In chemistry, the equilibrium constant is a quantity characterizing a chemical equilibrium in a chemical reaction which is a useful tool to determine the concentration of various reactants or products in a system where chemical equilibrium occurs.

A typical equilibrium situation is as below:

				$cC\; +\; dD\; \backslash !\backslash$

where A and B are reactant molecules or atoms, C and D are product molecules or atoms, and a, b, c, and d are the stoichiometric coefficients of the respective reactants and products.

Equilibrium occurs when the forward reaction rate equals the backward reaction rate; expressed mathematically,

$$

k_{f} \left\left^*^c" target="_blank" >\left[D\right^d

where $k\_\{f\}$ and $k\_\{b\}$ are the forward and backward reaction rate constants, respectively. Cross-dividing yields the equilibrium constant

$$

K_c \equiv \frac{k_{f}}{k_{b}} = \frac{\left\left^*^a" target="_blank" >\left[B\right^b}

which depends mainly on temperature. The reactants A-D are usually in solution or in the gas phase, because solids and liquids generally do not enter into the rate equations. More generally, the concentrations of A, B, etc. should be replaced with their effective concentrations, i.e., their chemical activities.

Equilibrium constants can be defined for many physical/chemical processes, by equating the forward and backward rates and separating constants (such as $k\_\{f\}$ and $k\_\{b\}$) from the variables (such as and [B). Examples include the acidity constant (the equilibrium constant for the dissociation of protons from acids) and the solubility constant (the equilibrium constant for precipitating out of solution).

The equilibrium constant is related to the Gibbs free energy through a Boltzmann distribution as:

$K\; =\; e^\{-\backslash frac\{\backslash Delta\; G^\backslash circ\}\{RT\}\}$

Where ΔG° is the energy difference between reactants and products, R is the gas constant and T the absolute temperature.

This relationship is also written as:

$\backslash \; \backslash Delta\; G^\backslash circ\; =\; -RT\; \backslash ln\; K$

The Van't Hoff equation relates the change in temperature to the change in the equilibrium constant given the enthalpy change. The related Nernst equation in electrochemistry gives the difference in electrode potential as a function of redox concentrations.

There are certain implications of the equilibrium constant. If the value is very large, over 1, the reaction is said to lie to the right (of the arrow) indicating a greater concentration of products; values less than 1 lie to the left higher formation rates of reactants, and values of one indicate equal concentrations. Knowledge of the equilibrium constant helps to determine, in an industrial setting for example, how to best produce a desirable material.

For example, in the Haber process for the formation of ammonia, the value of K is around 30 at pressures and temperatures standard for the process. In an equilibrium between two conformers with energy difference 0, the equilibrium constant is 1 and both conformers are present in a 1:1 ratio. When the energy difference increases to 1 kcal/mol, the equilibrium constant at 25°C becomes around 5 and the concentration of the more stable conformer gets 85%. Note that all the above applies only to static equilibria, when concentrations change such as when an equilibrium is established and then additional substances are added, calculations and concepts become less straightforward. This latter situation is known as a dynamic equilibrium.

When molecules on each side of the equilibrium are able to further react in secondary reactions the final product ratio is determined according to the Curtin-Hammett principle.

See also

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• Chemical equilibrium

References

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1. Zumdahl, Steven; Zumdahl, Susan. Zumdahl Chemistry, 4th Edition.

External links

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• "Equilibrium constant" from the IUPAC "Gold Book"

Physical chemistry

Gleichgewichtskonstante | Constante d'équilibre | Evenwichtsconstante | Stała równowagi