Respuesta :
The question is incomplete. The complete question is :
Hydrogen is manufactured on an industrial scale by this sequence of reactions:
[tex]$CH_3(g) + H_2O(g) \rightleftharpoons CO(g) + 3H_2(g ) \ \ \ \ \ \ \ \ \ \ K_1$[/tex]
[tex]$CO(g) + H_2O(g) \rightleftharpoons CO_2(g) + H_2(g) \ \ \ \ \ \ \ \ \ \ \ \ K_2$[/tex]
The net reaction is :
[tex]$CH_4(g) + 2H_2O(g) \rightleftharpoons CO_2(g) + 4H_2(g) \ \ \ \ \ \ \ \ \ K$[/tex]
Write an equation that gives the overall equilibrium constant [tex]K[/tex] in terms of the equilibrium constants [tex]K_1[/tex] and [tex]K_2[/tex]. If you need to include any physical constants, be sure you use their standard symbols, which you'll find in the ALEKS Calculator.
Solution :
[tex]$CH_3(g) + H_2O(g) \rightleftharpoons CO(g) + 3H_2(g ) \ \ \ \ \ \ \ \ \ \ K_1$[/tex]
[tex]$K_1 = \frac{[CO][H_2]^3}{[CH_4][H_2O]}$[/tex] ...............(1)
[tex]$CO(g) + H_2O(g) \rightleftharpoons CO_2(g) + H_2(g) \ \ \ \ \ \ \ \ \ \ \ \ K_2$[/tex]
[tex]$K_2 = \frac{[CO_2][H_2]}{[CO][H_2O]}$[/tex] ...................(2)
[tex]$CH_4(g) + 2H_2O(g) \rightleftharpoons CO_2(g) + 4H_2(g) \ \ \ \ \ \ \ \ \ K$[/tex]
[tex]$K=\frac{[CO_2][H_2]^4}{[CH_4][H_2O]^2}$[/tex]
On multiplication of equation (1) and (2), we get
[tex]$K_1 \times K_2=\frac{[CO][H_2]^3}{[CH_4][H_2O]} \times \frac{[CO_2][H_2]}{[CO][H_2O]}$[/tex]
[tex]$K_1K_2=\frac{[CO_2][H_2]^4}{[CH_4][H_2O]^2}$[/tex] .................(4)
Comparing equation (3) and equation (4), we get
[tex]$K=K_1K_2$[/tex]
