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Reaction Quotient

PCl5 dissocia...

Question

$P C l_{5}$ dissociates according to the reaction $P C l_{5} ⇌ P C l_{3} (g) + C l_{2} (g) .$ At $523 K, K_{p} = 1.78 a t m .$ Find the density of the equilibrium mixture at a total pressure of 1 atm.

2.96 g/ml

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4.51 g/ml

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6.73 g/ml

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3.44 g/ml

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Solution

The correct option is A 2.96 g/ml
Let at equilibrium, 1 mole each of $P C l_{3}$ and $C l_{2}$ are present.
The $x$ moles of $P C l_{5}$ is obtained from the equilibrium constant expression.
$K_{p} = \frac{1 \times 1}{x} = 1.78$
$\Rightarrow x = 0.56$
The average molecular mass of the gaseous mixture is as calculated below.
$\frac{0.56 (208.5) + 1 (137.5) + 1 (71)}{2.56} = 127$
The expression for the density is $ρ = \frac{P M}{R T} = \frac{1 \times 127}{0.082 \times 523} = 2.96 g / m l .$

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