Chemical equilibrium is the thermodynamic equilibrium in a system where direct and reverse chemical reactions are possible. If chemical equilibrium takes place in the system, the rates of all reactions proceeding in two opposite directions are equal. Therefore, the macroscopic parameters of the system do not change and the relationship between concentrations of reacting substances remains constant at a given temperature. Equilibrium for any chemical reaction is expressed by an equality ∑ν_{i}μ_{i} = 0, where μ_{i} is the chemical potential of each reagent (i = 1,2, . . .) and ν_{i} is the stoichiometric coefficient of each substance in an equation of chemical reaction (it is positive for initial substances and negative for products of a reaction).

The dependence of chemical equilibrium on external conditions is expressed by the *Le Chatelier-Braun principle* (1885-1886). It consists of the following correlation: Let equilibrium take place and then influence the system, changing some external conditions (temperature, pressure, concentrations of reacting substances). The equilibrium of a reaction tends to follow such direction that allows the reduction of an external influence. A temperature increase will cause a displacement of the equilibrium to the direction of such reaction that proceeds with heat absorption. A pressure increase will cause equilibrium displacement to follow the direction of such reaction that leads to a volume decrease. The introduction of any additional reagent in the system will propel equilibrium displacement to a direction where this reagent is consumed.

The total *Gibbs energy* change of a chemical reaction aA + bB = cC + dD (when temperature and pressure are constant) is expressed by the equation

where R is the gas constant, p is the pressure, T is the absolute temperature, α_{i} refers to the activities of the reacting substances and
is the standard Gibbs energy's change of that reaction (α_{i} = 1). The value of
can be calculated on the basis of standard values of the Gibbs energies of formation (Δ_{f}G^{0}) of the reagents at 298.15 K and of known thermodynamic relationships that determine the temperature and pressure dependencies of Gibbs energy change.

If equilibrium is attained, then

Here, α_{equil} are the activities corresponding to the equilibrium state and K_{a} is the equilibrium constant expressed in terms of activities. Hence, it follows that
. The last relationship is the van't Hoff isotherm equation (or *van't Hoff equation*). It permits the determination of a probable direction of the reaction under given conditions. The process will take place when Δ_{r}G_{P,T} < 0, i.e., when
. Analogous relationships can be obtained when the equilibrium constant (K_{p}) is expressed in terms of partial pressures (P_{i}) of the reagents:

The "equilibrium constant of reaction" is the result of the mass action law, which determines a correlation between the masses of reacting substances under equilibrium. According to this law, the reaction's rate depends on the concentrations of reacting substances. The rate constant of a given reaction at fixed temperature is a constant value; therefore, the relationship of the rate constants of direct and reverse reactions is a constant value too. This relationship is a function of temperature only.

The equations that express a relationship between the
-value and equilibrium constant of reaction allow the calculation of the equilibrium of chemical reactions, avoiding expensive and prolonged experiments. For such calculations, it is necessary to have reliable values of thermodynamic functions for all reacting substances.

Various experimental methods are used to determine equilibrium constants of chemical reactions. There are static and dynamic methods as well as the circulation method. The last is a specific combination of the static and dynamic methods. When static methods are used, the reaction mixture stays at a given temperature until an adjustment of the equilibrium takes place. Then "tempering" and chemical analysis of the reaction mixture are carried out. "Equilibrium tempering" is the fast-cooling of the reaction mixture to a low temperature where the rate of reaction is very small.

The more common dynamic method of defining equilibrium constants has often been called the transportation method. A steady stream of inert gas is passed over the mixture of substances that is maintained at a constant temperature. This "carrier" gas removes the volatile components of the reaction at a rate that depends on the rate of gas flow. The vapors of the reagents are condensed or collected by absorption or chemical combination at the colder portion of the apparatus. The experiments are carried out at different rates of gas flow. The equilibrium pressures of volatile reagents are determined by extrapolation of the results up to zero rate of the carrier gas.

A modification of the dynamic method used for investigating heterogeneous equilibria is the circulation method. The gas mixture is circulated in a closed space; circulation is carried out by means of electromagnetic pump. Equilibrium is attained when passing this mixture many times over the solid phase into the furnace. Tempering of the gas mixture is done when it is taken out from the hot zone and passed through a capillary. In view of the large linear rate of gas flow, this mixture becomes cold rapidly and its composition is not changed.

The most direct way of measuring equilibrium constants of chemical reactions is through the measurement of electromotive forces (the e.m.f. method). For example, the reaction

is a process of potential generation for the Daniel galvanic element:Zn^{0}/Zn^{2+}//Cu^{0}/Cu^{2+} A zinc plate (one electrode) is immersed into a solution of zinc sulfate and a copper plate (the other electrode) is immersed into a solution of copper sulfate. A galvanic element (source of electromotive force) can be created if both electrodes are connected by a tube that contains a solution-conductor. The dissolution of zinc (process: Zn^{0} = Zn^{2+} + 2e) takes place at one electrode; the precipitation of copper (process: Cu^{2+} + 2e = Cu^{0}) takes place at the second electrode. Therefore, the common potential forming reaction is: Zn^{0} + Cu^{2+} = Zn^{2+} + Cu^{0} The Gibbs energy change for such reaction is given by the formula
, where n is the number of gramme-equivalents of reagent; F is Faraday's constant (nF is the number of coulombs of electricity passed); and E_{T} is the electromotive force of the galvanic element at a given temperature. The value of the Gibbs energy of reaction can be used for calculating its equilibrium constant (K):
.

The equilibrium state is a thermodynamic state of a system that is permanent in time. This invariability is not connected with some external process taking place. There are different kinds of equilibria. If the equilibrium is "steady," then any adjacent states of the system are less steady. It would be necessary to spend external work for transition from the equilibrium state to these adjacent states. It is also typical that steady equilibrium can be approached from two opposite directions. However, this discussion is concerned with steady equilibria only or "chemical equilibria." From the physicist's point of view, steady equilibrium is dynamic. It is attained when the rates of direct and reverse reactions are equal, but not under conditions when the process is stopped in general. The equality dG = 0 is a general condition for "steady" and "unsteady" equilibria, but the value of the second differential of Gibbs energy is positive under steady equilibrium (d^{2}G > 0) and negative under unsteady equilibrium (d^{2}G < 0). The conditions of stability of the equilibrium can be deduced using the *second law of thermodynamics*. These are: 1) the pressure increases at a constant temperature if volume decreases [(dP/dV)_{T} < 0]; and 2) the value of heat capacity is positive (C_{p} > 0).

The degree of stability of the different states of chemical systems can vary. States which possess some relative stability are called "metastable" states. Such states have often arisen due to kinetic factors, which create difficulties for the transition of a system from the metastable (unsteady) state to a steady equilibrium state.

The development of thermodynamic theory of equilibria—in particular, equilibria of chemical reactions—owed much to J. W. Gibbs (1873-1878) and Le Chatelier (1885), who discovered the principle of displacement of equilibria under conditions of external change. The theory of chemical equilibria was developed further by F. H. van't Hoff (1884-1886).

#### REFERENCES

Gibbs, J. W. (1950) *Thermodynamic Works*. Translation from English, Gostekhteorizdat, M.-L.

Munster, A. (1971) *Chemical Thermodynamics*. Translation from German.

Kubaschewski, O. and Alcock, C. B. (1979) *Metallurgical Thermochemistry*, Pergamon Press Ltd., Oxford. New York. Toronto. Sydney. Paris. Frankfurt.

Karapetyans, M. Kh. (1981) *Introduction to Theory of Chemical Processes*, Vysshaya Shkola, M. (in Russian).

Vasiliev, V. P. (1982) *Thermodynamic Properties of Solutions of Electrolytes*, Vysshaya Shkola, M. (in Russian).