Part 3: Kc expressions for homogeneous and heterogeneous systems

Turn a balanced equation into an equilibrium-concentration expression, with coefficient powers and carefully chosen terms for different phases.

Kc describes an equilibrium composition relationship

For a given reaction at a fixed temperature, equilibrium concentrations satisfy a constant relationship. Square brackets mean equilibrium concentration, normally expressed in mol dm⁻³ in this course. They do not mean starting amount, total mass or the balancing coefficient. The subscript c indicates that the expression is written using concentrations.

For aA + bB ⇌ cC + dD in a homogeneous system, Kc = [C]ᶜ[D]ᵈ / ([A]ᵃ[B]ᵇ). Products go in the numerator, reactants in the denominator, and the balanced coefficients become powers. Multiplying [NH₃] by 2 is not the same operation as squaring [NH₃].

This AS topic requires deducing expressions for homogeneous and heterogeneous systems. Numerical equilibrium calculations, units and Kp are developed in Year 13 Topic 11. You still need the conceptual distinction now: changing the mixture at a fixed temperature does not change the temperature's Kc; reaction adjusts concentrations until the equilibrium relationship holds again.

Homogeneous systems have one phase

A homogeneous equilibrium has all participants in one phase, such as a gas mixture or one aqueous solution. For N₂(g) + 3H₂(g) ⇌ 2NH₃(g), Kc = [NH₃]² / ([N₂][H₂]³). The hydrogen term is cubed because its coefficient is three; the subscript 2 within H₂ is part of its identity and does not set the exponent.

For N₂O₄(g) ⇌ 2NO₂(g), Kc = [NO₂]²/[N₂O₄]. If the reaction is written in reverse, the corresponding expression is the reciprocal, [N₂O₄]/[NO₂]². An equilibrium constant belongs to a specified equation, just as a reaction enthalpy does.

For Fe³⁺(aq) + SCN⁻(aq) ⇌ [FeSCN]²⁺(aq), all three species are included: Kc = [[FeSCN]²⁺] / ([Fe³⁺][SCN⁻]). The charge 2+ labels the complex ion; it is not an exponent for concentration. In plain text the nested brackets look awkward, so always identify the chemical species before applying the outer concentration brackets.

Pure solids and pure liquid phases have constant activity

A heterogeneous equilibrium contains more than one phase. A pure solid's amount can change without changing its composition or density. Its constant contribution is absorbed into Kc rather than written as a variable concentration term. The same reasoning applies to a separate pure liquid phase. This simplification assumes the relevant pure phase is still present.

For CaCO₃(s) ⇌ CaO(s) + CO₂(g), Kc = [CO₂]. Both pure solids are omitted, but the gaseous product remains. Adding more pure carbonate does not create a new concentration term while both solid phases are present; it may affect how much material is available or how quickly a state is reached.

For Fe₃O₄(s) + 4H₂(g) ⇌ 3Fe(s) + 4H₂O(g), Kc = [H₂O]⁴/[H₂]⁴. Water is included because it is a gas here. Omitting a species just because its name is water ignores the state symbols and changes the expression.

Do not turn 'pure liquid' into 'every liquid'

In a dilute aqueous acid equilibrium, solvent water is commonly treated as effectively constant and absorbed into the constant. By contrast, components of a reacting homogeneous liquid mixture can have changing concentrations and must not all be omitted simply because their state symbols are (l). A liquid mixture is not a collection of separate pure liquid phases.

For an esterification model in which acid, alcohol, ester and water form one liquid mixture and all their concentrations vary, the concentration expression is Kc = [ester][water] / ([acid][alcohol]). This is an application of the general rule; detailed esterification calculations follow in Topic 11. If a question specifies water as a constant solvent or a separate pure phase, use that stated model instead.

The scientific reason for omission is constancy of the contribution under the adopted model, not that a substance is unimportant or does not react. Solids and solvent still appear in balanced chemical equations even when their terms are absent from a simplified Kc expression.

A systematic expression-writing method

First balance the equation and retain states. Next decide which species have variable equilibrium concentrations in the model. Put included products over included reactants. Convert coefficients to exponents and check that subscripts and charges stayed attached to the species. Finally re-read the direction of the equation: reversing it reverses numerator and denominator.

For NH₄HS(s) ⇌ NH₃(g) + H₂S(g), only the gases remain, so Kc = [NH₃][H₂S]. For 2NO(g) + O₂(g) ⇌ 2NO₂(g), Kc = [NO₂]²/([NO]²[O₂]). These expressions differ in both included phases and coefficient powers, even though each describes products forming from reactants.

Do not infer rate from an equilibrium expression

Kc describes a relationship once equilibrium has been established; it does not tell you how fast that state is approached. A catalyst can change the speed without changing Kc at the same temperature. Equally, a mixture with constant concentrations is not automatically at equilibrium if material is continually entering and leaving; a flow process may maintain a steady state for different reasons.

Concentrations in an expression are equilibrium values. You cannot insert initial values and call the result Kc unless the initial mixture is already at equilibrium. For quantitative problems, first establish the equilibrium composition; that calculation is the next-stage learning in Equilibrium II.

Quick checks

Original Finesse questions. Reveal the indicative worked solutions after attempting each question; these are not official Edexcel mark allocations.

Sources