In thermodynamics, chemical thermodynamics is the mathematical study of the interrelation of heat and work with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics. Chemical thermodynamics can be generally thought of as the application of mathematical methods to the study of chemical questions and is concerned with 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.

History
The primary objective of chemical thermodynamics is the establishment of a criterion for the determination of the feasibility or spontaneity of a given transformation. In this manner, chemical thermodynamics is typically used to predict the energy exchanges that occur in the following processes:
The following state functions are of primary concern in chemical thermodynamics:
Most identities in chemical thermodynaimcs arise from application of the first and second laws of thermodynamics, particularly the law of conservation of energy, to these state functions.

Chemical reactions
Phase changes
The formation of solutions
Internal energy (U)
Enthalpy (H).
Entropy (S)
Gibbs free energy (G) Overview
It is the potential of a chemical substance to undergo a transformation through a chemical reaction or transform other chemical substances. Breaking or making of chemical bonds, involves energy, that may be either absorbed or evolved from a chemical system.
Energy that can be released (or absorbed) because of a reaction between a set of chemical substances 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 reaction. It can be calculated using the formula
ΔU_products is the internal energy of formation of the product molecules. The internal energy change of a process is equal to the heat change if it is measured under conditions of constant volume, as in a closed rigid container such as a bomb calorimeter. However, under conditions of constant pressure, as in reactions in vessels open to the atmosphere, the heat change measured is not always equal to the internal energy change, because pressure-volume work also releases or absorbs energy. (The heat change at constant pressure is called the enthalpy change, in this case the enthalpy of formation).
Another useful term is the heat of combustion, it is the energy released due to a combustion reaction and often applied in the study of fuels. Food is similar to hydrocarbon fuel and carbohydrate fuels, and when it is oxidized, its caloric content is similar (though not assessed in the same way as a hydrocarbon fuel-- see food energy).
In chemical thermodynamics the term used for the chemical potential energy is chemical potential and for chemical transformation an equation most often used is Gibbs-Duhem equation


Chemical energy
In most cases of interest in chemical thermodynamics there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which always create entropy unless they are at equilibrium, or are maintained at a "running equilibrium" through "quasi-static" changes by being coupled to constraining devices, such as pistons or electrodes, to deliver and receive external work. Even for homogeneous "bulk" materials, the free energy functions depend on the composition, as do all the extensive thermodynamic potentials, including the internal energy. If the quantities { N_i }, the number of chemical species, are omitted from the formulae, it is impossible to describe compositional changes.

Gibbs function

Main article: Chemical affinity Chemical affinity
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 entropy produced by spontaneous chemical reactions in situations where there is no work being done; or at least no "useful" work; i.e., other than perhaps some ± PdV. The assertion that all spontaneous reactions have a negative ΔG is merely a restatement of the combined law of thermodynamics, giving it the physical dimensions of energy and somewhat obscuring its significance in terms of entropy. When there is no useful work 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.

Solutions

Main article: non-equilibrium thermodynamics Non equilibrium
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 homogenous, 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 reaction which results in an increase in the number of molecules will lead to an increase in volume at constant external pressure. If it occurs inside a cylinder closed with a piston, the equilibrated reaction can proceed only by doing work against an external force on the piston. The extent variable for the reaction can increase only if the piston moves, and conversely, if the piston is pushed inward, the reaction is driven backwards.
Similarly, a redox reaction might occur in an electrochemical cell with the passage of current in wires connecting the electrodes. The half-cell reactions at the electrodes are constrained if no current is allowed to flow. The current might be dissipated as joule heating, or it might in turn run an electrical device like a motor doing mechanical work. An automobile lead-acid battery can be recharged, driving the chemical reaction backwards. In this case as well, the reaction is not an independent process. Some, perhaps most, of the Gibbs free energy of reaction may be delivered as external work.
The hydrolysis of ATP to ADP and phosphate can drive the force times distance work delivered by living muscles, and synthesis of ATP is in turn driven by a redox chain in mitochondria and chloroplasts, which involves the transport of ions across the membranes of these cellular organelles. The coupling of processes here, and in the previous examples, is often not complete. Gas can leak slowly past a piston, just as it can slowly leak out of a rubber balloon. Some reaction may occur in a battery even if no external current is flowing. There is usually a coupling coefficient, which may depend on relative rates, which determines what percentage of the driving free energy is turned into external work, or captured as "chemical work", a misnomer for the free energy of another chemical process.

System constraints
In the preface section to popular book Basic Chemical Thermodynamics by physical chemist Brian Smith, originally published in 1973, and now in the 5th edition, we find the following overview of the subject as it is perceived in college:

See also