Many chemical reactions do not proceed to completion; instead, they reach a state in which the forward and reverse reactions occur at equal rates, leaving the concentrations of reactants and products constant. This dynamic state is called chemical equilibrium. It is a dynamic state because the reactions continue at the molecular level even though no net change is observable.
Equilibrium can be of two types: physical equilibrium, which involves a phase change such as the equilibrium between a solid and its saturated solution or a liquid and its vapour, and chemical equilibrium, which involves reactants and products. The equilibrium constant provides a quantitative measure of the extent of a reaction, telling us whether products or reactants dominate at equilibrium.
Equilibria in aqueous solution are of special importance in chemistry and biology. Acid-base equilibria, governed by the ionisation of acids and bases and the self-ionisation of water, determine the pH of solutions. Solubility equilibria control the concentrations of sparingly soluble salts. Together with Le Chatelier's principle, these ideas explain how systems respond to changes in concentration, pressure and temperature.
Physical processes also reach equilibrium. When a liquid is placed in a closed container, the rates of evaporation and condensation become equal, and the vapour pressure becomes constant. Similarly, the solubility of a solid in a liquid reaches equilibrium when the rate of dissolution equals the rate of crystallisation. In these equilibria, the concentrations or pressures involved are constant at a given temperature.
The equilibrium between ice and water is a physical equilibrium in which the rates of melting and freezing are equal. The vapour pressure of a liquid increases with temperature, and equilibrium constants for physical processes are temperature dependent. For example, the Henry's law constant relates the solubility of a gas to its partial pressure, and the equilibrium is disturbed by changes in pressure.
These physical equilibria obey the same thermodynamic principles as chemical equilibria. The position of a physical equilibrium shifts with temperature according to the sign of the enthalpy change, exactly as described by Le Chatelier's principle.
A chemical reaction reaches equilibrium when the rate of the forward reaction equals the rate of the reverse reaction. Consider a general reaction:
$$aA + bB \rightleftharpoons cC + dD$$
The law of chemical equilibrium states that at equilibrium, the ratio of the product of the concentrations of products to the product of the concentrations of reactants, each raised to their stoichiometric coefficients, is constant at a given temperature:
$$K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$$
Kc is the equilibrium constant in terms of concentrations. For gaseous reactions, the equilibrium constant can also be expressed in terms of partial pressures, giving Kp:
$$K_p = \frac{p_C^c p_D^d}{p_A^a p_B^b}$$
The two constants are related by:
$$K_p = K_c (RT)^{\Delta n}$$
where delta n is the change in the number of moles of gas. When delta n = 0, Kp equals Kc.
The magnitude of K gives the extent of reaction: a large K means the reaction goes far toward products, while a small K means reactants dominate. The value of K depends only on temperature, not on the initial concentrations or the direction from which equilibrium is approached.
In a homogeneous equilibrium, all reactants and products are in the same phase, such as the ionisation of acetic acid in water. In a heterogeneous equilibrium, the species are in different phases, such as the decomposition of calcium carbonate into calcium oxide and carbon dioxide.
For heterogeneous equilibria, the concentrations of pure solids and pure liquids are constant and are not included in the expression for the equilibrium constant. For the reaction:
$$\text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g)$$
$$K_p = p_{\text{CO}_2}$$
The equilibrium constant contains only the partial pressure of carbon dioxide. Similarly, the equilibrium constant for the dissolution of a sparingly soluble salt, called the solubility product (Ksp), involves only the concentrations of the dissolved ions.
Le Chatelier's principle states that if a system at equilibrium is disturbed by a change in concentration, pressure or temperature, the equilibrium shifts in the direction that tends to undo the effect of the disturbance.
An increase in the concentration of a reactant shifts the equilibrium to the right, consuming some of the added reactant. An increase in pressure shifts the equilibrium toward the side with fewer moles of gas. For example, in the synthesis of ammonia, N2 + 3H2 gives 2NH3, four moles of gas become two, so high pressure favours the formation of ammonia.
A temperature increase shifts the equilibrium in the endothermic direction, absorbing the added heat, while a temperature decrease favours the exothermic direction. A catalyst does not change the position of equilibrium; it only speeds up the attainment of equilibrium by lowering the activation energy of both directions equally.
Acids and bases in aqueous solution reach ionisation equilibria. A strong acid like hydrochloric acid ionises completely, while a weak acid like acetic acid ionises only partially, establishing an equilibrium described by its ionisation constant Ka. Similarly, weak bases have an ionisation constant Kb.
Water undergoes self-ionisation:
$$\text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^-$$
At 25 degrees Celsius, the ionisation constant of water is:
$$K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14}$$
The pH of a solution is defined as:
$$\text{pH} = -\log_{10}[\text{H}^+]$$
At 25 degrees Celsius, a neutral solution has pH 7, an acidic solution has pH less than 7, and a basic solution has pH greater than 7. The Henderson-Hasselbalch equation relates the pH of a buffer to the pKa and the concentrations of the acid and its conjugate base:
$$\text{pH} = \text{p}K_a + \log\frac{[\text{salt}]}{[\text{acid}]}$$
A buffer solution resists changes in pH when small amounts of acid or base are added. An acidic buffer contains a weak acid and its salt with a strong base, such as acetic acid and sodium acetate. A basic buffer contains a weak base and its salt with a strong acid, such as ammonium hydroxide and ammonium chloride. Buffers work because the weak acid neutralises added base and the conjugate base neutralises added acid.
The pH of a buffer is given by the Henderson-Hasselbalch equation. The buffer capacity is greatest when the concentrations of the acid and salt are equal. Biological fluids, such as blood, are buffered to maintain nearly constant pH.
Salt hydrolysis is the reaction of an ion from a salt with water. Salts of weak acids and strong bases give basic solutions, salts of strong acids and weak bases give acidic solutions, and salts of strong acids and strong bases give neutral solutions. The pH of a salt solution can be calculated from the hydrolysis constant.
For a sparingly soluble salt like silver chloride, an equilibrium exists between the solid and its ions in solution:
$$\text{AgCl}(s) \rightleftharpoons \text{Ag}^+ + \text{Cl}^-$$
The solubility product is:
$$K_{sp} = [\text{Ag}^+][\text{Cl}^-]$$
The solubility product is the product of the molar concentrations of the ions, each raised to its stoichiometric coefficient. For AxBy salt dissolving to give xA and yB:
$$K_{sp} = x^x y^y (s)^{x+y}$$
where s is the molar solubility. The solubility product is a constant at a given temperature and can be used to predict whether a precipitate will form. If the ionic product exceeds Ksp, precipitation occurs; if it is less than Ksp, the solution is unsaturated.
| Constant | Expression | Used for |
|---|---|---|
| Kc | [C]^c [D]^d / [A]^a [B]^b | Reactions in solution |
| Kp | pC^c pD^d / pA^a pB^b | Gaseous reactions |
| Ka | [H+][A-] / [HA] | Weak acid ionisation |
| Kb | [BH+][OH-] / [B] | Weak base ionisation |
| Kw | [H+][OH-] = 1.0 x 10^-14 | Water ionisation |
| Ksp | [Ag+][Cl-] | Sparingly soluble salts |
| Disturbance | Response of equilibrium |
|---|---|
| Increase reactant concentration | Shifts right |
| Increase pressure (fewer gas moles on product side) | Shifts right |
| Increase temperature | Shifts in endothermic direction |
| Add catalyst | No change in position, faster attainment |
| Add inert gas at constant volume | No change |
| Salt type | Example | Solution pH |
|---|---|---|
| Strong acid + strong base | NaCl | Neutral (7) |
| Weak acid + strong base | CH3COONa | Basic (> 7) |
| Strong acid + weak base | NH4Cl | Acidic (< 7) |
| Weak acid + weak base | CH3COONH4 | Depends on Ka and Kb |
Equilibrium governs the extent to which reactions proceed and the composition of reacting mixtures. The equilibrium constant quantifies this extent, and Le Chatelier's principle predicts how systems respond to disturbances, providing the basis for industrial processes such as the Haber process. In solution, ionic equilibria control the pH of acids, bases, buffers and salt solutions, while the solubility product governs precipitation and dissolution. These ideas connect directly to thermodynamics through delta G degree = -RT ln K and are essential for understanding electrochemistry, analysis and the chemistry of living systems. A firm grasp of equilibrium transforms many of the apparently separate facts of chemistry into a coherent, predictive framework.