P_{CO} = P_{H_{2} O} = 4.0 ba r$ , what will be the partial pressure of $H_{2}$ at equilibrium? $K_{P} = 0.1$ at $400^{o} C$ ?

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 (g) + H_{2} O (g) ⇌ CO_{2} (g) + H_{2} (g)

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} = 4.0 ba r

, what will be the partial pressure of

H_{2}

at equilibrium?

K_{P} = 0.1

at

400^{o} C

?

Filo · Accepted Answer

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, p an d p

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 - 0.316 p

p = 0.96

bar.

Question Text	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, $CO (g) + H_{2} O (g) ⇌ CO_{2} (g) + H_{2} (g)$ If a reaction vessel at $400^{o} C$ is charged with an equimolar mixture of $CO$ and steam such that $P_{CO} = P_{H_{2} O} = 4.0 ba r$ , what will be the partial pressure of $H_{2}$ at equilibrium? $K_{P} = 0.1$ at $400^{o} C$ ?
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