1. Tardigrade
  2. Question
  3. Chemistry
  4. For the following three reactions (i), (ii) and (iii), equilibrium constants are given (i) CO(g) + H2O(g) <=> CO2(g) + H2(g) ; K1 (ii) CH4(g) + H2O(g) <=> CO(g) 3H2(g) ; K2 (iii) CH4(g) + 2H2O(g) <=> CO2(g) + 4H2(g) ; K 3 Which of the following relation is correct?

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Q. For the following three reactions (i), (ii) and (iii), equilibrium constants are given
(i) $\ce{CO_{(g)} + H_2O_{(g)} <=> CO_{2(g)} + H_{2(g)} ; K_1}$
(ii) $\ce{ CH_{4(g)} + H_2O_{(g)} <=> CO_{(g)} 3H_{2(g)} ; K_2}$
(iii) $\ce{CH_{4(g)} + 2H_2O_{(g)} <=> CO_{2(g)} + 4H_{2(g)} ; K _3}$ Which of the following relation is correct?

UPSEEUPSEE 2019

Solution:

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