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Derivation of Kp and Kc

The value of ...

Question

The value of $K_{p}$ for the reaction, $2 H_{2} O (g) + 2 {C l}_{2} (g) ⇌ 4 H C l (g) + O_{2} (g)$ , is $0.035 a t m$ at $400^{o} C$ , when the partial pressures are expressed in atmosphere. Calculate the value of $K_{c}$ for the same reaction.

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Solution

The given reaction is :-
$2 H_{2} O (g) + 2 {C l}_{2} (g) ⇌ 4 H C l (g) + O_{2} (g)$
We have, $T = 400^{0} C = 400 + 273 = 673 K$
$K_{P} = K_{C} {(R T)}^{△ n}$
Here, $△ n = 4 + 2 - 2 - 2 = 2$
$\Rightarrow K_{P} = K_{C} {(R T)}^{2} \Rightarrow K_{C} = \frac{K_{P}}{{(R T)}^{2}} = \frac{0.035}{{(0.0821 \times 673)}^{2}} = 1.1 \times 10^{- 5} m$

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