At 500 K, one mole of gaseous NOCl is placed in a one-liter container. At equilibrium the NOCl is 9%?

Question

dissociated according to the equation 2NOCl = 2NO + Cl>2 Determine the equilibrium constant

Answer 1

In general the equilibrium constant is defined in terms of activities. Assumed an ideal mixture the activities of the components are equal to their mole fractions and the equilibrium constant is:
K = y(NO)² · y(Cl ₂ ) / y(NOCl)²

For the calculation of the mole fractions evaluate how the amounts of the components change due to reaction.
Let x be the number moles of chlorine formed in equilibrium. Then there must have formed 2x moles of nitric oxide and 2x moles of nitrosyl chloride have reacted away. The number of moles are:
n(Cl ₂ ) = x
n(NO) = 2·x
n(NOCl) = n(NOCl)₀ - 2·x = 1 - 2x
The total number of moles in the container in equilibrium is:
ntot = n(Cl ₂ ) + n(NO) + n(NOCl) = 1 +·x

The molar fractions are:
y(Cl ₂ ) = n(Cl ₂ ) / ntot = x / (1 + x)
y(NO) = n(NO) / ntot = 2·x / (1 + x)
y(NOCl) = n(NOCl) / ntot = (1 - 2·x) / (1 + x)

From the given concentration of nitrosyl chloride you get x:
y(NOCl) = (1 - 2·x) / (1 + x) = 0.09
→
x = (1 - 0.09) / (2 + 0.09) = 0.4354
The mole fractions of chlorine and nitric oxide are
y(Cl ₂ ) = 0.4354 / (1 + 0.4354) = 0.3033
y(NO) = 2·0.4354 / (1 + 0.4354) = 0.6067

Hence the equilibrium constant is:
K = (0.6067)² · 0.3033 / (0.09)² = 13.78