# Chemical equilibrium

Chemical equilibrium is the state in which a chemical reaction proceeds at the same rate as its reverse reaction; the rates of the forward and reverse reactions are equal, and the concentration of the reactants and products stop changing. When this condition is met, there is no change in the proportions of the various compounds involved, and the reaction ceases to progress. A common example given is the Haber-Bosch process, in which hydrogen and nitrogen combine to form ammonia. Equilibrium is reached when the rate of production of ammonia equals its rate of decomposition. Le Chatelier's principle describes qualitative predictions that can be made about chemical equilibrium.

The equilibrium position of a reaction is said to lie far to the right if nearly all the reactants are used up and far to the left if hardly any product is formed from the reactants. Changing the conditions of a reaction can result in a shift to the right or to the left of the equilibrium position.

Without energy input chemical reactions always proceed towards equilibrium. For a reaction at equilibrium:

[itex]kA + mB \leftrightarrow nC + pD[itex]

The concentrations of reactants and products are related by the following equation:

[itex]K = \frac{\left[C\right]^n \left[D\right]^p} {\left[A\right]^k \left[B\right]^m}[itex]

where K is a constant called the equilibrium constant. This equation was discovered by Cato Guldberg and Peter Waage. The brackets in an equilibrium constant expression denote molarity of the involved substances. The right side of the equation is called the mass action expression and is denoted Q for a generic state (not necessarily in equilibrium). In this form it is called a reaction quotient. Since chemical reactions tend to equilibrium, if one or several reactants are added to a system at equilibrium (thus changing the value of Q), the formation of products will be favoured for an interval of time, until Q equals K; and vice versa. It is important to notice that only solvents or solids are not included in the equilibrium constant equation.

The value of the equilibrium constant for a given system depends only on temperature. One important implication of that is the possibility of shifting an equilibrium in order to favour the formation of either reactants or products through temperature changes.

For a single-step reaction, the equilibrium can easily be derived just by considering the kinetics involved. Unlike rate equations, though, it still holds for multi-step reactions since the expressions for each step just multiply together in order to compose the global process equation.

In a more rigorous approach, the behaviour of a system at chemical equilibrium can be analysed by thermodynamics. Chemical systems tend to equilibrium because it is the state in which global entropy is the highest ("global" refers to the sum of the entropy of the system and of its surroundings). As a consequence, the value of equilibrium constants depends on thermodynamic potentials of the system. The dependance of thermodynamic potentials explains why equilibrium constants are related to it. The value of K is related to temperature according to the following expression:

[itex]K_T = K_\infty e^{-\frac{\Delta E}{RT}}[itex]

where ΔE is the difference in energy per mole between reactants and products, e is the base of the natural logarithm, and R is the gas constant. The constant is mainly influenced by entropy change; however, analysing it using enthropy is more difficult - whereas energy is roughly constant against concentration, entropy varies logarithmically so it is required to refer back to a particular state. The relationship makes the most sense in terms of the free energy difference, ΔF* = ΔE - TΔS*, which represents the total work that can be done by the system as it develops. At equilibrium ΔF = 0, which gives us

[itex]\Delta F^* = RT \ln {\left(\frac{Q^*}{K}\right)}[itex]

Very often the system is considered to be at standard state, where Q = 1 in appropriate units, which can then be neglected. Note that all this applies to a reaction at constant temperature only. For a reaction at constant pressure (which is actually somewhat more typical) the thermodynamic potential to be used would be the Gibbs free energy, ΔG* = ΔH - TΔS*, where ΔH is the change in enthalpy. Using Gibbs free energy makes it possible to write an alternative equation:

[itex]\Delta G^* = -RT \ln {K}[itex]

It is possible to derive from those thermodynamical relations that the equilibrium constant equals to the mass action expression at equilibrium; however, this relationship is not always strictly true. In a [[solution, for instance, interactions between the involved substances (both solutes and solvents) could affect the equilibrium constant. Therefore, the equilibrium constant is more rigorously defined by the substances activity coefficients, which are usually assumed to be equal to the molarities of solutes or equal to one for solids and solvents.

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