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Effective Equilibrium Constant

In which one ...

Question

In which one of the following reactants, $K_{p}$ is less than $K_{c}$ ?

2 S O_{3} (g) ⇌ 2 S O_{2} (g) + O_{2} (g)

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

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

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H_{2} (g) + I_{2} (g) ⇌ 2 H I (g)

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Solution

The correct option is B $N_{2} (g) + 3 H_{2} (g) ⇌ 2 N H_{3} (g)$
$K_{p}$ is less than $K_{C}$ for $N_{2} (g) + 3 H_{2} (g) ⇌ 2 N H_{3} (g)$
$△$ n = number of moles of gaseous products - number of moles of gaseous reactants
$△ n = 2 - (2 + 1)$
$△ n = - 1$
$K_{p} = K_{c} (R T)^{△ n}$
$K_{p} - K_{c} (R T)^{- 1}$
$K_{p} = \frac{K_{c}}{R T}$
$R T > 1$
$\frac{1}{R T} < 1$
$∴ K_{p} < K_{c}$

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