The Equilibrium Constant Kp

This lesson covers Kp for gaseous equilibria, partial pressures, mole fractions, and Kp calculations.

Partial Pressures

In a mixture of gases, the partial pressure of a gas is the pressure that gas would exert if it alone occupied the entire volume.

Dalton's Law: The total pressure is the sum of the partial pressures of all gases in the mixture.

P(total) = p(A) + p(B) + p(C) + ...

The partial pressure of a gas is related to the total pressure by:

p(A) = x(A) × P(total)

where x(A) is the mole fraction of gas A:

x(A) = moles of A / total moles of gas

The sum of all mole fractions equals 1.

For a gaseous equilibrium: aA(g) + bB(g) ⇌ cC(g) + dD(g)

Kp = p(C)^c × p(D)^d / (p(A)^a × p(B)^b)

where p(X) is the equilibrium partial pressure of X.

PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)

1.0 mol of PCl₅ is heated in a sealed container. At equilibrium at 500 K, 40% has dissociated. The total pressure is 200 kPa. Calculate Kp.

Step 1: Find equilibrium moles.

Total moles = 0.60 + 0.40 + 0.40 = 1.40

Step 2: Calculate mole fractions.

x(PCl₅) = 0.60/1.40 = 3/7 x(PCl₃) = 0.40/1.40 = 2/7 x(Cl₂) = 0.40/1.40 = 2/7

Step 3: Calculate partial pressures.

p(PCl₅) = (3/7) × 200 = 85.7 kPa p(PCl₃) = (2/7) × 200 = 57.1 kPa p(Cl₂) = (2/7) × 200 = 57.1 kPa

Step 4: Calculate Kp.

Kp = p(PCl₃) × p(Cl₂) / p(PCl₅) = (57.1 × 57.1) / 85.7 = 3265 / 85.7 = 38.1 kPa

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

At equilibrium at 500 K and 10000 kPa total pressure, the mole fractions are: x(N₂) = 0.20, x(H₂) = 0.60, x(NH₃) = 0.20. Calculate Kp.

Partial pressures: