Gaseous phosphorous pentachloride decomposes to gaseous phosphorus trichloride and chlorine at a temperature where K=1.0x10^-3 mol/L. Suppose 2.0 mole of phosphorus pentachloride in a 2.0-L vessel is allowed to come to equilibrium. Calculate the equilibrium concentrations of all species.

[PCl₃] = 0.031M

[Cl₂] = 0.031M

[PCl₅] = 0.969M

Explanation:

Based on the reaction:

PCl₅(g) ⇄ PCl₃(g) + Cl₂(g)

Where Keq = 1.0x10⁻³ = [PCl₃] [Cl₂] / [PCl₅]

Inital [PCl₅] = 2.0mol / 2.0L = 1M.

In equilibrium:

[PCl₃] = X

[Cl₂] = X

[PCl₅] = 1M-X

Where X is reaction coordinate

Replacing:

1.0x10⁻³ = [X] [X] / [1-X]

1.0x10⁻³ - 1.0x10⁻³X = X²

1.0x10⁻³ - 1.0x10⁻³X - X² = 0

Solving for X:

X = -0.032M. False solution, there is no negative concentration

X = 0.031M

That means equlibrium concentrations are:

[PCl₃] = 0.031M

[Cl₂] = 0.031M

[PCl₅] = 1-0.031M = 0.969M

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