# Thermodynamics, Chemical

## Thermodynamics, Chemical

a branch of physical chemistry concerned with thermodynamic phenomena in chemistry, as well as with the dependence of the thermodynamic properties of substances on the substances’ composition and aggregation state. Chemical thermodynamics is closely associated with thermochemistry and with the theory of chemical equilibrium and solutions (electrolytes in particular), the theory of electrode potentials, and the thermodynamics of surface phenomena.

Chemical thermodynamics is based on the general assumptions and conclusions of thermodynamics, above all, on the first and second laws of thermodynamics. The first law and its extremely important corollary—Hess’s law—serve as the basis for thermochemistry. A major role in thermochemical calculations is assigned to the heats of formation of substances, the values of which for each reaction substance make it possible to readily compute the heat effect of reactions; heats of combustion play a similar role in calculations dealing with organic substances. In addition to measuring the heat effects of various processes, determinations of the bond energies between atoms on the basis of spectral data are also employed, as are various approximate laws. The first law of thermodynamics forms the basis for Kirchhoff’s equation, which expresses the temperature dependence of the heat effect of a chemical reaction.

The second law of thermodynamics provides the basis for the study of equilibrium, chemical equilibrium in particular. It was first applied to the study of chemical reactions by J. Gibbs, A. L. Potylitsyn, H. Helmholtz, J. van’t Hoff, and H. L. Le Châtelier. In chemical thermodynamics, the second law makes it possible to determine how a change in external conditions (temperature, pressure) affects equilibrium and, consequently, what conditions are necessary for the process in question to proceed spontaneously, that is, without any expenditure of work from the outside, in the desired direction and with optimum results.

Various thermodynamic functions are employed in chemical thermodynamics to determine the characteristics of a process. Apart from entropy *S*, whose change characterizes in simplest fashion processes in isolated systems, thermodynamic potentials are widely used; these potentials permit a determination of the characteristics of processes under various conditions. Since chemical reactions generally occur at a constant temperature *T*, pressure *p*, or volume *V*, the following functions have the greatest practical value:

(1) *G* = *H* – *TS*

(2) *A* = *U* – *TS*

where *G* is the Gibbs free energy, *A* the Helmholtz free energy, *H* the enthalpy, and *U* the internal energy. On the basis of (1) and (2), we have the relations

(3) Δ*G* = Δ*H* – *T*Δ*S*

(4) Δ*A* = Δ*U* – *T*Δ*S*

where Δ*H* and Δ*U* are, respectively, the isobaric and isochoric heat effects of the reaction. Spontaneous processes occurring under the conditions *p*, *T* = const are possible only in a direction involving a decrease in *G*; their occurrence is limited, that is, equilibrium is reached, when the minimum value of *G* is attained. The course of processes occurring at *V*, *T* = const is traced according to the change in *A*. The sign and magnitude of Δ*G* (Δ*A*) depend on the relationship between the terms of equation (3) or (4): the heat effect Δ*H*(Δ*U*) and the entropy factor *T*Δ*S*. The relative value of the former increases with a decrease in temperature, while that of the latter increases with an increase in temperature.

Chemical potentials play an important role in chemical thermodynamics since any transition of a substance from one phase to another, for example, upon dissolution, is possible only in the direction involving an equalization of potentials. Equilibrium requires that the chemical potentials of all the components in all the phases of a system be equal. From these conditions, we derive the phase rule, a fundamental generalization describing equilibrium in any heterogeneous system.

Various relationships have great importance in chemical thermodynamics. Examples include the law of mass action; the equation for the isotherm of a reaction, which characterizes the dependence of Δ*G*(Δ*A*) on the concentration (thermodynamic activity) and partial pressures (fugacity) of the reaction substances and expresses the magnitude of the maximum work of a reaction; and the equation for the isobar (isochor) of a reaction, which characterizes the effect of temperature on chemical equilibrium.

The standard states of substances are very important in equilibrium calculations. If all the reaction substances are in the standard state, the following relationship holds:

(5) Δ*G*^{0} = –*RT* ln *K*

where *G*^{0} is the standard Gibbs free energy, *R* the gas constant, and *K* the equilibrium constant. Equations (3) and (5) yield the relation

(6) –*RT* ln *K* = Δ*H*^{0} – *T*Δ*S*^{0}

which permits the calculation of various equilibriums according to standard entropies and heats of formation, including equilibriums of chemical reactions, phase equilibriums in single-component and multicomponent systems, and equilibriums involving the dissociation of electrolytes, in particular, complex compounds.

The third law of thermodynamics is important in the calculation of chemical equilibrium. It can be used to find the entropy of a substance under given conditions based on the results of calorimetric determinations. These determinations include those of the temperature dependence of the substance’s heat capacity (from a temperature close to absolute zero to the given temperature), the phase transition temperatures, and the heats of phase transition (within the corresponding temperature range). It is then easy to compute Δ*S* (Σ*S*_{prod} – Δ*S*_{init}) for a reaction using the values of *S* for each substance involved in the reaction. (*S*_{prod} and *S*_{init} represent the entropies of the reaction products and the reactants, respectively.)

Quantum-mechanical calculations of thermodynamic properties and characteristics of processes, for example, heats of formation, occupy an important place in chemical thermodynamics. Methods of statistical thermodynamics can be used to compute the value of various thermodynamic functions on the basis of spectral data by matching the data with the structure of molecules.

Among the other trends in chemical thermodynamics, an important place is occupied by the thermodynamics of solutions. Although a general theory of solutions has not yet been developed, the concept of activity has greatly facilitated the use of thermodynamic equations (given corresponding experimental data).

Results and techniques in chemical thermodynamics dealing with thermochemistry, the properties of solutions, and the theory of chemical equilibrium are widely used in physics, heat and power engineering, geology, geochemistry, and biology. They are also used in solving problems of a practical nature in, for example, the chemical, petrochemical, metallurgical, and fuel industries. Achievements in chemical thermodynamics provide the theoretical basis for, and aid in the realization of, processes that are in the planning stage or that are being reintroduced. They can also lead to an intensification of established processes.

The thermodynamics of nonequilibrium processes and of high-temperature chemical reactions have been undergoing development since the mid-20th century.

### REFERENCES

*Kurs fizicheskoi khimii*, 2nd ed. Moscow, 1969.

Eremin, E. N.

*Osnovy khimicheskoi termodinamiki.*Moscow, 1974.

Karapet’iants, M. Kh.

*Khimicheskaia termodinamika*, 3rd ed. Moscow, 1975.

Prigogine, L., and R. Defay.

*Khimicheskaia termodinamika.*Novosibirsk, 1966. (Translated from English.)

Glasstone, S.

*Thermodynamics for Chemists.*New York, 1947.

Aston, J., and J. Fritz.

*Thermodynamics and Statistical Thermodynamics.*New York-London, 1959.

Lewis, G., and M. Randall.

*Thermodynamics*, 2nd ed. New York-London-Toronto, 1961.

M. KH. KARAPETIANTS