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Derivation of Kp and 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 gas 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 C $0.4 m o l L^{- 1}$
$\begin{matrix} S O_{2} (g) & + & N O_{2} (g) & ⇌ & S O_{3} (g) & + & N O_{(} g) 1 & 1 & 1 & 1 & 1 & I n i t i a l c o n c . 1 - x & 1 - x & 1 + x & 1 + x & 1 & A t e q u i l i b r i u m \end{matrix}$

$K = \frac{[S O_{3}] [N O]}{[S O_{2}] [N O_{2}]} = \frac{(1 + x) (1 + x)}{(1 - x) (1 - x)}$
$16 = \frac{(1 + x)^{2}}{(1 - x)^{2}} \Rightarrow \frac{(1 + x)}{(1 - x)} = 4 o r x = 0.6$
$[N O_{2}] = 1 - x = 1 - 0.6 = 0.4 m o l L^{- 1} .$

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