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Order of Reaction

Assume that t...

Question

Assume that the decomposition of $H N O_{3}$ can be represented by the following equation
$4 H N O_{3} (g) ⇌ 4 N O_{2} (g) + 2 H_{2} O (g) + O_{2} (g)$
and the reaction approaches equilibrium at $400 K$ temperature and 30 atm pressure. At equilibrium partial pressure of $H N O_{3}$ is $2 a t m$ . Calculate $K_{c}$ at $400 K$ :
(Use R= 0.08 Latm/molK)

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Solution

We know,
$P_{t o t a l} = P_{H N O_{3}} + P_{N O_{2}} + P_{H_{2} O} + P_{O_{2}}$
From the equation,
$P_{N O_{2}} = 4 P O_{2}$
$P_{H_{2} O} = 2 P O_{2}$
So, $P_{t o t a l} = P_{H N O_{3}} + 7 P_{O_{2}}$
$\Rightarrow 30 - 2 = 7 P_{O_{2}}$
$\Rightarrow P_{O_{2}} = 4 a t m$
We have, $K_{p} = \frac{P_{N O_{2}}^{4} . P_{H_{2} O}^{2} . P_{O_{2}}}{P_{H N O_{3}}^{4}}$
$\Rightarrow K_{p} = \frac{(4 \times 4)^{4} \times (2 \times 4)^{2} \times 4}{2^{4}} = 2^{20}$
We know, $K_{p} = K_{c} (R T)^{Δ n_{g}}$
$\Rightarrow K_{c} = \frac{2^{20}}{32^{3}} = 32$

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