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Characteristics of Chemical Equilibrium

Pure PCl5 i...

Question

Pure $P C l_{5}$ is introduced into an evacuated chamber and comes to equilibrium at $250^{0} C$ and 2 atmosphere. The equilibrium mixture contain 40.7% $C l_{2}$ volume/volume. What is $K_{p}$ (atm) (nearest integer)?

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Solution

Percent by volume can be approximated by mole fraction.

Hence, the mole fraction of chlorine will be $0.407$ .
The mole fraction of phosphorous trichloride will also be $0.407$ .
The mole fraction of phosphorous pentachloride will be $1 - 0.407 - 0.407 = 0.186$
The equilibrium constant expression is $K_{p} = \frac{P_{P C l_{3}} P_{C l_{2}}}{P_{P C l_{5}}}$
Partial pressure of a component is equal to its mole fraction and total pressure.
$K_{p} = \frac{0.407 \times 2 \times 0.407 \times 2}{0.186 \times 2} = 1.78 \approx 2$

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