Writing Kc Expressions: Heterogeneous Equilibria, Units and Reversed Reactions
Many students know the idea of equilibrium but still lose marks on the very first step: writing the equilibrium constant expression correctly. This page covers the rules that board and entrance papers test most often — which species go in, which stay out, what units Kc has, and how K changes when the equation is reversed, multiplied or added.
The basic expression
For a general reaction at equilibrium, aA + bB ⇌ cC + dD:
Square brackets mean concentration in mol/L at equilibrium. The powers are the coefficients of the balanced equation. Products go on top, reactants at the bottom. Kc depends only on temperature (and on how the equation is written), not on the starting amounts.
Rule 1: pure solids and pure liquids are left out
The concentration of a pure solid or pure liquid is fixed by its density, so it does not change during the reaction. Such species are taken as 1 in the expression. Only gases and dissolved species (aq) appear.
| Reaction | Kc expression |
|---|---|
| CaCO3(s) ⇌ CaO(s) + CO2(g) | Kc = [CO2] |
| N2(g) + 3 H2(g) ⇌ 2 NH3(g) | Kc = [NH3]2 / ([N2][H2]3) |
| Fe3+(aq) + SCN−(aq) ⇌ FeSCN2+(aq) | Kc = [FeSCN2+] / ([Fe3+][SCN−]) |
| C(s) + CO2(g) ⇌ 2 CO(g) | Kc = [CO]2 / [CO2] |
Water as a solvent is also left out in dilute aqueous reactions, because its concentration (about 55 mol/L) hardly changes.
Rule 2: units of Kc
Kc has units (mol/L) raised to the power Δn, where Δn = (number of moles of gaseous or dissolved products) − (number of moles of reactants) in the expression. If Δn = 0, Kc has no unit. Some books treat K as a pure number (using activities); if your question asks for units, write them.
Rule 3: how K changes when the equation changes
| Change in the equation | New K |
|---|---|
| Reverse the reaction | 1 / K |
| Multiply all coefficients by n | Kn |
| Halve all coefficients | √K |
| Add two reactions | K1 × K2 |
Worked example 1: N2O4 and NO2
For N2O4(g) ⇌ 2 NO2(g), the equilibrium concentrations are [NO2] = 0.0600 mol/L and [N2O4] = 0.0200 mol/L. Find Kc and its unit.
Kc = [NO2]2 / [N2O4] = (0.0600)2 / 0.0200 = 0.00360 / 0.0200 = 0.180.
Δn = 2 − 1 = 1, so the unit is mol/L: Kc = 0.180 mol L−1.
Worked example 2: reversed and halved reactions
Using Kc = 0.180 for N2O4 ⇌ 2 NO2, find Kc for (a) 2 NO2 ⇌ N2O4 and (b) ½ N2O4 ⇌ NO2.
(a) Reversed: K = 1 / 0.180 = 5.56.
(b) Halved: K = √0.180 = 0.424.
Check (b): [NO2] / [N2O4]½ = 0.0600 / √0.0200 = 0.0600 / 0.14142 = 0.424. It matches.
Worked example 3: adding two reactions
Reaction 1 has K1 = 2.0 and reaction 2 has K2 = 3.0 (practice values). Adding them gives the overall reaction. Find K for the overall reaction.
K = K1 × K2 = 2.0 × 3.0 = 6.0.
If instead you needed reaction 1 reversed plus reaction 2, you would use (1 / 2.0) × 3.0 = 1.5. Write the operation before you multiply.
Worked example 4: a heterogeneous equilibrium
For CaCO3(s) ⇌ CaO(s) + CO2(g), Kc = 2.0 × 10−4 mol/L at a given temperature (practice value). What is the equilibrium [CO2] if some solid CaCO3 and CaO are both present?
The expression is Kc = [CO2], so [CO2] = 2.0 × 10−4 mol/L.
This does not depend on how much solid is present, as long as both solids are there. That is why adding more CaCO3 does not shift this equilibrium.
Common mistakes
- Putting solids or pure liquids in the expression. They are taken as 1.
- Using the coefficient as a multiplier instead of as a power: [NH3] × 2 is wrong; it is [NH3]2.
- Using initial concentrations instead of equilibrium concentrations.
- Writing products below. Products are always on top.
- Forgetting that K belongs to the equation as written. A halved equation has a different K.
- Quoting K without the temperature. K changes with temperature.
Exam relevance
| Question type | Key idea |
|---|---|
| Write Kc for a reaction | Powers = coefficients; leave out solids and liquids |
| Find Kc from data | Use equilibrium concentrations only |
| Find the unit of Kc | (mol/L)Δn |
| K for a changed equation | Reverse → 1/K; multiply → Kn; add → multiply K values |
For how to use K to find unknown concentrations, see the ICE-table article linked below. Check your current syllabus for whether your exam wants units written.
Once you know Kc, you can check concentration arithmetic with the Concentration calculator.
Open the Concentration Calculator →Reaction mechanisms stick only with practice: attempt previous-year CSIR-NET questions and a timed quiz.
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