Chemical thermodynamics

Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and the spontaneity of processes.

The structure of chemical thermodynamics is based on the first two laws of thermodynamics. Starting from the first and second laws of thermodynamics, four equations called the "fundamental equations of Gibbs" can be derived. From these four, a multitude of equations, relating the thermodynamic properties of the thermodynamic system can be derived using relatively simple mathematics. This outlines the mathematical framework of chemical thermodynamics.^[1]

In 1865, the German physicist

The primary objective of chemical thermodynamics is the establishment of a criterion for determination of the feasibility or spontaneity of a given transformation.^[3] In this manner, chemical thermodynamics is typically used to predict the energy exchanges that occur in the following processes:

1. Chemical reactions
2. Phase changes
3. The formation of solutions

The following state functions are of primary concern in chemical thermodynamics:

• Internal energy (U)
• Enthalpy (H)
• Entropy (S)
• Gibbs free energy (G)

Most identities in chemical thermodynamics arise from application of the first and second laws of thermodynamics, particularly the law of conservation of energy, to these state functions.

The three laws of thermodynamics (global, unspecific forms):

1. The energy of the universe is constant.
2. In any spontaneous process, there is always an increase in entropy of the universe.
3. The entropy of a perfect crystal (well ordered) at 0 Kelvin is zero.

Chemical energy is the energy that can be released when chemical substances undergo a transformation through a chemical reaction. Breaking and making chemical bonds involves energy release or uptake, often as heat that may be either absorbed by or evolved from the chemical system.

Energy released (or absorbed) because of a reaction between chemical substances ("reactants") is equal to the difference between the energy content of the products and the reactants. This change in energy is called the change in internal energy of a chemical system. It can be calculated from ${\displaystyle \Delta _{\rm {f}}U_{\mathrm {reactants} }^{\rm {o}}}$, the internal energy of formation of the reactant molecules related to the bond energies of the molecules under consideration, and ${\displaystyle \Delta _{\rm {f}}U_{\mathrm {products} }^{\rm {o}}}$, the internal energy of formation of the product molecules. The change in internal energy is equal to the heat change if it is measured under conditions of constant volume (at STP condition), as in a closed rigid container such as a

A related term is the

In most cases of interest in chemical thermodynamics there are internal

For an unstructured, homogeneous "bulk" system, there are still various extensive compositional variables { N_i } that G depends on, which specify the composition (the amounts of each chemical substance, expressed as the numbers of molecules present or the numbers of moles). Explicitly,

$${\displaystyle G=G(T,P,\{N_{i}\})\,.}$$

For the case where only PV work is possible,

$${\displaystyle \mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,}$$

a restatement of the fundamental thermodynamic relation, in which μ_i is the chemical potential for the i-th component in the system

$${\displaystyle \mu _{i}=\left({\frac {\partial G}{\partial N_{i}}}\right)_{T,P,N_{j\neq i},etc.}\,.}$$

The expression for dG is especially useful at constant T and P, conditions, which are easy to achieve experimentally and which approximate the conditions in living creatures

$${\displaystyle (\mathrm {d} G)_{T,P}=\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,.}$$

While this formulation is mathematically defensible, it is not particularly transparent since one does not simply add or remove molecules from a system. There is always a process involved in changing the composition; e.g., a chemical reaction (or many), or movement of molecules from one phase (liquid) to another (gas or solid). We should find a notation which does not seem to imply that the amounts of the components ( N_i ) can be changed independently. All real processes obey conservation of mass, and in addition, conservation of the numbers of atoms of each kind.

Consequently, we introduce an explicit variable to represent the degree of advancement of a process, a progress variable ξ for the extent of reaction (Prigogine & Defay, p. 18; Prigogine, pp. 4–7; Guggenheim, p. 37.62), and to the use of the partial derivative ∂G/∂ξ (in place of the widely used "ΔG", since the quantity at issue is not a finite change). The result is an understandable expression for the dependence of dG on chemical reactions (or other processes). If there is just one reaction $${\displaystyle (\mathrm {d} G)_{T,P}=\left({\frac {\partial G}{\partial \xi }}\right)_{T,P}\,\mathrm {d} \xi .\,}$$

If we introduce the

$${\displaystyle \nu _{i}=\partial N_{i}/\partial \xi \,}$$

(negative for reactants), which tells how many molecules of i are produced or consumed, we obtain an algebraic expression for the partial derivative

$${\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{T,P}=\sum _{i}\mu _{i}\nu _{i}=-\mathbb {A} \,}$$

where we introduce a concise and historical name for this quantity, the "affinity", symbolized by A, as introduced by Théophile de Donder in 1923.(De Donder; Progogine & Defay, p. 69; Guggenheim, pp. 37, 240) The minus sign ensures that in a spontaneous change, when the change in the Gibbs free energy of the process is negative, the chemical species have a positive affinity for each other. The differential of G takes on a simple form that displays its dependence on composition change

$${\displaystyle (\mathrm {d} G)_{T,P}=-\mathbb {A} \,d\xi \,.}$$

If there are a number of chemical reactions going on simultaneously, as is usually the case,

$${\displaystyle (\mathrm {d} G)_{T,P}=-\sum _{k}\mathbb {A} _{k}\,d\xi _{k}\,.}$$

with a set of reaction coordinates { ξ_j }, avoiding the notion that the amounts of the components ( N_i ) can be changed independently. The expressions above are equal to zero at thermodynamic equilibrium, while they are negative when chemical reactions proceed at a finite rate, producing entropy. This can be made even more explicit by introducing the reaction rates dξ_j/dt. For every physically independent process (Prigogine & Defay, p. 38; Prigogine, p. 24)

$${\displaystyle \mathbb {A} \ {\dot {\xi }}\leq 0\,.}$$

This is a remarkable result since the chemical potentials are intensive system variables, depending only on the local molecular milieu. They cannot "know" whether temperature and pressure (or any other system variables) are going to be held constant over time. It is a purely local criterion and must hold regardless of any such constraints. Of course, it could have been obtained by taking partial derivatives of any of the other fundamental state functions, but nonetheless is a general criterion for (−T times) the entropy production from that spontaneous process; or at least any part of it that is not captured as external work. (See Constraints below.)

We now relax the requirement of a homogeneous "bulk" system by letting the chemical potentials and the affinity apply to any locality in which a chemical reaction (or any other process) is occurring. By accounting for the entropy production due to irreversible processes, the equality for dG is now replaced by

$${\displaystyle \mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+\mathrm {\delta } W'\,}$$

or

$${\displaystyle \mathrm {d} G_{T,P}=-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+\mathrm {\delta } W'.\,}$$

Any decrease in the

In solution chemistry and biochemistry, the Gibbs free energy decrease (∂G/∂ξ, in molar units, denoted cryptically by ΔG) is commonly used as a surrogate for (−T times) the global entropy produced by spontaneous chemical reactions in situations where no work is being done; or at least no "useful" work; i.e., other than perhaps ± P dV. The assertion that all spontaneous reactions have a negative ΔG is merely a restatement of the second law of thermodynamics, giving it the physical dimensions of energy and somewhat obscuring its significance in terms of entropy. When no useful work is being done, it would be less misleading to use the Legendre transforms of the entropy appropriate for constant T, or for constant T and P, the Massieu functions −F/T and −G/T, respectively.

Generally the systems treated with the conventional chemical thermodynamics are either at equilibrium or near equilibrium. Ilya Prigogine developed the thermodynamic treatment of open systems that are far from equilibrium. In doing so he has discovered phenomena and structures of completely new and completely unexpected types. His generalized, nonlinear and irreversible thermodynamics has found surprising applications in a wide variety of fields.

The non-equilibrium thermodynamics has been applied for explaining how ordered structures e.g. the biological systems, can develop from disorder. Even if Onsager's relations are utilized, the classical principles of equilibrium in thermodynamics still show that linear systems close to equilibrium always develop into states of disorder which are stable to perturbations and cannot explain the occurrence of ordered structures.

Prigogine called these systems

In this regard, it is crucial to understand the role of walls and other constraints, and the distinction between independent processes and coupling. Contrary to the clear implications of many reference sources, the previous analysis is not restricted to homogeneous, isotropic bulk systems which can deliver only PdV work to the outside world, but applies even to the most structured systems. There are complex systems with many chemical "reactions" going on at the same time, some of which are really only parts of the same, overall process. An independent process is one that could proceed even if all others were unaccountably stopped in their tracks. Understanding this is perhaps a "thought experiment" in chemical kinetics, but actual examples exist.

A gas-phase reaction at constant temperature and pressure which results in an increase in the number of molecules will lead to an increase in volume. Inside a cylinder closed with a piston, it can proceed only by doing work on the piston. The extent variable for the reaction can increase only if the piston moves out, and conversely if the piston is pushed inward, the reaction is driven backwards.

Similarly, a

The

• Thermodynamic databases for pure substances
• laws of thermodynamics

• Herbert B. Callen (1960). Thermodynamics. Wiley & Sons. The clearest account of the logical foundations of the subject.
  ISBN 0-471-13035-4
  . Library of Congress Catalog No. 60-5597
• Ilya Prigogine & R. Defay, translated by D.H. Everett; Chapter IV (1954). Chemical Thermodynamics. Longmans, Green & Co. Exceptionally clear on the logical foundations as applied to chemistry; includes non-equilibrium thermodynamics.{{cite book}}: CS1 maint: multiple names: authors list (link)
• Ilya Prigogine (1967). Thermodynamics of Irreversible Processes, 3rd ed. Interscience: John Wiley & Sons. A simple, concise monograph explaining all the basic ideas. Library of Congress Catalog No. 67-29540
• E.A. Guggenheim (1967). Thermodynamics: An Advanced Treatment for Chemists and Physicists, 5th ed. North Holland; John Wiley & Sons (Interscience). A remarkably astute treatise. Library of Congress Catalog No. 67-20003
• Th. De Donder (1922). "L'affinite. Applications aux gaz parfaits". Bulletin de la Classe des Sciences, Académie Royale de Belgique. Series 5. 8: 197–205.
• Th. De Donder (1922). "Sur le theoreme de Nernst". Bulletin de la Classe des Sciences, Académie Royale de Belgique. Series 5. 8: 205–210.

• Chemical Thermodynamics - University of North Carolina
• Chemical energetics (Introduction to thermodynamics and the First Law)
• Thermodynamics of chemical equilibrium (Entropy, Second Law and free energy)