Question

Hydrogen is manufactured on an industrial scale by this sequence of reactions: Write an equation that gives the overall equilibrium constant in terms of the equilibrium constants and . If you need to include any physical constants, be sure you use their standard symbols, which you'll find in the ALEKS Calculator.

Answer 1

The question is incomplete. The complete question is :

Hydrogen is manufactured on an industrial scale by this sequence of reactions:

`$CH_3(g) + H_2O(g) \rightleftharpoons CO(g) + 3H_2(g ) \ \ \ \ \ \ \ \ \ \ K_1$`

`$CO(g) + H_2O(g) \rightleftharpoons CO_2(g) + H_2(g) \ \ \ \ \ \ \ \ \ \ \ \ K_2$`

The net reaction is :

`$CH_4(g) + 2H_2O(g) \rightleftharpoons CO_2(g) + 4H_2(g) \ \ \ \ \ \ \ \ \ K$`

Write an equation that gives the overall equilibrium constant
`K` in terms of the equilibrium constants
`K_1` and
`K_2`. If you need to include any physical constants, be sure you use their standard symbols, which you'll find in the ALEKS Calculator.

Solution :

`$CH_3(g) + H_2O(g) \rightleftharpoons CO(g) + 3H_2(g ) \ \ \ \ \ \ \ \ \ \ K_1$`

`$K_1 = ([CO][H_2]^3)/([CH_4][H_2O])$` ...............(1)

`$CO(g) + H_2O(g) \rightleftharpoons CO_2(g) + H_2(g) \ \ \ \ \ \ \ \ \ \ \ \ K_2$`

`$K_2 = ([CO_2][H_2])/([CO][H_2O])$` ...................(2)

`$CH_4(g) + 2H_2O(g) \rightleftharpoons CO_2(g) + 4H_2(g) \ \ \ \ \ \ \ \ \ K$`

`$K=([CO_2][H_2]^4)/([CH_4][H_2O]^2)$`

On multiplication of equation (1) and (2), we get

`$K_1 * K_2=([CO][H_2]^3)/([CH_4][H_2O]) * ([CO_2][H_2])/([CO][H_2O])$`

`$K_1K_2=([CO_2][H_2]^4)/([CH_4][H_2O]^2)$` .................(4)

Comparing equation (3) and equation (4), we get

`$K=K_1K_2$`