1.12.2 Kp Calculations

1.12.2 Kp Calculations: Use mole fractions and partial pressures to calculate equilibrium partial pressures, and work out Kp and its units for a gas-phase equilibrium.

Mole fraction

The moles of one gas divided by the total moles of gas in the mixture, always a number between 0 and 1.

Partial pressure

The pressure a gas would exert if it alone occupied the container; p = mole fraction × total pressure.

Total pressure

The sum of all the partial pressures in the mixture, according to Dalton's law.

Check

The mole fractions of all gases must add up to 1, which gives a quick check on the arithmetic.

Kp Expression

Definition

Kp is the ratio of partial pressures of products to reactants, each raised to the power of its coefficient.

Notation

Use p(X) for a partial pressure of gas X, never [X], which is reserved for concentration.

Units

Combine the units of pressure in the expression; for N₂ + 3H₂ ⇌ 2NH₃, Kp has units of pressure⁻² such as kPa⁻².

Dependence

Kp changes only with temperature; pressure changes and catalysts do not alter it.

Write the balanced equation and the Kp expression for it.

Use initial moles and the change given to find the equilibrium moles of each gas.

Add the equilibrium moles to get the total, then divide each by it to find mole fractions.

Multiply each mole fraction by the total pressure to obtain the equilibrium partial pressures.

Substitute the partial pressures into the Kp expression, calculate and state the correct units.

Question: 1.00 mol N₂ and 3.00 mol H₂ reach equilibrium in a vessel at 200 kPa total pressure: N₂(g) + 3H₂(g) ⇌ 2NH₃(g). The equilibrium mixture contains 0.80 mol N₂, 2.40 mol H₂ and 0.40 mol NH₃. Calculate Kp.

Total moles = 0.80 + 2.40 + 0.40 = 3.60 mol.
Mole fractions: N₂ 0.222, H₂ 0.667, NH₃ 0.111.
Partial pressures: p(N₂) = 44.4 kPa, p(H₂) = 133.3 kPa, p(NH₃) = 22.2 kPa.
Kp = p(NH₃)² / (p(N₂) × p(H₂)³).
What the symbols mean: K_p = equilibrium constant in terms of partial pressures · p = partial pressure of each gas at equilibrium (Pa or kPa) · powers come from the balanced equation
Kp = 22.2² / (44.4 × 133.3³) = 4.69 × 10⁻⁶.

Answer: Kp = 4.69 × 10⁻⁶ kPa⁻².

1.12.2 – Key Points for the Exam

Partial pressure: The pressure contributed by one gas in a mixture of gases.
Mole fraction: Moles of a component divided by the total moles in the mixture.
Kp: The equilibrium constant expressed in terms of partial pressures.
Dalton's law: The total pressure of a gas mixture equals the sum of the partial pressures.

Common Mistakes

Using initial moles rather than equilibrium moles to find mole fractions.
Forgetting to raise partial pressures to the power of the stoichiometric coefficients.
Leaving out units, or writing units that do not match the expression.
Including solids or liquids in a Kp expression.