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Dalton's Law of Partial Pressures

A sample of p...

Question

A sample of pure $N O_{2}$ gas heated to $1000 K$ decomposes: $2 N O_{2} (g) ⇌ 2 N O (g) + O_{2} (g)$ . The equilibrium constant $K_{P}$ is $100 a t m$ . Analysis shows that the partial pressure of $O_{2}$ is $0.25 a t m$ at equilibrium. The partial pressure of $N O_{2}$ at equilibrium is:

A

0.03

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B

0.25

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C

0.025

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D

0.05

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Solution

The correct option is D $0.05$
${2 N O_{2}}_{(g)} ⇋ {2 N O}_{(g)} + {O_{2}}_{(g)}$
At $t = 0$ $P_{o}$
At time $t$ $P_{o} - 2 x$ $2 x$ $x$
Given, $x = 0.25$ $a t m$
$∴ K_{p} = \frac{(2 x^{2}) \times x}{(P_{o} - 2 x)^{2}}$
$∴ 100 = \frac{4 x^{2}}{(P_{o} - 2 x)^{2}}$
$⟹ 5 = \frac{x}{P_{o} - 2 x}$
$∴ 5 P_{o} = 11 x = 11 \times 0.25$
$∴ P_{o} = 0.55$
$∴$ Pressure of $N O_{2}$ at equillibrium $= P_{o} - 2 x$
$0.55 - 2 (0.25)$
$= 0.05$ $a t m$

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