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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 - CBSE (Science) Class 11 - Chemistry

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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,

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 CO H2O p = p = 4.0 bar, what will be the partial pressure of H2 at equilibrium? Kp= 10.1 at 400°C

Solution 1

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

                                                 `CO_(g)           +                               H_2O_(g)      ↔                      CO_(2(g))    +                       H_(2(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)`

`=> (pxxp)/((4.0 - p)(4.0 - p)) = 10.1`

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

`=> p = 12.712 - 3.178p`

`=> 4.178 p = 12.712`

`=> p = 3.04`

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

Solution 2

Let the partial pressure of hydrogen (`H_2`) at equilibrium point = p  bar

                              `CO(g)     + H_2O(g) ⇌ CO_2(g) + H_2(g)`

Initial pressure          4.0 bar       4.0 bar        0             0 

Eqm Pressure            (4-p)bar    (4-p)bar     p bar    p bar

`K_p = (p_(CO_2) xx p_(H_2))/(p_(CO) xx p_(H_2O))`   or

`0.1= ((p "bar")  xx (p "bar"))/((4-p)"bar" xx (4-p)"bar"`

`p^2/(4-p)^2 = 0.1 or p/(4-p) = (0.1)^"1/2" = 0.316`

`p = 0.316(4-p) or p = 1.264 - 0.316 p`

`1.316 p = 1.264 or p = 1.264/1.316 = 0.96 "bar"`

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Solution 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 Concept: Equilibrium in Chemical Processes - Dynamic Equilibrium.
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