$K_{p}$ for the following reaction at 700 K is $1.3 \times 10^{- 3} {atm}^{- 1}$ .The $K_{c}$ at same temperature for the reaction $2 S O_{2} + O_{2} ⇌ 2 {SO}_{3}$ will be

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$1.1 \times 10^{- 2}$

$7.4 \times 10^{- 2}$

$5.2 \times 10^{- 2}$

$3.1 \times 10^{- 2}$

answer is D.

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Detailed Solution

$\begin{array}{l} K_{p} = K_{c} (R T)^{Δ n} ⇌ R = Gas constant \\ K_{c} = \frac{K_{p}}{(R T)^{Δ n}} = \frac{1.3 \times 10^{- 3}}{(0.0821 \times 700)^{- 1}} = 7.4 \times 10^{- 2} \end{array}$

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