Chemical thermodynamics

(physical chemistry) The application of thermodynamic principles to problems of chemical interest.

The application of thermodynamic principles to systems involving physical and chemical transformations in order to (1) develop quantitative relationships among the identifiable forms of energy and their conjugate variables, (2) establish the criteria for spontaneous change, for equilibrium, and for thermodynamic stability, and (3) provide the macroscopic base for the statistical-mechanical bridge to atomic and molecular properties. The thermodynamic principles applied are the conservation of energy as embodied in the first law of thermodynamics, the principle of internal entropy production as embodied in the second law of thermodynamics, and the principle of absolute entropy and its statistical thermodynamic formulation as embodied in the third law of thermodynamics.

The basic goal of thermodynamics is to provide a description of a system of interest in order to investigate the nature and extent of changes in the state of that system as it undergoes spontaneous change toward equilibrium and interacts with its surroundings. This goal implicitly carries with it the concept that there are measurable properties of the system which can be used to adequately describe the state of the system and that the system is enclosed by a boundary or wall which separates the system and its surroundings. Properties that define the state of the system can be classified as extensive and intensive properties. Extensive properties are dependent upon the mass of the system, whereas intensive properties are not. Typical extensive properties are the energy, volume, and numbers of moles of each component in the system, while typical intensive properties are temperature, pressure, density, and the mole fractions or concentrations of the components.

The concept of a boundary enclosing the system and separating it from the surroundings requires specification of the nature of the boundary and of any constraints the boundary places upon the interaction of the system and its surroundings. Boundaries that restrain a system to a particular value of an extensive property are said to be restrictive with respect to that property. A boundary which restrains the system to a given volume is a fixed wall. A boundary which is restrictive to one component of a system but not to the other components is a semipermeable wall or membrane. A system whose boundaries are restrictive to energy and to mass or moles of components is said to be an isolated system. A system whose boundaries are restrictive only to mass or moles of components is a closed system, whereas an open system has nonrestrictive walls and hence can exchange energy, volume, and mass with its surroundings. Boundaries can be restrictive with respect to specific forms of energy, and two important types are those restrictive to thermal energy but not work (adiabatic walls) and those restrictive to work but not thermal energy (diathermal walls).

Changes in the state of the system can result from processes taking place within the system and from processes involving exchange of mass or energy with the surroundings. After a process is carried out, if it is possible to restore both the system and the surroundings to their original states, the process is said to be reversible; otherwise the process is irreversible. All naturally occurring spontaneous processes are irreversible. The first law defines the internal energy as a state function or property of the state of a system, and restricts the system and its surroundings to those processes which conserve energy. The second law establishes which of the permissible processes can occur spontaneously.

According to the first law of thermodynamics, the total energy E of a system is the sum of its kinetic energy T, its potential energy V, and its internal energy U, Eq. (1). If a system has
1.
constant mass and its center of mass is moving with uniform velocity in a uniform potential, then changes in the total energy of the system δE are equal to changes in its internal energy δU. Chemical thermodynamics concentrates on the internal energy of the system, but kinetic and potential energy changes of the system as a whole can be important for chemical systems. The principle of conservation of energy requires that the change in the internal energy of a system be the result of energy transfer between the system and its surroundings. The internal energy U is a function of the set of extensive variables associated with the various forms of internal energy. Each form of internal energy is manifest by the product of an extensive variable and its conjugate intensive variable.

Thermal energy exchange or heat (that form of energy transferred as a result of temperature differences between a system and its surroundings) plays a central role in thermodynamics, and is singled out from the other forms of energy or work. This is expressed by Eq. (2), where δq is the differential thermal energy
2.
(heat) absorbed by the system from the surroundings and δω is the differential work performed on the system by the surroundings. It is convenient to write Eqs. (3), where T is temperature, S
3a.

3b.
is the entropy, and (−δa) is a sum of the nonthermal differential work terms. The term δa can be either zero or nonzero. If it is zero, the heat absorbed by the system is equal to TdS. In an adiabatic process δq is zero and TdS − δa, and hence if δa is nonzero, it must correspond to an internally generated thermal energy. This is frequently referred to as the uncompensated heat of a process, since it does not result from the transfer of heat from the surroundings.

The heat capacity of a system is of particular importance in such thermochemical calculations. The heat capacity is the amount of thermal energy that can be absorbed by a system for a unit rise in temperature. This is defined by Eq. (4),
4.
where C_process is the heat capacity of a system for a given type of process. See also Heat capacity.

There are many possible and essentially equivalent statements of the second law of thermodynamics. It will suffice to state the empirical result that in all spontaneous processes the uncompensated heat δa in Eqs. (3) is always positive. Equation (3a) can be rewritten as Eq. (5), where the term δq/T is the contribution to the
5.
entropy due to heat exchange with the surrounding (d_eS), while δa/T is the contribution to the entropy produced as a result of the interconversion of work terms (d_iS). The second law can then be summarized as Eqs. (6), where d_iS greater than zero applies
6a.

6b.
to irreversible process. When d_iS = 0, that is, for a reversible process, Eq. (7) holds. This is the basic equation for establishing
7.
the thermodynamic temperature scale based upon the theoretical limits of reversible cycles. The requirement that d_iS > 0 for spontaneous processes provides the criteria for examining the specific conditions for spontaneous paths, and the criteria for establishing the equilibrium state of a system.

Many chemical systems can be considered closed systems in which a single parameter ξ can be defined as a measure of the extent of the reaction or the degree of achievement of a process. If the reaction proceeds or the process advances spontaneously, entropy must be produced according to the second law and δa must be positive. In terms of the advancement parameter ξ, this uncompensated heat δa can be given by Eq. (8), where is the
8.
affinity of the process or reaction. The affinity is related to internal entropy production by Eq. (9). The condition that the entropy
9.
production is zero represents equilibrium, and hence is an equivalent condition for equilibrium in a closed system. For spontaneous processes, since the signs of A and dξ must be the same, for positive the process must advance or go in a forward direction in the usual sense of chemical reactions or physical processes, while for negative the process must proceed in the reverse direction.

The affinity of a chemical reaction establishes the spontaneous direction of the reaction, and consequently methods for determining the affinity are important in thermochemical studies. The affinity is simply related to the stoichiometric coefficients of the reaction and the chemical potentials of the reactants and products in the reaction.

Classical equilibrium thermodynamics is primarily concerned with calculations for reversible processes, and deals with irreversibility in terms of inequalities. In the case of irreversible processes in systems slightly removed from equilibrium, the rate of internal entropy production d_iS/dt is related to the fluxes J_i associated with thermal, concentration, or other differences in intensive parameters or potentials X_i. This entropy production is then given by Eq. (10). The fluxes include heat conduction, diffusion, electric conduction, and other direct effects.
10.

In addition, a flux of one type may be coupled to a potential difference of another type. For example, a thermal gradient can result in a mass flux (thermal diffusion), or a concentration gradient in any energy flux. Thermal conductivity, thermo-osmosis, and thermoelectric effects are all coupled effects.

Far removed from equilibrium, thermodynamics must be formulated somewhat differently and more cautiously. The interplay of thermodynamic stability and kinetics can give rise to macroscopic structures with both temporal and spatial coherence called dissipative structures. Much theoretical effort is being directed to these studies because of their apparent relevance to biological structures, but it is still too early to assess how far-reaching these theories will be in the future.