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Effect on Kc

At a certain ...

Question

At a certain temperature, the equilibrium constant $K_{c}$ is $16$ for the reaction, $S O_{2} (g) + N O_{2} (g) ⇌ S O_{3} (g) + N O (g)$ .
If $1.0$ mol each of all the four gases is taken in a one-litre container the concentration of $N O_{2}$ at equilibrium would be:

1.6 m o l L^{- 1}

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0.8 m o l L^{- 1}

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0.4 m o l L^{- 1}

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0.6 m o l L^{- 1}

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Solution

The correct option is B $0.4 m o l L^{- 1}$
The equilibrium reaction is $S O_{2} (g) + N O_{2} (g) ⇌ S O_{2} (g) + N O (g) .$
The inital concentrations of all the four gases are 1 M each.
The equilibrium concentrations of $S O_{2}, N O_{2}, S O_{2} a n d N O$ are $(1 - x) M, (1 - x) M, (1 + x) M, (1 + x) M .$
The expression for the equilibrium constant is $K = \frac{[S O_{3}] [N O]}{[S O_{2}] [N O_{2}]} = \frac{(1 + x) (1 + x)}{(1 - x) (1 - x)} .$
$16 = \frac{(1 + x)^{2}}{(1 - x)^{2}}$
$\frac{(1 + x)}{(1 - x)} = 4$
Thus $[N O_{2}] = 1 - x = 1 - 0.6 = 0.4 m o l L^{- 1} .$

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