Equilibrium Constant Formula
The equilibrium constant Keq expression relates product and reactant concentrations at equilibrium.
Learn chemical equilibrium with examples.
The Formula
For a general reversible reaction: aA + bB ⇌ cC + dD
The equilibrium constant (Keq) is a number that describes the ratio of product concentrations to reactant concentrations when a reversible reaction reaches equilibrium. Each concentration is raised to the power of its stoichiometric coefficient.
A large Keq (much greater than 1) means the reaction strongly favors products at equilibrium. A small Keq (much less than 1) means reactants are favored. When Keq is close to 1, significant amounts of both reactants and products are present.
The equilibrium constant depends on temperature but does not change with concentration or pressure changes. This is one of the most powerful concepts in chemistry for predicting reaction outcomes.
Variables
| Symbol | Meaning |
|---|---|
| Keq | Equilibrium constant (dimensionless for Kc in thermodynamic convention, but units vary in practice) |
| [A], [B] | Molar concentrations of reactants at equilibrium (mol/L) |
| [C], [D] | Molar concentrations of products at equilibrium (mol/L) |
| a, b, c, d | Stoichiometric coefficients from the balanced equation |
Important Notes
- Pure solids and pure liquids are excluded from the expression (their activity is 1)
- Kp uses partial pressures instead of concentrations for gas-phase reactions
- Kp = Kc(RT)Δn, where Δn = (c + d) − (a + b) for gaseous species
Example 1
For the reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g), at equilibrium the concentrations are: [N₂] = 0.50 M, [H₂] = 0.30 M, [NH₃] = 0.20 M. Calculate Keq.
Write the expression: Keq = [NH₃]² / ([N₂][H₂]³)
Substitute values: Keq = (0.20)² / (0.50 × (0.30)³)
Keq = 0.04 / (0.50 × 0.027) = 0.04 / 0.0135
Keq ≈ 2.96
Example 2
For the reaction 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), Keq = 800 at a certain temperature. If [SO₂] = 0.10 M and [O₂] = 0.20 M at equilibrium, what is [SO₃]?
Write the expression: Keq = [SO₃]² / ([SO₂]²[O₂])
Rearrange: [SO₃]² = Keq × [SO₂]² × [O₂]
[SO₃]² = 800 × (0.10)² × 0.20 = 800 × 0.01 × 0.20 = 1.6
[SO₃] = √1.6
[SO₃] ≈ 1.26 M
When to Use It
Use the equilibrium constant expression to analyze reversible chemical reactions.
- Predicting whether a reaction favors products or reactants
- Calculating unknown concentrations at equilibrium
- Determining the direction a reaction will shift when disturbed (Le Chatelier's principle)
- Relating Kc and Kp for gas-phase reactions
- Solving acid-base equilibrium problems using Ka and Kb