Thermodynamics |
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In thermodynamics, the **Gibbs free energy** (or **Gibbs energy**; symbol ) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions.

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

The Gibbs free energy change (, measured in joules in SI) is the *maximum* amount of non-expansion work that can be extracted from a closed system (one that can exchange heat and work with its surroundings, but not matter) at fixed temperature and pressure. This maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state under these conditions, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces.^{ [1] }

The Gibbs energy is the thermodynamic potential that is minimized when a system reaches chemical equilibrium at constant pressure and temperature when not driven by an applied electrolytic voltage. Its derivative with respect to the reaction coordinate of the system then vanishes at the equilibrium point. As such, a reduction in is necessary for a reaction to be spontaneous under these conditions.

The concept of 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^{ [2] }^{: 400 }

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.

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.

If the reactants and products are all in their thermodynamic standard states, then the defining equation is written as , where * is enthalpy, is absolute temperature, and ** is entropy.*

According to the second law of thermodynamics, for systems reacting at fixed temperature and pressure without input of non-*Pressure Volume* (PV) work, there is a general natural tendency to achieve a minimum of the Gibbs free energy.

A quantitative measure of the favorability of a given reaction under these conditions 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-pressure-volume (non-*PV*, e.g. electrical) work, which is often equal to zero (then 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 a reversible process. If analysis indicates a positive Δ*G* for a 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.^{ [3] }^{: 298–299 }

One can think of ∆G as the amount of "free" or "useful" energy available to do non-*PV* work at constant temperature and pressure. The equation can be also seen from the perspective of the system taken together with its surroundings (the rest of the universe). First, one assumes 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 an exergonic process.

If two chemical reactions are coupled, then an otherwise endergonic 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 change 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".^{ [1] } The characterization becomes more precise if we add the qualification that it is the energy available for non-pressure-volume work.^{ [4] } (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 removal of the adjective "free" was recommended.^{ [5] }^{ [6] }^{ [7] } This standard, however, has not yet been universally adopted.

The name "free enthalpy" was also used for *G* in the past.^{ [6] }

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, Josiah 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:^{ [2] }

If we wish to express in a single equation the necessary and sufficient condition of thermodynamic equilibrium for a substance when surrounded by a medium of constant pressure

pand temperatureT, this equation may be written:δ(ε−Tη+pν) = 0when

δrefers to the variation produced by any variations in the state of the parts of the body, and (when different parts of the body are in different states) in the proportion in which the body is divided between the different states. The condition of stable equilibrium is that the value of the expression in the parenthesis shall be a minimum.

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.^{ [8] }^{: 206 }

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^{ [9] }or joules per mole^{ [1] })*N*_{i}is the number of particles (or number of moles) composing the*i*-th chemical component.

This is one form of the **Gibbs fundamental equation**.^{ [10] } 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.^{ [11] }

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^{ [12] }

or more conveniently as its chemical potential:

In non-ideal systems, fugacity comes into play.

The Gibbs free energy total differential with respect to 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^{ [13] }

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

Because *S*, *V*, and *N*_{i} are extensive variables, an Euler relation allows easy integration of d*U*:^{ [13] }

Because some of the natural variables of *G* are intensive, d*G* may not be integrated using Euler relations 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*:^{ [13] }

This result shows that the chemical potential of a substance * is its (partial) mol(ecul)ar Gibbs free energy. It applies to homogeneous, macroscopic systems, but not to all thermodynamic systems.*^{ [14] }

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 at constant temperature (in a heat bath), , and so it follows that

Assuming that only mechanical work is done, this simplifies to

This means that for such a system when not in equilibrium, the Gibbs energy will always be decreasing, and in equilibrium, 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 charge *dQ*_{ele} is passed between the electrodes of an electrochemical cell generating an emf , a electrical work term appears in the expression for the change in Gibbs energy:

where *S* is the entropy, *V* is the system volume, *p* is its pressure and *T* is its absolute temperature.

The combination (, *Q _{ele}*) is an example of a conjugate pair of variables. At constant pressure the above equation produces a Maxwell relation that links the change in open cell voltage with temperature

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

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) |

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 ),

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. 298 K, 100 kPa, 1 M of each reactant and product), *R*, gas constant,*T*, absolute temperature,- ln, natural logarithm,
*Q*_{r}, reaction quotient (unitless),*K*_{eq}, equilibrium constant (unitless),*w*_{elec,rev}, electrical work in a reversible process (chemistry sign convention),*n*, number of moles of electrons transferred in the reaction,*F*=*N*_{A}*e*≈ 96485 C/mol, Faraday constant (charge per mole of electrons),- , cell potential,
- , 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° | |
---|---|---|

(kJ/mol) | (kcal/mol) | |

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, in 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}

where *Q _{f}* is the reaction quotient.

At equilibrium, Δ_{f}*G* = 0, and *Q _{f}* =

- Δ
_{f}*G*˚ = −*RT*ln*K*,

where *K* is the equilibrium constant of the formation reaction of the substance from the elements in their standard states.

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.^{ [17] } Thus, in order to understand the concept of Gibbs free energy, it may help to understand its interpretation by Gibbs as section AB on his figure 3, and as Maxwell sculpted that section on his 3D surface figure.

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

- 1 2 3 Perrot, Pierre (1998).
*A to Z of Thermodynamics*. Oxford University Press. ISBN 0-19-856552-6. - 1 2 Gibbs, Josiah Willard (December 1873). "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces" (PDF).
*Transactions of the Connecticut Academy of Arts and Sciences*.**2**: 382–404. - ↑ 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. - ↑ Calvert, J. G. (1 January 1990). "Glossary of atmospheric chemistry terms (Recommendations 1990)".
*Pure and Applied Chemistry*.**62**(11): 2167–2219. doi: 10.1351/pac199062112167 . - 1 2 "Gibbs energy (function), G".
*IUPAC Gold Book (Compendium of Chemical Technology)*. IUPAC (International Union of Pure and Applied Chemistry). 2008. doi:10.1351/goldbook.G02629 . Retrieved 24 December 2020.It was formerly called free energy or free enthalpy.

- ↑ Lehmann, H. P.; Fuentes-Arderiu, X.; Bertello, L. F. (1 January 1996). "Glossary of terms in quantities and units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)".
*Pure and Applied Chemistry*.**68**(4): 957–1000. doi:10.1351/pac199668040957. S2CID 95196393. - ↑ Henry Marshall Leicester (1971).
*The Historical Background of Chemistry*. Courier Corporation. ISBN 978-0-486-61053-5. - ↑ 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. - ↑ Atkins, Peter; de Paula, Julio (2006).
*Atkins' Physical Chemistry*(8th ed.). W. H. Freeman. p. 109. ISBN 0-7167-8759-8. - 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.
- ↑ 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.

- 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)

In a chemical reaction, **chemical equilibrium** is the state in which both the 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. 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 they are equal. Thus, there are no net changes in the concentrations of the reactants and products. Such a state is known as dynamic equilibrium.

**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.

**Entropy** is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication.

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 the 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 a chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction from the standard electrode potential, absolute temperature, the number of electrons involved in the oxydo-reduction reaction, and activities of the chemical species undergoing reduction and oxidation respectively. It was named after Walther Nernst, a German physical chemist who formulated the equation.

The **second law of thermodynamics** is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects, unless energy is supplied to reverse the direction of heat flow. Another definition is: "Not all heat energy can be converted into work in a cyclic process."

In chemistry, the **standard molar entropy** is the entropy content of one mole of pure substance at a standard state of pressure and any temperature of interest. These are often chosen to be the standard temperature and pressure.

In thermodynamics, the **chemical potential** of a species is the 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. When both temperature and pressure are held constant, and the number of particles is expressed in moles, the 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. In a system in diffusion equilibrium, the chemical potential of any chemical species is uniformly the same everywhere throughout the system.

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*.

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 (isothermal). 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 temperature is held constant. At constant temperature, the Helmholtz free energy is minimized at equilibrium.

In physics, a **partition function** describes the statistical properties of a system in thermodynamic equilibrium. Partition functions are functions of the thermodynamic state variables, such as the temperature and volume. Most of the aggregate thermodynamic variables of the system, such as the total energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives. The partition function is dimensionless.

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

The **laws of thermodynamics** define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium. The laws also use various parameters for thermodynamic processes, such as thermodynamic work and heat, and establish relationships between them. They state empirical facts that form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general, and are applicable in other natural sciences.

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.

Thermodynamics is expressed by a mathematical framework of *thermodynamic equations* which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics.

In chemical thermodynamics, the **reaction quotient** is a dimensionless quantity that provides a measurement of the relative amounts 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. In equilibrium, the reaction quotient is constant over time and is equal to the equilibrium constant.

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_{r}*H*^{⊖}, for the process. It was proposed by Dutch chemist Jacobus Henricus van 't Hoff in 1884 in his book *Études de Dynamique chimique*.

The concept **entropy** was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory. The **statistical entropy** perspective was introduced in 1870 by Austrian physicist Ludwig Boltzmann, who established a new field of physics that provided the descriptive linkage between the macroscopic observation of nature and the microscopic view based on the rigorous treatment of a large ensembles of microstates that constitute thermodynamic systems.

In thermodynamics, the **fundamental thermodynamic relation** are four fundamental equations which demonstrate how four important thermodynamic quantities depend on variables that can be controlled and measured experimentally. Thus, they are essentially equations of state, and using the fundamental equations, experimental data can be used to determine sought-after quantities like *G* or *H*. The 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.

This article is a summary of common equations and quantities in thermodynamics.

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