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Thermodynamics | ||||||||||||
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In thermodynamics, the **Gibbs free energy** (IUPAC recommended name: **Gibbs energy** or **Gibbs function**; also known as **free enthalpy**^{ [1] } to distinguish it from Helmholtz free energy) is a thermodynamic potential that can be used to calculate the maximum of reversible work that may be performed by a thermodynamic system at a constant temperature and pressure (isothermal, isobaric). The Gibbs free energy (; J in SI units) is the *maximum* amount of non-expansion work that can be extracted from a thermodynamically closed system (one that can exchange heat and work with its surroundings, but not matter); this maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces.^{ [2] }

**Thermodynamics** is the branch of physics that deals with heat and temperature, and their relation to energy, work, radiation, and properties of matter. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, chemical engineering and mechanical engineering, but also in fields as complex as meteorology.

The **International Union of Pure and Applied Chemistry** is an international federation of National Adhering Organizations that represents chemists in individual countries. It is a member of the International Council for Science (ICSU). IUPAC is registered in Zürich, Switzerland, and the administrative office, known as the "IUPAC Secretariat", is in Research Triangle Park, North Carolina, United States. This administrative office is headed by IUPAC's executive director, currently Lynn Soby.

In thermodynamics, the **Helmholtz free energy** is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature and volume. The negative of the change in the Helmholtz energy during a process is equal to the maximum amount of work that the system can perform in a thermodynamic process in which volume is held constant. If the volume were not held constant, part of this work would be performed as boundary work. This makes the Helmholtz energy useful for systems held at constant volume. Furthermore, at constant temperature, the Helmholtz energy is minimized at equilibrium.

- Overview
- History
- Graphical interpretation
- Definitions
- Derivation
- Homogeneous systems
- Gibbs free energy of reactions
- In electrochemical thermodynamics
- Useful identities to derive the Nernst equation
- Standard energy change of formation
- See also
- Notes and references
- External links

The Gibbs energy (also referred to as ) is also the thermodynamic potential that is minimized when a system reaches chemical equilibrium at constant pressure and temperature. Its derivative with respect to the reaction coordinate of the system vanishes at the equilibrium point. As such, a reduction in is a necessary condition for the spontaneity of processes at constant pressure and temperature.

In a chemical reaction, **chemical equilibrium** is the state in which both reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. Usually, this state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but equal. Thus, there are no net changes in the concentrations of the reactant(s) and product(s). Such a state is known as dynamic equilibrium.

**Pressure** is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure.

**Temperature** is a physical quantity expressing what is commonly understood as hot and cold. In physics, it is a defining property of thermodynamic systems that determines thermal equilibrium. It is measured with a thermometer calibrated in one or more temperature scales. The most commonly used scales are the Celsius scale, Fahrenheit scale, and Kelvin scale. The kelvin is the unit of temperature in the International System of Units (SI). The Kelvin scale is widely used in science and technology.

The Gibbs free energy, originally called *available energy*, was developed in the 1870s by the American scientist Josiah Willard Gibbs. In 1873, Gibbs described this "available energy" as

**Josiah Willard Gibbs** was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous inductive science. Together with James Clerk Maxwell and Ludwig Boltzmann, he created statistical mechanics, explaining the laws of thermodynamics as consequences of the statistical properties of ensembles of the possible states of a physical system composed of many particles. Gibbs also worked on the application of Maxwell's equations to problems in physical optics. As a mathematician, he invented modern vector calculus.

the greatest amount of mechanical work which can be obtained from a given quantity of a certain substance in a given initial state, without increasing its total volume or allowing heat to pass to or from external bodies, except such as at the close of the processes are left in their initial condition.

^{ [3] }In thermodynamics, the

volumeof a system is an important extensive parameter for describing its thermodynamic state. Thespecific volume, an intensive property, is the system's volume per unit of mass. Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law.

The initial state of the body, according to Gibbs, is supposed to be such that "the body can be made to pass from it to states of dissipated energy by reversible processes". In his 1876 magnum opus * On the Equilibrium of Heterogeneous Substances *, a graphical analysis of multi-phase chemical systems, he engaged his thoughts on chemical free energy in full.

In thermodynamics, a reversible process is a process whose direction can be "reversed" by inducing infinitesimal changes to some property of the system via its surroundings. Throughout the entire reversible process, the system is in thermodynamic equilibrium with its surroundings. Having been reversed, it leaves no change in either the system or the surroundings. Since it would take an infinite amount of time for the reversible process to finish, perfectly reversible processes are impossible. However, if the system undergoing the changes responds much faster than the applied change, the deviation from reversibility may be negligible. In a *reversible cycle*, a cyclical reversible process, the system and its surroundings will be returned to their original states if one half cycle is followed by the other half cycle.

**Masterpiece**, **magnum opus** or * chef-d’œuvre* in modern use is a creation that has been given much critical praise, especially one that is considered the greatest work of a person's career or to a work of outstanding creativity, skill, profundity, or workmanship. Historically, a "masterpiece" was a work of a very high standard produced to obtain membership of a guild or academy in various areas of the visual arts and crafts.

In the history of thermodynamics, * On the Equilibrium of Heterogeneous Substances* is a 300-page paper written by American chemical physicist Willard Gibbs. It is one of the founding papers in thermodynamics, along with German physicist Hermann von Helmholtz's 1882 paper "

According to the second law of thermodynamics, for systems reacting at STP (or any other fixed temperature and pressure), there is a general natural tendency to achieve a minimum of the Gibbs free energy.

The **second law of thermodynamics** states that the total entropy of an isolated system can never decrease over time. The total entropy of a system and its surroundings can remain constant in ideal cases where the system is in thermodynamic equilibrium, or is undergoing a (fictive) reversible process. In all processes that occur, including spontaneous processes, the total entropy of the system and its surroundings increases and the process is irreversible in the thermodynamic sense. The increase in entropy accounts for the irreversibility of natural processes, and the asymmetry between future and past.

A quantitative measure of the favorability of a given reaction at constant temperature and pressure is the change Δ*G* (sometimes written "delta *G*" or "d*G*") in Gibbs free energy that is (or would be) caused by the reaction. As a necessary condition for the reaction to occur at constant temperature and pressure, Δ*G* must be smaller than the non-PV (e.g. electrical) work, which is often equal to zero (hence Δ*G* must be negative). Δ*G* equals the maximum amount of non-*PV* work that can be performed as a result of the chemical reaction for the case of reversible process. If the analysis indicated a positive Δ*G* for the reaction, then energy — in the form of electrical or other non-*PV* work — would have to be added to the reacting system for Δ*G* to be smaller than the non-*PV* work and make it possible for the reaction to occur.^{ [4] }^{:298–299}

We can think of ∆G as the amount of "free" or "useful" energy available to do work. The equation can be also seen from the perspective of the system taken together with its surroundings (the rest of the universe). First, assume that the given reaction at constant temperature and pressure is the only one that is occurring. Then the entropy released or absorbed by the system equals the entropy that the environment must absorb or release, respectively. The reaction will only be allowed if the total entropy change of the universe is zero or positive. This is reflected in a negative Δ*G*, and the reaction is called exergonic.

If we couple reactions, then an otherwise endergonic chemical reaction (one with positive Δ*G*) can be made to happen. The input of heat into an inherently endergonic reaction, such as the elimination of cyclohexanol to cyclohexene, can be seen as coupling an unfavourable reaction (elimination) to a favourable one (burning of coal or other provision of heat) such that the total entropy change of the universe is greater than or equal to zero, making the *total* Gibbs free energy difference of the coupled reactions negative.

In traditional use, the term "free" was included in "Gibbs free energy" to mean "available in the form of useful work".^{ [2] } The characterization becomes more precise if we add the qualification that it is the energy available for *non-volume* work^{[ clarification needed ]}.^{ [5] } (An analogous, but slightly different, meaning of "free" applies in conjunction with the Helmholtz free energy, for systems at constant temperature). However, an increasing number of books and journal articles do not include the attachment "free", referring to *G* as simply "Gibbs energy". This is the result of a 1988 IUPAC meeting to set unified terminologies for the international scientific community, in which the adjective "free" was supposedly banished.^{ [6] }^{ [7] }^{ [8] } This standard, however, has not yet been universally adopted.

The quantity called "free energy" is a more advanced and accurate replacement for the outdated term *affinity*, which was used by chemists in the earlier years of physical chemistry to describe the *force* that caused chemical reactions.

In 1873, Willard Gibbs published *A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces*, in which he sketched the principles of his new equation that was able to predict or estimate the tendencies of various natural processes to ensue when bodies or systems are brought into contact. By studying the interactions of homogeneous substances in contact, i.e., bodies composed of part solid, part liquid, and part vapor, and by using a three-dimensional volume-entropy-internal energy graph, Gibbs was able to determine three states of equilibrium, i.e., "necessarily stable", "neutral", and "unstable", and whether or not changes would ensue. Further, Gibbs stated:^{ [9] }

In this description, as used by Gibbs, *ε* refers to the internal energy of the body, *η* refers to the entropy of the body, and *ν* is the volume of the body.

Thereafter, in 1882, the German scientist Hermann von Helmholtz characterized the affinity as the largest quantity of work which can be gained when the reaction is carried out in a reversible manner, e.g., electrical work in a reversible cell. The maximum work is thus regarded as the diminution of the free, or available, energy of the system (*Gibbs free energy**G* at *T* = constant, *P* = constant or *Helmholtz free energy**F* at *T* = constant, *V* = constant), whilst the heat given out is usually a measure of the diminution of the total energy of the system (internal energy). Thus, *G* or *F* is the amount of energy "free" for work under the given conditions.

Until this point, the general view had been such that: "all chemical reactions drive the system to a state of equilibrium in which the affinities of the reactions vanish". Over the next 60 years, the term affinity came to be replaced with the term free energy. According to chemistry historian Henry Leicester, the influential 1923 textbook *Thermodynamics and the Free Energy of Chemical Substances* by Gilbert N. Lewis and Merle Randall led to the replacement of the term "affinity" by the term "free energy" in much of the English-speaking world.^{ [10] }^{:206}

Gibbs free energy was originally defined graphically. In 1873, American scientist Willard Gibbs published his first thermodynamics paper, "Graphical Methods in the Thermodynamics of Fluids", in which Gibbs used the two coordinates of the entropy and volume to represent the state of the body. In his second follow-up paper, "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces", published later that year, Gibbs added in the third coordinate of the energy of the body, defined on three figures. In 1874, Scottish physicist James Clerk Maxwell used Gibbs' figures to make a 3D energy-entropy-volume thermodynamic surface of a fictitious water-like substance.^{ [11] } Thus, in order to understand the very difficult concept of Gibbs free energy one must be able to understand its interpretation as Gibbs defined originally by section AB on his figure 3 and as Maxwell sculpted that section on his 3D surface figure.

The Gibbs free energy is defined as

which is the same as

where:

*U*is the internal energy (SI unit: joule),*p*is pressure (SI unit: pascal),*V*is volume (SI unit: m^{3}),*T*is the temperature (SI unit: kelvin),*S*is the entropy (SI unit: joule per kelvin),*H*is the enthalpy (SI unit: joule).

The expression for the infinitesimal reversible change in the Gibbs free energy as a function of its "natural variables" *p* and *T*, for an open system, subjected to the operation of external forces (for instance, electrical or magnetic) *X _{i}*, which cause the external parameters of the system

where:

*μ*_{i}is the chemical potential of the*i*th chemical component. (SI unit: joules per particle^{ [12] }or joules per mole^{ [2] })*N*_{i}is the number of particles (or number of moles) composing the*i*th chemical component.

This is one form of **Gibbs fundamental equation**.^{ [13] } In the infinitesimal expression, the term involving the chemical potential accounts for changes in Gibbs free energy resulting from an influx or outflux of particles. In other words, it holds for an open system or for a closed, chemically reacting system where the *N _{i}* are changing. For a closed, non-reacting system, this term may be dropped.

Any number of extra terms may be added, depending on the particular system being considered. Aside from mechanical work, a system may, in addition, perform numerous other types of work. For example, in the infinitesimal expression, the contractile work energy associated with a thermodynamic system that is a contractile fiber that shortens by an amount −d*l* under a force *f* would result in a term *f* d*l* being added. If a quantity of charge −d*e* is acquired by a system at an electrical potential Ψ, the electrical work associated with this is −Ψ d*e*, which would be included in the infinitesimal expression. Other work terms are added on per system requirements.^{ [14] }

Each quantity in the equations above can be divided by the amount of substance, measured in moles, to form *molar Gibbs free energy*. The Gibbs free energy is one of the most important thermodynamic functions for the characterization of a system. It is a factor in determining outcomes such as the voltage of an electrochemical cell, and the equilibrium constant for a reversible reaction. In isothermal, isobaric systems, Gibbs free energy can be thought of as a "dynamic" quantity, in that it is a representative measure of the competing effects of the enthalpic^{[ clarification needed ]} and entropic driving forces involved in a thermodynamic process.

The temperature dependence of the Gibbs energy for an ideal gas is given by the Gibbs–Helmholtz equation, and its pressure dependence is given by

If the volume is known rather than pressure, then it becomes

or more conveniently as its chemical potential:

In non-ideal systems, fugacity comes into play.

The Gibbs free energy total differential natural variables may be derived by Legendre transforms of the internal energy.

The definition of *G* from above is

- .

Taking the total differential, we have

Replacing d*U* with the result from the first law gives^{ [15] }

The natural variables of *G* are then *p*, *T*, and {*N*_{i}}.

Because *S*, *V*, and *N*_{i} are extensive variables, an Euler integral allows easy integration of d*U*:^{ [15] }

Because some of the natural variables of *G* are intensive, d*G* may not be integrated using Euler integrals as is the case with internal energy. However, simply substituting the above integrated result for *U* into the definition of *G* gives a standard expression for *G*:^{ [15] }

This result applies to homogeneous, macroscopic systems, but not to all thermodynamic systems.^{ [16] }

The system under consideration is held at constant temperature and pressure, and is closed (no matter can come in or out). The Gibbs energy of any system is and an infinitesimal change in *G*, at constant temperature and pressure yields:

By the first law of thermodynamics, a change in the internal energy *U* is given by

where *δQ* is energy added as heat, and *δW* is energy added as work. The work done on the system may be written as *δW* = −*PdV* + *δW _{x}*, where −

and the infinitesimal change in *G* is:

The second law of thermodynamics states that for a closed system, , and so it follows that:

This means that for a system which is not in equilibrium, its Gibbs energy will always be decreasing, and when it is in equilibrium (i.e. no longer changing), the infinitesimal change *dG* will be zero. In particular, this will be true if the system is experiencing any number of internal chemical reactions on its path to equilibrium.

When electric charged *dQ* is passed in an electrochemical cell the emf ℰ yields a thermodynamic work term that appears in the expression for the change in Gibbs energy:

where *G* is the Gibb's free energy, *S* is the entropy, *V* is the system volume, *P* is its pressure and *T* is its absolute temperature.

The combination ( ℰ, *Q* ) is an example of a conjugate pair of variables. At constant pressure the above relationship produces a Maxwell relation that links the change in open cell voltage with temperature *T* (a measurable quantity) to the change in entropy *S* when charge is passed isothermally and isobarically. The latter is closely related to the reaction entropy of the electrochemical reaction that lends the battery its power. This Maxwell relation is:^{ [17] }^{[ citation needed ]}

If a mole of ions goes into solution (for example, in a Daniell cell, as discussed below) the charge through the external circuit is:

where *n*_{0} is the number of electrons/ion, and *F*_{0} is the Faraday constant and the minus sign indicates discharge of the cell. Assuming constant pressure and volume, the thermodynamic properties of the cell are related strictly to the behavior of its emf by:</ref>

where Δ*H* is the enthalpy of reaction. The quantities on the right are all directly measurable.

This section may be confusing or unclear to readers. In particular, the physical situation is not explained. Also, the circle notation is not well explained (even in the one case where it is attempted). It's just bare equations.(March 2015) (Learn how and when to remove this template message) |

During a reversible electrochemical reaction at constant temperature and pressure, the following equations involving the Gibbs free energy hold:

- (see chemical equilibrium),
- (for a system at chemical equilibrium),
- (for a reversible electrochemical process at constant temperature and pressure),
- (definition of
*E*°),

and rearranging gives

which relates the cell potential resulting from the reaction to the equilibrium constant and reaction quotient for that reaction (Nernst equation),

where

- Δ
_{r}*G*= Gibbs free energy change per mole of reaction, - Δ
_{r}*G°*= Gibbs free energy change per mole of reaction for unmixed reactants and products at standard conditions (i.e. 298K, 100kPa, 1M of each reactant and product), *R*= gas constant,*T*= absolute temperature,- ln = natural logarithm,
*Q*= reaction quotient (unitless),_{r}*K*= equilibrium constant (unitless),_{eq}*w*_{elec,rev}= electrical work in a reversible process (chemistry sign convention),*n*= number of moles of electrons transferred in the reaction,*F*= Faraday constant = 96485 C/mol (charge per mole of electrons),*E*= cell potential,*E°*= standard cell potential.

Moreover, we also have:

which relates the equilibrium constant with Gibbs free energy. This implies that at equilibrium

- and

Substance (State) | Δ_{f}G° | Δ_{f}G° |
---|---|---|

NO(g) | 87.6 | 20.9 |

NO_{2}(g) | 51.3 | 12.3 |

N_{2}O(g) | 103.7 | 24.78 |

H_{2}O(g) | −228.6 | −54.64 |

H_{2}O(l) | −237.1 | −56.67 |

CO_{2}(g) | −394.4 | −94.26 |

CO(g) | −137.2 | −32.79 |

CH_{4}(g) | −50.5 | −12.1 |

C_{2}H_{6}(g) | −32.0 | −7.65 |

C_{3}H_{8}(g) | −23.4 | −5.59 |

C_{6}H_{6}(g) | 129.7 | 29.76 |

C_{6}H_{6}(l) | 124.5 | 31.00 |

The standard Gibbs free energy of formation of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of that substance from its component elements, at their standard states (the most stable form of the element at 25 °C and 100 kPa). Its symbol is Δ_{f}*G*˚.

All elements in their standard states (diatomic oxygen gas, graphite, etc.) have standard Gibbs free energy change of formation equal to zero, as there is no change involved.

- Δ
_{f}*G*= Δ_{f}*G*˚ +*RT*ln*Q*;_{f}*Q*is the reaction quotient._{f}

- At equilibrium, Δ
_{f}*G*= 0, and*Q*=_{f}*K*, so the equation becomes Δ_{f}*G*˚ = −*RT*ln*K*(where*K*is the equilibrium constant).

- Calphad
- Electron equivalent
- Enthalpy-entropy compensation
- Free entropy
- Grand potential
- Thermodynamic free energy
- Spinodal – Spinodal Curves (Hessian matrix)
- Critical point (thermodynamics)
- Non-random two-liquid model (NRTL model) – Gibbs energy of excess and mixing calculation and activity coeffients
- UNIQUAC model – Gibbs energy of excess and mixing calculation and activity coeffients

- ↑ Greiner, Walter; Neise, Ludwig; Stöcker, Horst (1995).
*Thermodynamics and statistical mechanics*. Springer-Verlag. p. 101. - 1 2 3 Perrot, Pierre (1998).
*A to Z of Thermodynamics*. Oxford University Press. ISBN 0-19-856552-6. - ↑ J.W. Gibbs, "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces,"
*Transactions of the Connecticut Academy of Arts and Sciences*2, Dec. 1873, pp. 382–404 (quotation on p. 400). - ↑ Peter Atkins; Loretta Jones (1 August 2007).
*Chemical Principles: The Quest for Insight*. W. H. Freeman. ISBN 978-1-4292-0965-6. - ↑ Reiss, Howard (1965).
*Methods of Thermodynamics*. Dover Publications. ISBN 0-486-69445-3. - ↑ International Union of Pure and Applied Chemistry Commission on Atmospheric Chemistry, J. G. (1990). "Glossary of Atmospheric Chemistry Terms (Recommendations 1990)".
*Pure Appl. Chem.***62**(11): 2167–2219. doi:10.1351/pac199062112167 . Retrieved 2006-12-28.^{[ permanent dead link ]} - ↑ International Union of Pure and Applied Chemistry Commission on Physicochemical Symbols Terminology and Units (1993).
*Quantities, Units and Symbols in Physical Chemistry (2nd Edition)*. Oxford: Blackwell Scientific Publications. p. 251. ISBN 0-632-03583-8 . Retrieved 2013-12-20.^{[ permanent dead link ]} - ↑ International Union of Pure and Applied Chemistry Commission on Quantities and Units in Clinical Chemistry, H. P.; International Federation of Clinical Chemistry Laboratory Medicine Committee on Quantities and Units (1996). "Glossary of Terms in Quantities and Units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)".
*Pure Appl. Chem.***68**(4): 957–1000. doi:10.1351/pac199668040957 . Retrieved 2006-12-28.^{[ permanent dead link ]} - ↑ J. W. Gibbs, "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces",
*Transactions of the Connecticut Academy of Arts and Sciences*2, Dec. 1873, pp. 382–404. - ↑ Henry Marshall Leicester (1971).
*The Historical Background of Chemistry*. Courier Corporation. ISBN 978-0-486-61053-5. - ↑ James Clerk Maxwell, Elizabeth Garber, Stephen G. Brush, and C. W. Francis Everitt (1995),
*Maxwell on heat and statistical mechanics: on "avoiding all personal enquiries" of molecules*, Lehigh University Press, ISBN 0-934223-34-3, p. 248. - ↑ Chemical Potential, IUPAC Gold Book.
- ↑ Müller, Ingo (2007).
*A History of Thermodynamics – the Doctrine of Energy and Entropy*. Springer. ISBN 978-3-540-46226-2. - ↑ Katchalsky, A.; Curran, Peter F. (1965).
*Nonequilibrium Thermodynamics in Biophysics*. Harvard University Press. CCN 65-22045. - 1 2 3 Salzman, William R. (2001-08-21). "Open Systems".
*Chemical Thermodynamics*. University of Arizona. Archived from the original on 2007-07-07. Retrieved 2007-10-11. - ↑ Brachman, M. K. (1954). "Fermi Level, Chemical Potential, and Gibbs Free Energy".
*The Journal of Chemical Physics*.**22**(6): 1152. Bibcode:1954JChPh..22.1152B. doi:10.1063/1.1740312. - ↑ H. S. Harned, B. B. Owen, The Physical Chemistry of Electrolytic Solutions, third edition, Reinhold Publishing Corporation, N.Y.,1958, p. 2-6
- ↑ CRC Handbook of Chemistry and Physics, 2009, pp. 5-4–5-42, 90th ed., Lide.

- IUPAC definition (Gibbs energy)
- Gibbs free energy calculator
- Gibbs energy – Florida State University
- Gibbs Free Energy – Eric Weissteins World of Physics
- Entropy and Gibbs Free Energy – www.2ndlaw.oxy.edu
- Gibbs Free Energy – Georgia State University
- Gibbs Free Energy Java Applet – University of California, Berkeley
- Using Gibbs Free Energy for prediction of chemical driven material ageing
- Topological Analysis of the Gibbs Energy Function (Liquid-Liquid Equilibrium Correlation Data). Including a Thermodinamic Review and a Graphical User Interface (GUI) for Surfaces/Tie-lines/Hessian matrix analysis – University of Alicante (Reyes-Labarta et al. 2015–18)

**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 **thermodynamic free energy** is a concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process at constant temperature, and its sign indicates whether a process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.

In electrochemistry, the **Nernst equation** is an equation that relates the reduction potential of an electrochemical reaction to the standard electrode potential, temperature, and activities of the chemical species undergoing reduction and oxidation. It was named after Walther Nernst, a German physical chemist who formulated the equation.

The **Gibbs–Helmholtz equation** is a thermodynamic equation used for calculating changes in the Gibbs energy of a system as a function of temperature.

In thermodynamics, **chemical potential** of a species is energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species in a mixture is defined as the rate of change of free energy of a thermodynamic system with respect to the change in the number of atoms or molecules of the species that are added to the system. Thus, it is the partial derivative of the free energy with respect to the amount of the species, all other species' concentrations in the mixture remaining constant. The molar chemical potential is also known as **partial molar free energy**. When both temperature and pressure are held constant, chemical potential is the partial molar Gibbs free energy. At chemical equilibrium or in phase equilibrium the total sum of the product of chemical potentials and stoichiometric coefficients is zero, as the free energy is at a minimum.

A **thermodynamic potential** is a scalar quantity used to represent the thermodynamic state of a system. The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term *fundamental functions*. One main thermodynamic potential that has a physical interpretation is the internal energy U. It is the energy of configuration of a given system of conservative forces and only has meaning with respect to a defined set of references. Expressions for all other thermodynamic energy potentials are derivable via Legendre transforms from an expression for U. In thermodynamics, external forces, such as gravity, are typically disregarded when formulating expressions for potentials. For example, while all the working fluid in a steam engine may have higher energy due to gravity while sitting on top of Mount Everest than it would at the bottom of the Mariana Trench, the gravitational potential energy term in the formula for the internal energy would usually be ignored because *changes* in gravitational potential within the engine during operation would be negligible. In a large system under even homogeneous external force, like the earth atmosphere under gravity, the intensive parameters should be studied locally having even in equilibrium different values in different places far from each other (see thermodynamic models of troposphere].

In chemical thermodynamics, an **endergonic reaction** is a chemical reaction in which the standard change in free energy is positive, and energy is absorbed. In layman's terms, the total amount of energy is a loss so the total energy is a negative net result. For an overall gain in the net result see exergonic reaction. Another way to phrase this is that energy is absorbed from the surroundings into the workable system.

The three **laws of thermodynamics** define physical quantities that characterize thermodynamic systems at thermal equilibrium. The laws describe how these quantities behave under various circumstances, and preclude the possibility of certain phenomena.

The **equilibrium constant** of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture. Thus, given the initial composition of a system, known equilibrium constant values can be used to determine the composition of the system at equilibrium. However, reaction parameters like temperature, solvent, and ionic strength may all influence the value of the equilibrium constant.

In chemical thermodynamics, the **fugacity** of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. It is equal to the pressure of an ideal gas which has the same temperature and molar Gibbs free energy as the real gas.

In chemical thermodynamics, the reaction quotient is a quantity that provides a measurement of the relative quantities of products and reactants present in a reaction mixture for a reaction with well-defined overall stoichiometry, at a particular point in time. Mathematically, it is defined as the ratio of the activities of the product species over those of the reactant species involved in the chemical reaction, taking stoichiometric coefficients of the reaction into account as exponents of the concentrations. This functional form obeys the law of mass action, and, in the special case that the reaction is at equilibrium, the reaction quotient is constant over time and is equal to the equilibrium constant.

The **Joule expansion** is an irreversible process in thermodynamics in which a volume of gas is kept in one side of a thermally isolated container, with the other side of the container being evacuated. The partition between the two parts of the container is then opened, and the gas fills the whole container.

The **van 't Hoff equation** relates the change in the equilibrium constant, *K*_{eq}, of a chemical reaction to the change in temperature, *T*, given the standard enthalpy change, Δ*H*^{⊖}, for the process. It was proposed by Dutch chemist Jacobus Henricus van 't Hoff in 1884 in his book *Études de dynamique chimique*. This equation is sometimes also referred to as the Vukančić–Vuković equation.

**Entropy** is a property of thermodynamical systems. The term entropy was introduced by Rudolf Clausius who named it from the Greek word τρoπή, "transformation". He considered transfers of energy as heat and work between bodies of matter, taking temperature into account. Bodies of radiation are also covered by the same kind of reasoning.

In thermodynamics, the **fundamental thermodynamic relation** is generally expressed as a microscopic change in internal energy in terms of microscopic changes in entropy, and volume for a closed system in thermal equilibrium in the following way.

**Entropy** is an important concept in the branch of physics known as thermodynamics. The idea of "irreversibility" is central to the understanding of entropy. Everyone has an intuitive understanding of irreversibility. If one watches a movie of everyday life running forward and in reverse, it is easy to distinguish between the two. The movie running in reverse shows impossible things happening – water jumping out of a glass into a pitcher above it, smoke going down a chimney, water in a glass freezing to form ice cubes, crashed cars reassembling themselves, and so on. The intuitive meaning of expressions such as "you can't unscramble an egg", or "you can't take the cream out of the coffee" is that these are irreversible processes. No matter how long you wait, the cream won't jump out of the coffee into the creamer.

**Thermodynamic databases** contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. Numerical values of these thermodynamic properties are collected as tables or are calculated from thermodynamic datafiles. Data is expressed as temperature-dependent values for one mole of substance at the standard pressure of 101.325 kPa, or 100 kPa. Unfortunately, both of these definitions for the standard condition for pressure are in use.

This article is a summary of common equations and quantities in thermodynamics. SI units are used for absolute temperature, not Celsius or Fahrenheit.

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