5.1.2 Equilibrium (Kc and Kp)

A mole fraction tells you what fraction of the total amount of gas is one particular gas. I always find the total moles first, then divide the moles of the gas you want by that total.

Mole fraction has no units, and all the mole fractions in the mixture add up to 1.

Once you know a gas's mole fraction, multiply it by the total pressure. The answer is that gas's partial pressure — the pressure it contributes to the mixture.

Use the same pressure unit as the total pressure. If you add all the partial pressures together, you should get the total pressure back.

Set the calculation out so you can see the initial amount, the change, and the equilibrium amount for each species. The balanced equation controls every change, so the other species must change in the ratio shown by the coefficients.

For N₂ + 3H₂ ⇌ 2NH₃, making 0.80 mol NH₃ uses 0.40 mol N₂ and 1.20 mol H₂. Once you have the equilibrium moles, convert to concentration or partial pressure only if the question needs it.

To find an equilibrium composition experimentally, keep the system at the chosen temperature until equilibrium is established, then measure the amount or concentration of at least one species. Depending on the system, you might use a titration, colorimetry or another measurement you can convert into a concentration or amount.

You can then use the balanced equation and the starting quantities to work out the other equilibrium amounts. The important practical point is that your measurement must give you the composition at equilibrium, not after you have allowed the system to move somewhere else.

Write products over reactants, use equilibrium concentrations, and turn each coefficient in the balanced equation into a power. For H₂(g) + I₂(g) ⇌ 2HI(g), you get [HI]² over [H₂][I₂].

For a heterogeneous equilibrium, leave out pure solids and pure liquids because their concentrations are effectively constant. So for CaCO₃(s) ⇌ CaO(s) + CO₂(g), Kc only contains the CO₂ term.

Kp has the same products-over-reactants pattern, but you use partial pressures instead of concentrations. For N₂(g) + 3H₂(g) ⇌ 2NH₃(g), the coefficients become powers in exactly the same way.

Only gaseous species appear in a Kp expression. Do not put square brackets around them — square brackets mean concentration, which belongs to Kc.

For a Kc calculation, write the expression first and then make sure every value you substitute is an equilibrium concentration. If the question gives equilibrium moles, divide by the volume in dm³ before you substitute.

I’d keep the algebra visible. It makes powers much harder to miss and gives you somewhere to check if the final value looks wrong.

For Kp, use a fixed route: equilibrium moles → total moles → mole fractions → partial pressures → Kp. If the question already gives partial pressures, you can start at the last step.

Do not substitute moles directly into a Kp expression. Kp is built from partial pressures.

Work the units through the expression using the same powers as the concentration or pressure terms. Do not assume Kc or Kp has no units; sometimes everything cancels and sometimes it does not.

For Kp, your final units must be built from the pressure unit used in the question. For Kc, they are built from mol dm⁻³.

Temperature is the condition that can change the value of Kc or Kp. For an exothermic forward reaction, increasing temperature favours the endothermic reverse direction, so the product-to-reactant ratio falls and K gets smaller.

For an endothermic forward reaction, increasing temperature favours products, so K gets larger. Lowering the temperature gives the opposite changes.

• exothermic forward reaction: higher temperature → smaller K
• endothermic forward reaction: higher temperature → larger K

At constant temperature, Kc keeps the same value. If you suddenly change a concentration, the mixture is no longer in the equilibrium ratio, so the forward and reverse reactions adjust the concentrations until the Kc expression has its original value again.

So you can get a new equilibrium composition without getting a new Kc.

Changing pressure can move the position of a gaseous equilibrium, but at the same temperature Kp does not change. The partial pressures rearrange until the same Kp relationship is restored.

A catalyst is different again: it speeds up both forward and reverse reactions, so equilibrium is reached faster. It changes neither K nor the equilibrium composition.

Look at the Kc expression itself. If you add a reactant, the denominator suddenly becomes larger, so the product-to-reactant ratio is too small for the existing Kc.

The reaction then moves towards products: reactant concentrations fall and product concentrations rise until the expression once again equals Kc. If you disturb a product concentration, use the same reasoning with the numerator.

For a gas equilibrium, changing the total pressure changes the partial pressures immediately. The Kp expression therefore no longer has the equilibrium value, and the reaction moves until the partial-pressure ratio is restored.

For N₂ + 3H₂ ⇌ 2NH₃, increasing pressure favours the product side because it has fewer moles of gas. That gas-mole shortcut is useful, but the Kp expression is the more general way to understand what is being restored.

A temperature change is different because the equilibrium constant itself changes. The mixture then shifts until its concentrations or partial pressures satisfy the new value of K.

For an exothermic forward reaction, heating lowers K and the equilibrium moves towards reactants. Cooling raises K and the equilibrium moves towards products. For an endothermic forward reaction, reverse those conclusions.

If OCR gives you an unfamiliar equilibrium constant, don’t get distracted by the new letter. Start with the equation and the expression you are given or asked to build, then use the same ideas: powers come from coefficients, only the appropriate species appear, and the constant has one value at a fixed temperature.

You will meet the same style of reasoning again with constants such as Ka and Kw. Read what each constant is built from before you decide which quantities belong in it.