Kp and calculating equilibrium constantsEdexcel A-Level Chemistry: Revision notes

In a gas mixture each gas contributes a partial pressure, the pressure it would exert if it alone occupied the container. The partial pressures add up to the total pressure.

$\text{mole fraction of A} = \frac{\text{moles of A}}{\text{total moles of gas}} \qquad p_A = \text{mole fraction of A} \times P_{\text{total}}$

The mole fractions of all the gases add up to 1. In Edexcel A Level questions partial pressures are given in atm.

For a gaseous equilibrium $aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g)$:

$K_p = \frac{p_C^{\,c}\,p_D^{\,d}}{p_A^{\,a}\,p_B^{\,b}}$

Products go on the top line, reactants on the bottom line, each partial pressure raised to the power of its coefficient.

In a heterogeneous equilibrium only the gases appear, because solids have no partial pressure:

• $\text{C}(s) + \text{CO}_2(g) \rightleftharpoons 2\text{CO}(g)$: $K_p = \frac{p_{\text{CO}}^2}{p_{\text{CO}_2}}$

Work the units out by substituting the units of each term into the expression and cancelling.

• $\text{N}_2\text{O}_4 \rightleftharpoons 2\text{NO}_2$: $K_p = \frac{p^2}{p}$, so the unit is atm.
• $\text{N}_2 + 3\text{H}_2 \rightleftharpoons 2\text{NH}_3$: $K_p = \frac{p^2}{p \times p^3}$, so the unit is atm⁻².
• $\text{H}_2 + \text{I}_2 \rightleftharpoons 2\text{HI}$: the units cancel, so no units.
• $2\text{SO}_2 + \text{O}_2 \rightleftharpoons 2\text{SO}_3$ (Kc): $\frac{(\text{mol dm}^{-3})^2}{(\text{mol dm}^{-3})^3}$, so the unit is dm³ mol⁻¹.

1. Write the balanced equation and the expression for Kc.
2. Use the initial amounts and the amount of one species at equilibrium to work out the amount of every species at equilibrium (use the mole ratio).
3. Divide the amounts by the volume (in dm³) to get concentrations.
4. Substitute and calculate, with units and an appropriate number of significant figures.

Worked example. 1.00 mol N₂ and 3.00 mol H₂ in a 2.00 dm³ vessel give 0.400 mol NH₃ at equilibrium.

N₂ = 1.00 − 0.200 = 0.800 mol, so [N₂] = 0.400 mol dm⁻³. H₂ = 3.00 − 0.600 = 2.40 mol, so [H₂] = 1.20 mol dm⁻³. [NH₃] = 0.200 mol dm⁻³.

$K_c = \frac{0.200^2}{0.400 \times 1.20^3} = 0.0579 \ \text{dm}^6\,\text{mol}^{-2}$

1. Work out the equilibrium amount of each gas.
2. Work out the total moles of gas and each mole fraction.
3. Multiply by the total pressure to get partial pressures.
4. Substitute into Kp and give units.

Worked example. The same equilibrium (0.800 mol N₂, 2.40 mol H₂, 0.400 mol NH₃; total 3.60 mol) at a total pressure of 10.0 atm.

$p_{\text{N}_2} = \frac{0.800}{3.60} \times 10.0 = 2.22$ atm, $p_{\text{H}_2} = 6.67$ atm, $p_{\text{NH}_3} = 1.11$ atm.

$K_p = \frac{1.11^2}{2.22 \times 6.67^3} = 1.88 \times 10^{-3} \ \text{atm}^{-2}$