Question

Dihydrogen gas used in Haber’s 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 H₂. In the second stage, CO formed in the first stage is reacted with more steam in water gas shift reaction,

\[\ce{CO (g) + H2O (g) ⇌ CO2 (g) + H2 (g)}\]

If a reaction vessel at 400°C is charged with an equimolar mixture of CO and steam such that `"p"_"CO" = "p"_("H"_2"O")` = 4.0 bar, what will be the partial pressure of H₂ at equilibrium? K_p = 10.1 at 400°C.

Answer 1

Let the partial pressure of both carbon dioxide and hydrogen gas be p. The given reaction is:

	CO(g)	+	H2O(g)	↔	CO2(g)	+	H2(g)
Initial conc.	4.0 bar		4.0 bar		0		0
At equilibrium	4.0 - p		4.0 - p		p		p

It is given that `"K"_"P"` = 10.1

Now

`("p"_("CO"_2) xx  "p"_("H"_2))/("p"_("COH") xx "p"_2)`

`=> ("p"xx"p")/((4.0 - "p")(4.0 - "p")) = 10.1`

`=> "p"/(4.0 - "p") = 3.178`

`=> "p" = 12.712 - 3.178"p"`

`=> 4.178 "p" = 12.712`

`=> "p" = 3.04`

Hence, at equilibrium, the partial pressure of H₂ will be 3.04 bar.