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Characteristics of Equilibrium Constant

At a given te...

Question

At a given temperature, $K c$ is $4$ for the reaction :
$H_{2 (g)} + C {O_{2}}_{(g)} \Leftrightarrow H_{2} O_{(g)} + C O_{(g)}$ .
Initially $0.6$ moles each of $H_{2}$ and $C O_{2}$ are taken in $1$ liter flask. The equilibrium concentration of $H_{2} O_{(g)}$ is :

A

0.4 M

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B

0.46 M

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C

0.2 M

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D

0.8 M

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Solution

The correct option is A $0.4 M$
Given, $K_{c} = 4 = \frac{[C O] [H_{2} O]}{[H_{2}] [{C O}_{2}]} ⟶ (1)$

$H_{2 (g)} + {C O}_{2 (g)} ⇌ H_{2} O_{(g)} + {C O}_{(g)}$

initial $0.6$ $0.6$ $0$ $0$
at equilibrium $0.6 - x$ $0.6 - x$ $x$ $x$

From $(1)$ , $K_{c} = \frac{(x) (x)}{(0.6 - x) (0.6 - x)}$

$(4) (x^{2} - 1.2 x + 0.36) = x^{2}$

${4 x}^{2} - 4.8 x + 14.4 = x^{2}$

${3 x}^{2} - 4.8 x + 1.44 = 0$

$x = (1.2)$ or $(0.4)$

initial moles are $0.6$ each only $\Rightarrow x \neq 1.2$

equilibrium concentration of $H_{2} O = \frac{x}{1 l i t r e} = 0.4 m o l ({l i t r e}^{- 1}) = 0.4 M$

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