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Chemistry Question on Equilibrium Constant

For the following three reactions (i), (ii) and (iii), equilibrium constants are given (i) CO(g)+H2O(g)<=>CO2(g)+H2(g);K1 {CO_{(g)} + H_2O_{(g)} <=> CO_{2(g)} + H_{2(g)} ; K_1} (ii) CH4(g)+H2O(g)<=>CO(g)3H2(g);K2 { CH_{4(g)} + H_2O_{(g)} <=> CO_{(g)} 3H_{2(g)} ; K_2} (iii) CH4(g)+2H2O(g)<=>CO2(g)+4H2(g);K3 {CH_{4(g)} + 2H_2O_{(g)} <=> CO_{2(g)} + 4H_{2(g)} ; K _3} Which of the following relation is correct?

A

K3.L23=K12K_3 . L_2^3 = K_1^2

B

K1K2=K3K_1 \sqrt{K_2} = K_3

C

K2K3=K1K_2K_3 = K_1

D

K3=K1K2K_3 = K_1 K_2

Answer

K3=K1K2K_3 = K_1 K_2

Explanation

Solution

Given reaction :
(i) CO(g)+H2O(g)<=>CO2(g)+H2(g);K1 {CO{(g)} + H_2O{(g)} <=> CO_2{(g)} + H_{2(g)} ; K_1}
Equilibrium constant (K1)=[CO2][H2][CO][H2O]\left(K_{1}\right)=\frac{[CO_{2}]\left[ H2\right]}{\left[CO\right]\left[H_{2}O\right]}
(ii) CH4(g)+H2O(g)<=>CO(g)3H2(g);K2 { CH_{4(g)} + H_2O{(g)} <=> CO{(g)} 3H_{2(g)} ; K_2}
Equilibrium constant (K2)=[CO][H2]3[CH4][H2O]\left(K_{2}\right)=\frac{\left[CO\right]\left[H_{2}\right]^{3}}{\left[CH_{4}\right]\left[H_{2}O\right]}
(iii) CH4(g)+2H2O(g)<=>CO2(g)+4H2(g);K3 {CH_{4(g)} + 2H_2O_{(g)} <=> CO_{2(g)} + 4H_{2(g)} ; K _3}
Equilibrium constant (K3)=[CO2][H2]4[CH4][H2O]2\left(K_{3}\right)=\frac{\left[CO_{2}\right]\left[H_{2}\right]^{4}}{\left[CH_{4}\right]\left[H_{2}O\right]^{2}}
So,K3=K1.K2 K_{3}=K_{1}.K_{2}