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For the following three reactions 1, 2 and 3, equilibrium constants are given
(1) ${CO}_{(g)} + H_{2} O_{(g)} ⇋ {CO}_{2 (g)} + H_{2 (g)}; K_{1}$
(2) ${CH}_{4 (g)} + H_{2} O_{(g)} ⇋ {CO}_{(g)} + 3 H_{2 (g)}; K_{2}$
(3) ${CH}_{4 (g)} + 2 H_{2} O_{(g)} ⇋ {CO}_{2 (g)} + 3 H_{2 (g)}; K_{3}$
Which of the following relations is correct ?

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$K_{1} \sqrt{K_{2}} = K_{3}$

$K_{3} = K_{1} = K_{2}$

$K_{3} . = K_{2}^{3} K_{1}^{2}$

$K_{2} K_{3} = K_{1}$

answer is C.

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Detailed Solution

${CO}_{(g)} + H_{2} O_{(g)} ⇋ {CO}_{2 (g)} + H_{2 (g)}; K_{1}$ ….(i)

${CH}_{4 (g)} + H_{2} O_{(g)} ⇋ {CO}_{(g)} + 3 H_{2 (g)}; K_{2}$ ….(ii)

${CH}_{4 (g)} + 2 H_{2} O_{(g)} ⇋ {CO}_{2 (g)} + 3 H_{2 (g)}; K_{3}$ ….(iii)

Eq. (iii) = eq. (i) + eq. (ii)

Thus, $K_{3} = K_{1} . K_{2}$

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