The equilibrium constant: how far reactions go
Learn what the equilibrium constant K means, how to write its expression, what large and small K values tell you, and why pure solids and liquids are left out.
Quick answer
The equilibrium constant K is the ratio of product concentrations to reactant concentrations at equilibrium, each raised to its stoichiometric coefficient. It measures how far a reaction proceeds.
Unit: unitless
Example: For N₂O₄(g) ⇌ 2NO₂(g) at 25 °C, Kc = 4.66 × 10⁻³. With [N₂O₄] = 0.050 M and [NO₂] = 0.015 M at equilibrium, Kc = (0.015)²/0.050 = 0.0045, matching the known value.
What you will learn
- Write the Kc expression for any balanced equation.
- Interpret large versus small K values in terms of reaction extent.
- Explain why pure solids and pure liquids are omitted from K expressions.
- Convert between K values for reversed or scaled equations.
The law of mass action
At equilibrium, the ratio of product concentrations to reactant concentrations settles at a fixed value — the equilibrium constant. For the general reaction
the concentration equilibrium constant is
This is the law of mass action: each concentration is raised to its stoichiometric coefficient. K is a property of the reaction at a given temperature — the same reaction at the same temperature always has the same K, regardless of starting amounts.
Reading K: large, small, and in-between
The magnitude of K is a direct readout of how far the reaction goes:
- K >> 1 (say, 10¹⁰): the reaction goes essentially to completion; products dominate at equilibrium.
- K << 1 (say, 10⁻¹⁰): the reaction barely proceeds; reactants dominate.
- K ≈ 1: significant amounts of both sides coexist at equilibrium.
For N₂O₄ ⇌ 2NO₂ at 25 °C, Kc = 4.66 × 10⁻³ — much less than 1, so an equilibrium mixture is mostly colorless N₂O₄ with a little brown NO₂. Warming the mixture darkens it as the equilibrium shifts — a visible K in action.
Why solids and liquids vanish from K
Pure solids and pure liquids never appear in K expressions. Their concentrations — amount per unit volume of the pure substance — are constant (density divided by molar mass does not change as the solid reacts), so they are folded into K itself.
For CaCO₃(s) ⇌ CaO(s) + CO₂(g), the expression is simply Kc = [CO₂]. Adding more solid limestone does not shift anything: only the gas concentration matters. The same logic applies to the solvent in dilute solutions — water is omitted from aqueous K expressions.
K and equation bookkeeping
K belongs to the equation as written. Manipulate the equation and K follows strict rules:
- Reverse the equation: K' = 1/K
- Multiply coefficients by n: K' = Kⁿ
- Add two equations: K' = K₁ × K₂
Related constants include Kp for gases (built from partial pressures instead of concentrations), connected by Kp = Kc(RT)^Δn where Δn is the change in moles of gas. And K always refers to one temperature — change T, and K changes (which direction depends on whether the reaction is exo- or endothermic).
Variables and units
| Symbol | Name | Unit | Meaning |
|---|---|---|---|
| Product concentration | M | Equilibrium concentration of a product species | |
| Coefficient | unitless | Stoichiometric coefficient in the balanced equation |
Common mistakes
K is pure thermodynamics: it describes the ratio of products to reactants at equilibrium. Speed is kinetics' business (rate constants). A huge K with a huge activation barrier means a reaction that 'wants' to happen but takes forever.
For the equilibrium expression, exponents are the stoichiometric coefficients from the balanced equation — always. Reaction orders are measured and belong to rate laws. The two look alike but come from completely different reasoning.
They are left out because their concentrations are effectively constant — a pure solid's 'concentration' (density/molar mass) does not change as it reacts. Constants get absorbed into K itself.
Real-world applications
Haber process: K values at different temperatures tell engineers the best compromise between yield and rate.
Solubility prediction: Ksp (a special K) predicts whether a precipitate forms.
Biochemistry: binding constants (a form of K) quantify how tightly drugs grip their targets.
Geochemistry: mineral stability in groundwater is computed from equilibrium constants.
Frequently asked questions
Does K have units?
Formally K is built from activities (effective concentrations relative to a standard state), which are unitless — so K itself is unitless. In practice, chemists often write concentrations in the expression, but the thermodynamic K carries no units.
What happens to K if I double the balanced equation?
Square the entire expression: for the doubled equation, K' = K². In general, multiplying an equation by n raises K to the nth power, and reversing the equation inverts K (K' = 1/K).
Does K depend on the starting concentrations?
No — K describes the ratio at equilibrium, not the route there. Different starting mixtures that reach the same equilibrium state give the same K. If your computed K varies with starting conditions, the system was not at equilibrium.
Can two sources list different K values for the 'same' reaction?
Only if the equation is written differently. K is tied to the balanced equation as written: 2HI ⇌ H₂ + I₂ has K' = 1/54.3 for the reverse of H₂ + I₂ ⇌ 2HI (K = 54.3). Always check which direction the equation faces.