# Chemical equilibrium

In a chemical reaction, chemical equilibrium is the state in which both reactants and products are present in concentrations which have no further tendency to change with time. [1] Usually, 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 equal. Thus, there are no net changes in the concentrations of the reactant(s) and product(s). Such a state is known as dynamic equilibrium. [2] [3]

## Historical introduction

Burette, a common laboratory apparatus for carrying out titration, an important experimental technique in equilibrium and analytical chemistry.

The concept of chemical equilibrium was developed after Berthollet (1803) 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 are equal. In the following chemical equation with arrows pointing 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:

${\displaystyle {\mbox{forward reaction rate}}=k_{+}\mathrm {A} ^{\alpha }\mathrm {B} ^{\beta }\,\!}$
${\displaystyle {\mbox{backward reaction rate}}=k_{-}\mathrm {S} ^{\sigma }\mathrm {T} ^{\tau }\,\!}$

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:

${\displaystyle k_{+}\left\{\mathrm {A} \right\}^{\alpha }\left\{\mathrm {B} \right\}^{\beta }=k_{-}\left\{\mathrm {S} \right\}^{\sigma }\left\{\mathrm {T} \right\}^{\tau }\,}$

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

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

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 SN1 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 failure 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,

CH3CO2H + H2O ⇌ CH
3
CO
2
+ H3O+

a proton may hop from one molecule of acetic acid on to a water molecule and then on to an acetate anion to form another molecule of acetic acid and leaving the number of acetic acid molecules unchanged. This is an example of dynamic equilibrium. Equilibria, like the rest of thermodynamics, are statistical phenomena, averages of microscopic behavior.

Le Châtelier's principle (1884) gives an idea of the behavior of an equilibrium system when changes to its reaction conditions occur. If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to partially reverse the change. For example, adding more S from the outside will cause an excess of products, and the system will try to counteract this by increasing the reverse reaction and pushing the equilibrium point backward (though the equilibrium constant will stay the same).

If mineral acid is added to the acetic acid mixture, increasing the concentration of hydronium ion, the amount of dissociation must decrease as the reaction is driven to the left in accordance with this principle. This can also be deduced from the equilibrium constant expression for the reaction:

${\displaystyle K={\frac$

If {H3O+} increases {CH3CO2H} must increase and CH
3
CO
2
must decrease. The H2O is left out, as it is the solvent and its concentration remains high and nearly constant.

A quantitative version is given by the reaction quotient.

J. W. Gibbs suggested in 1873 that equilibrium is attained when the Gibbs free energy of the system is at its minimum value (assuming the reaction is carried out at constant temperature and pressure). What this means is that the derivative of the Gibbs energy with respect to reaction coordinate (a measure of the extent of reaction that has occurred, ranging from zero for all reactants to a maximum for all products) vanishes, signalling a stationary point. This derivative is called the reaction Gibbs energy (or energy change) and corresponds to the difference between the chemical potentials of reactants and products at the composition of the reaction mixture. [1] This criterion is both necessary and sufficient. If a mixture is not at equilibrium, the liberation of the excess Gibbs energy (or Helmholtz energy at constant volume reactions) is the "driving force" for the composition of the mixture to change until equilibrium is reached. The equilibrium constant can be related to the standard Gibbs free energy change for the reaction by the equation

${\displaystyle \Delta _{r}G^{\ominus }=-RT\ln K_{\mathrm {eq} }}$

where R is the universal gas constant and T the temperature.

When the reactants are dissolved in a medium of high ionic strength the quotient of activity coefficients may be taken to be constant. In that case the concentration quotient, Kc,

${\displaystyle K_{\mathrm {c} }={\frac {[\mathrm {S} ]^{\sigma }[\mathrm {T} ]^{\tau }}{[\mathrm {A} ]^{\alpha }[\mathrm {B} ]^{\beta }}}}$

where [A] is the concentration of A, etc., is independent of the analytical concentration of the reactants. For this reason, equilibrium constants for solutions are usually determined in media of high ionic strength. Kc varies with ionic strength, temperature and pressure (or volume). Likewise Kp for gases depends on partial pressure. These constants are easier to measure and encountered in high-school chemistry courses.

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