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Relation between Kp and Kc

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Question

Find out the value of K_c for each of the following equilibria from the value of $K_{p}$ :
(i) $2 N O C l (g) \leftrightarrow 2 N O (g) + C l_{2} (g) : K_{p} = 1.8 \times 10^{- 2} a t 500 K$

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Solution

The relation between $K_{p}$ and $K_{c}$ is given as:
$K_{p} = K_{c} (R T)^{Δ n}$

(i) Here,
$Δ n = 3 - 2 = 1 R = 0.0831 b a r L m o l^{- 1} K^{- 1} T = 500 K K_{p} = 1.8 \times 10^{- 2}$
Now,
$K_{p} = K_{c} (R T)^{Δ n} \Rightarrow 1.8 \times 10^{- 2} = K_{c} (0.0831 \times 500)^{1} \Rightarrow K_{c} = \frac{1.8 \times 10^{- 2}}{0.0831 \times 500} = 4.38 \times 10^{- 4}$

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