Chemical Equilibrium

Chemical equilibrium is the state of a reversible chemical reaction in which forward and reverse reactions occur at equal rates, so there is no net change in the amounts of reactants and products. It is dynamic: molecular transformations continue even though the macroscopic composition remains constant. Equilibrium does not require equal concentrations of reactants and products, and its composition depends on the reaction and imposed conditions. The concept connects chemical kinetics with thermodynamics. (openstax.org)

Dynamic balance

A reversible reaction is conventionally written with opposing arrows:

where the letters denote chemical species and the coefficients specify their stoichiometric proportions. Starting with reactants, product formation generally makes the reverse reaction increasingly important. Equilibrium is reached when the opposing rates balance, not when molecular activity stops. Different initial mixtures can reach different equilibrium concentrations while satisfying the same equilibrium relation. (openstax.org)

An illustrative gas-phase reaction is

Colorless dinitrogen tetroxide dissociates into brown nitrogen dioxide, while nitrogen dioxide combines to regenerate dinitrogen tetroxide. At fixed conditions, an equilibrium mixture maintains a constant color although both processes continue. Equilibria are called homogeneous when all participating substances occupy one phase and heterogeneous when they occupy multiple phases. (openstax.org)

Reaction quotient and equilibrium constant

The reaction quotient, $Q$, expresses a mixture’s composition. Its rigorous thermodynamic form uses dimensionless activities, which represent composition through their relationship to chemical potential. For the general reaction above,

Here $a_i$ denotes the activity of species $i$, not a stoichiometric coefficient. At equilibrium, $Q$ equals the equilibrium constant, $K$. This relationship is commonly described as the law of mass action. (goldbook.iupac.org)

For dilute solutions, activities are often approximated by concentrations divided by a standard concentration. For an ideal gas, activity is its partial pressure divided by the standard pressure. Textbook concentration and pressure expressions are commonly designated $K_c$ and $K_p$; the activity-based thermodynamic constant is dimensionless. Pure solids and pure liquids have unit activity in their standard states and therefore do not appear explicitly in the usual equilibrium expression. (iupac.qmul.ac.uk)

A large $K$ indicates that the equilibrium expression favors products, whereas a small $K$ favors reactants. Neither specifies how quickly equilibrium is attained. Reversing the written reaction replaces $K$ by $1/K$; multiplying every coefficient by a factor $n$ replaces it by $K^n$. Thus, a quoted constant must be accompanied by its reaction equation and temperature. (openstax.org)

Thermodynamic criterion

For a closed system at constant temperature and pressure, stable equilibrium minimizes Gibbs free energy subject to conservation constraints. The reaction Gibbs energy satisfies

where $R$ is the molar gas constant, $T$ is absolute temperature, and $\Delta_rG^\circ$ is the standard reaction Gibbs energy. At equilibrium,

These equations connect measurable equilibrium composition with thermodynamic properties. Importantly, $\Delta_rG$, rather than necessarily $\Delta_rG^\circ$, vanishes at equilibrium. (goldbook.iupac.org)

If $Q<K$, the forward reaction decreases Gibbs free energy; if $Q>K$, the reverse reaction does so. At $Q=K$, neither direction has a net thermodynamic driving force. This criterion predicts direction but not reaction speed: kinetic barriers may prevent a mixture from reaching its equilibrium composition on an experimentally accessible timescale. (openstax.org)

Response to changed conditions

Le Châtelier’s principle describes how an equilibrium system responds to a disturbance: the resulting net reaction tends to oppose the imposed change. Quantitatively, a disturbance changes $Q$, $K$, or both, and the system reacts until the equilibrium relation is restored. Adding a reactant or removing a product commonly promotes net product formation without changing $K$ at fixed temperature under the same standard-state convention. (openstax.org)

Compressing an ideal-gas equilibrium mixture at constant temperature favors the side containing fewer stoichiometric moles of gas. If both sides contain equal gaseous mole totals, compression produces no ideal-gas composition shift. Adding an inert gas at constant volume does not change the reacting gases’ partial pressures and therefore does not shift their equilibrium. (openstax.org)

Temperature changes can alter $K$. Heating favors the endothermic direction, while cooling favors the exothermic direction, reflecting the role of reaction enthalpy. Catalysis, by contrast, accelerates approach to equilibrium without changing its constant or final composition under otherwise identical conditions. (openstax.org)

Calculations and industrial application

Equilibrium calculations combine equilibrium expressions with material balances. For a single reaction, an ICE table records initial concentrations, stoichiometric changes, and equilibrium concentrations in terms of an unknown reaction extent. Substitution into the equilibrium expression yields an equation whose physically admissible solution gives the final composition. Any simplifying approximation must be checked against the resulting concentrations. (openstax.org)

The Haber process illustrates the distinction between equilibrium yield and production rate:

Formation of ammonia is exothermic and reduces gaseous mole numbers. Higher pressure therefore favors ammonia, while lower temperature favors its equilibrium formation but slows reaction. Industrial operation combines elevated pressure, a practicable temperature, and a catalyst; ammonia removal and recycling of unreacted gases increase overall conversion beyond the yield of a single pass. (openstax.org)