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Characteristics of Equilibrium Constant

For the react...

Question

For the reaction,
${C O}_{2} (g) + H_{2} (g) ⇌ C O (g) + H_{2} O (g)$
the value of Kc at $552^{\circ} C$ is 0.137. If 5 moles of ${C O}_{2}$ , 5 moles of $H_{2}$ , 1 mole of $C O$ and 1 mole of $H_{2} O$ are initially present what are the actual concentrations of ${C O}_{2}, H_{2}, C O, H_{2} O$ at equilibrium?

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Solution

${C O}_{2 (g)} + H_{2 (g)} ⇌ {C O}_{(g)} + H_{2} O_{(g)}$
$5$ $5$ $1$ $1$ initial
$5 - x$ $5 - x$ $1 + x$ $1 + x$ equilibrium
$K_{C} = \frac{[C O] [H_{2} O]}{[{C O}_{2}] [H_{2}]} \Rightarrow 0.137 = \frac{{(1 + x)}^{2}}{{(5 - x)}^{2}}$
$0.137 \times {(5 - x)}^{2} = {(1 + x)}^{2}$
$6.3 x^{2} + 24.6 x - 17.7 = 0$
$∴ x = 0.62$
$[C O] = 1 + x = 1.62 [H_{2} O] = 1 + x = 1.62 [{C O}_{2}] = 5 - x = 4.38 [H_{2}] = 5 - x = 4.38$

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