One mole of $PCl X_{5}$ and $3.0$ mol of an inert gas are kept at a constant total pressure of $1.0 atm$ and a temperature at which $K_{p} = 0.50 atm$ for $PCl X_{5} (g) PCl X_{3} (g) + Cl X_{2} (g)$ . Find the degree of dissociation $α$ of $PCl X_{5}$ to two decimal places.

Numerical answer type, tolerance 0.01.

Answer: 0.76

Moles:

PCl X_{5}

1 - α

PCl X_{3}

α

Cl X_{2}

α

, inert

3

; total

N = 4 + α

K_{p} = α^{2} P / [(1 - α) N]

, so

α^{2} = 0.50 (1 - α) (4 + α)

, i.e.

1.5 α^{2} + 1.5 α - 2 = 0

. Solving gives

α = 0.7583

, i.e. 0.76.