CS Knowledge Base

In a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system.^[1] This state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but they are equal. Thus, there are no net changes in the concentrations of the reactants and products. Such a state is known as dynamic equilibrium.^[2]^[3] It is the subject of study of equilibrium chemistry.

Historical introduction

The concept of chemical equilibrium was developed in 1803, after Berthollet found that some chemical reactions are reversible.^[4] For any reaction mixture to exist at equilibrium, the rates of the forward and backward (reverse) reactions must be equal. In the following chemical equation, arrows point both ways to indicate equilibrium.^[5] A and B are reactant chemical species, S and T are product species, and α, β, σ, and τ are the stoichiometric coefficients of the respective reactants and products:

α A + β B ⇌ σ S + τ T

The equilibrium concentration position of a reaction is said to lie "far to the right" if, at equilibrium, nearly all the reactants are consumed. Conversely the equilibrium position is said to be "far to the left" if hardly any product is formed from the reactants.

Guldberg and Waage (1865), building on Berthollet's ideas, proposed the law of mass action:

{\begin{aligned}{\text{forward reaction rate}}&=k_{+}{\mathrm {A} }^{\alpha }{\mathrm {B} }^{\beta }\\{\text{backward reaction rate}}&=k_{-}{\mathrm {S} }^{\sigma }{\mathrm {T} }^{\tau }\end{aligned}}

where A, B, S and T are active masses and k₊ and k₋ are rate constants. Since at equilibrium forward and backward rates are equal:

k_{+}\left\{{\ce {A}}\right\}^{\alpha }\left\{{\ce {B}}\right\}^{\beta }=k_{-}\left\{{\ce {S}}\right\}^{\sigma }\left\{{\ce {T}}\right\}^{\tau }

and the ratio of the rate constants is also a constant, now known as an equilibrium constant.

K_{c}={\frac {k_{+}}{k_{-}}}={\frac {\{{\ce {S}}\}^{\sigma }\{{\ce {T}}\}^{\tau }}{\{{\ce {A}}\}^{\alpha }\{{\ce {B}}\}^{\beta }}}

By convention, the products form the numerator. However, the law of mass action is valid only for concerted one-step reactions that proceed through a single transition state and is not valid in general because rate equations do not, in general, follow the stoichiometry of the reaction as Guldberg and Waage had proposed (see, for example, nucleophilic aliphatic substitution by S_N1 or reaction of hydrogen and bromine to form hydrogen bromide). Equality of forward and backward reaction rates, however, is a necessary condition for chemical equilibrium, though it is not sufficient to explain why equilibrium occurs.

Despite the limitations of this derivation, the equilibrium constant for a reaction is indeed a constant, independent of the activities of the various species involved, though it does depend on temperature as observed by the van 't Hoff equation. Adding a catalyst will affect both the forward reaction and the reverse reaction in the same way and will not have an effect on the equilibrium constant. The catalyst will speed up both reactions thereby increasing the speed at which equilibrium is reached.^[2]^[6]

Although the macroscopic equilibrium concentrations are constant in time, reactions do occur at the molecular level. For example, in the case of acetic acid dissolved in water and forming acetate and hydronium ions,

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