The law of mass action
For a reversible reaction at equilibrium
aA + bB ⇌ cC + dD
the ratio of product and reactant concentrations, each raised to the power of its coefficient, is constant at a given temperature. This is the law of mass action, stated by Guldberg and Waage in 1864:
Kc = [C]^c [D]^d / ([A]^a [B]^b)
Concentrations are in mol/L. Pure solids, pure liquids and the solvent, such as water in a dilute solution, are left out of the expression. Enter a coefficient of 0 for a species that does not exist in your reaction.
Reaction quotient Q
The same expression calculated with concentrations that are not at equilibrium is the reaction quotient Q. Comparing Q with K tells you which way the reaction will move:
- Q < K: too few products; the reaction goes forward.
- Q > K: too many products; the reaction goes in reverse.
- Q = K: the system is at equilibrium.
Example: ammonia synthesis
For N2 + 3H2 ⇌ 2NH3, with [N2] = 0.25, [H2] = 0.75 and [NH3] = 0.1 mol/L:
Kc = 0.1² / (0.25 × 0.75³) = 0.01 / 0.1055 ≈ 0.0948
From Kc to Kp
For gases, the constant can also be written with partial pressures. The two are linked by:
Kp = Kc × (RT)^Δn
where R = 0.08206 L·atm/(mol·K), T is in kelvin and Δn is the change in moles of gas, (c + d) − (a + b). For ammonia, Δn = 2 − 4 = −2, so at 298.15 K Kp ≈ 0.0948 × 24.47⁻² ≈ 1.6 × 10⁻⁴.
Link with Gibbs energy
ΔG° = −RT ln K, with R = 8.314 J/(mol·K). A K above 1 gives a negative ΔG°: products are favored. A K below 1 gives a positive ΔG°. For the example, ΔG° ≈ +5.8 kJ/mol.
What changes K, and what does not
- Temperature changes K. For an exothermic reaction like ammonia synthesis, K falls as temperature rises.
- Concentration, pressure and catalysts do not change K. They change Q or the speed at which equilibrium is reached. Le Chatelier’s principle describes how the system shifts back toward equilibrium.
Strictly, K uses activities rather than concentrations, so this calculation is most accurate for dilute solutions and ideal gases.