For which of the following reactions, $K_{p} = K_{c}$ ?

P C l_{3 (g)} + C l_{2 (g)} ⇌ P C l_{5 (g)}

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H_{2 (g)} + C l_{2 (g)} ⇌ 2 H C l_{(} g)

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N_{2 (g)} + 3 H_{2 (g)} ⇌ 2 N H_{3 (g)}

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C a C O_{3 (s)} ⇌ C a O (s) + C O_{2 (g)}

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Solution

The correct option is B $H_{2 (g)} + C l_{2 (g)} ⇌ 2 H C l_{(} g)$
$K_{p} = K_{c} (R T)^{Δ n}$
If $Δ n = 0, K_{p} = K_{c}$
If $Δ n > 0, t h e n K_{p} > K_{c}$
If $Δ n < 0, t h e n K_{p} < K_{c}$
For the reaction: $H_{2} (g) + C l_{2} (g) ⇌ 2 H C l_{(} g)$
$Δ n$ is the number of moles of gaseous products - number of moles of gaseous reactants in a balanced equation.
$Δ n = 2 - (1 + 1) = 0$
$∴ K_{p} = K_{c}$

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