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Characteristics of Equilibrium Constant

The value of ...

Question

The value of $K_{c} = 4.24$ at $800 K$ for the reaction
$C O (g) + H_{2} O (g) ⇌ C O_{2} (g) + H_{2} (g)$
Calculate equilibrium concentrations of $C O_{2}, H_{2}, C O$ and $H_{2} O$ at $800 K$ , if only $C O$ and $H_{2} O$ are present initially at concentration of $0.10 M$ each?

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Solution

Given eqilibrium is:
$C O (g) + H_{2} O (g) ⇌ C O_{2} (g) + H_{2} (g)$
Initial concentrations
$0.1 0.1 00$
At eqilibrium:
$0.1 - x 0.1 - x x x$

Using the relation:
$K_{C} = \frac{[C O_{2}] [H_{2}]}{[C O] [H_{2} O]}$ = $4.24$ at $800 K$

Upon substitution we get:

$4.24 = \frac{x \times x}{(0.1 - x) (0.1 - x)}$

$\Rightarrow x / (0.1 - x) = 2.059$

$x = 0.067$

$∴$ eqilibrium concentrations are:

$C O_{2} = 0.033 M, H_{2} = 0.033 M, C O = 0.067 M$ and $H_{2} O = 0.067 M$

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