Learning path

Full curriculum

Full curriculum

Unit content

Equilibrium expressions and the equilibrium constant

For a reversible reaction at a fixed temperature, equilibrium compositions obey a characteristic quantitative relation.

For

$$a\mathrm A+b\mathrm B\rightleftharpoons c\mathrm C+d\mathrm D,$$

an introductory concentration-based equilibrium expression is

$$K_c=\frac{[\mathrm C]^c[\mathrm D]^d}{[\mathrm A]^a[\mathrm B]^b},$$

where square brackets denote equilibrium molar concentrations and the exponents are the stoichiometric coefficients from the balanced equation.

For example, for

$$\mathrm{N_2O_4\rightleftharpoons2NO_2},$$

$$K_c=\frac{[\mathrm{NO_2}]^2}{[\mathrm{N_2O_4}]}.$$

The value of $K_c$ describes where equilibrium lies. A very large value means the equilibrium composition is product-rich relative to reactants according to the expression; a very small value means reactants predominate. $K_c\approx1$ indicates that neither side is overwhelmingly favored.

The equilibrium constant does not describe reaction speed. Two reactions can have similar $K_c$ values while reaching equilibrium on very different time scales.

The numerical value of an equilibrium constant is tied to the reaction equation as written. Reversing the reaction inverts the constant:

$$K_{\mathrm{reverse}}=\frac1{K_{\mathrm{forward}}}.$$

Multiplying every stoichiometric coefficient by a factor $n$ raises the equilibrium constant to that power:

$$K_{n\times\mathrm{reaction}}=K^n.$$

When reactions are added to produce an overall reaction, their equilibrium constants multiply. These rules follow directly from multiplying and rearranging the corresponding equilibrium expressions.

This concentration form is the standard introductory model for solution chemistry. A more rigorous thermodynamic treatment replaces raw concentrations by dimensionless activities, and gas-phase equilibria are often expressed using partial pressures. Those refinements preserve the same underlying structure.