Gibbs free energy

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$S = k_B \, \ln\Omega$

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Internal energy · Enthalpy Helmholtz free energy Gibbs free energy

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In thermodynamics, the Gibbs free energy (IUPAC recommended name: Gibbs energy or Gibbs function) is a thermodynamic potential which measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system. Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics In Thermodynamics, statistical thermodynamics is the study of the microscopic behaviors of Thermodynamic systems using Probability theory. Kinetic theory (or kinetic theory of gases) attempts to explain Macroscopic properties of Gases such as pressure temperature or volume by considering A thermodynamic potential is a Scalar potential function used to represent the Thermodynamic state of a system. In Thermodynamics, the internal energy of a Thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes In Thermodynamics and molecular chemistry, the enthalpy (denoted as H, h, or rarely as χ) is a quotient or description of In Thermodynamics, the Helmholtz free energy is a Thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization A thermodynamic potential is a Scalar potential function used to represent the Thermodynamic state of a system. An isothermal process is a Thermodynamic process in which the Temperature of the System stays Constant: &Delta T = 0 An isobaric process is a Thermodynamic process in which the pressure stays constant \Delta p = 0 The term derives from the Greek isos "equal" In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration Technically, the Gibbs free energy is the maximum amount of non-expansion work which can be extracted from a closed system or this maximum can be attained only in a completely reversible process. A Closed system is a System in the state of being isolated from the environment When a system changes from a well-defined initial state to a well-defined final state, the Gibbs free energy ΔG equals the work exchanged by the system with its surroundings, less the work of the pressure forces, during a reversible transformation of the system from the same initial state to the same final state. ^[1]

Gibbs energy is also the chemical potential that is minimized when a system reaches equilibrium at constant pressure and temperature. As such, it is a convenient criterion of spontaneity for processes with constant pressure and temperature.

The Gibbs free energy, originally called available energy, was developed in the 1870s by the American mathematical physicist Willard Gibbs. Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist In 1873, in a footnote, Gibbs defined what he called the “available energy” of a body as such:

“

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. In Physics, mechanical work is the amount of Energy transferred by a Force. The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature

”

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". Friction is the Force resisting the relative motion of two Surfaces in contact or a surface in contact with a fluid (e 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. Magnum opus (sometimes Opus magnum, plural magna opera) from the Latin meaning great work, refers to the best the greatest In the History of thermodynamics, On the Equilibrium of Heterogeneous Substances is a 300-page paper written by American mathematical-engineer Willard Gibbs

1 Definitions
2 Derivation
3 Overview
4 History
5 What does the term ‘free’ mean?
6 Free energy of reactions
7 Useful identities
8 Standard change of formation
9 Table of Selected Substances
10 See also
11 References
12 External links

Definitions

Willard Gibbs’ 1873 available energy (free energy) graph, which shows a plane perpendicular to the axis of v (volume) and passing through point A, which represents the initial state of the body. Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically MN is the section of the surface of dissipated energy. Friction is the Force resisting the relative motion of two Surfaces in contact or a surface in contact with a fluid (e Qε and Qη are sections of the planes η = 0 and ε = 0, and therefore parallel to the axes of ε (internal energy) and η (entropy) respectively. In Thermodynamics, the internal energy of a Thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy AD and AE are the energy and entropy of the body in its initial state, AB and AC its available energy (Gibbs free energy) and its capacity for entropy (the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume) respectively.

The Gibbs free energy is defined as:

$G = U+pV-TS \,$

which is the same as:

$G = H-TS \,$

where:

U is the internal energy (SI unit: joule)
p is pressure (SI unit: pascal)
V is volume (SI unit: m³)
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, for an open system, subjected to the operation of external forces X_i, which cause the external parameters of the system a_i to change by an amount da_i, is given by:

$\mathrm{d}G =V\mathrm{d}p-S\mathrm{d}T+\sum_{i=1}^k \mu_i \,\mathrm{d}N_i + \sum_{i=1}^n X_i \,\mathrm{d}a_i + \ldots \,$

$T d S = d q = d U + p d V,$ where:

$μ i$ is the chemical potential of the i-th chemical component. In Thermodynamics, the internal energy of a Thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy In Thermodynamics and molecular chemistry, the enthalpy (denoted as H, h, or rarely as χ) is a quotient or description of In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical Chemical species are Atoms Molecules molecular fragments Ions etc (SI unit: joules per particle^[2] or joules per mol^[1])
$N i$ is the number of particles (or number of moles) composing the i-th chemical component. The particle number, N, is the number of so called ' Elementary particles (or elementary constituents in a thermodynamical system.

This is one form of Gibbs fundamental equation. ^[3] 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. For a closed system, this term may be dropped. A Closed system is a System in the state of being isolated from the environment

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. In Physics, mechanical work is the amount of Energy transferred by a Force. For example, in the infinitesimal expression, the contractile work energy associated with a thermodynamic system that is a contractile fiber which shortens by an amount -dl under a force f would result in a term fdl being added. If a quantity of charge -de is acquired by a system at an electrical potential Ψ, the electrical work associated with this is -Ψde, which would be included in the infinitesimal expression. Other work terms are added on per system requirements. ^[4]

Each quantity in the equations above can be divided by the amount of substance, measured in moles, to form molar Gibbs free energy. The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this 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. Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical An electrochemical cell is a device used for generating an Electromotive force ( Voltage) and current from chemical reactions. For a general Chemical reaction \alpha A +\beta B. \rightleftharpoons \sigma S+\tau T. A reversible reaction is a Chemical reaction that results in an equilibrium mixture of Reactants and products. 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 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:

$\frac{G}{N} = \frac{G}{N}^\circ + kT\ln \frac{p}{{p^\circ }}$

if the volume is known rather than pressure then it becomes:

$\frac{G}{N} = \frac{G}{N}^\circ + kT\ln \frac{V^\circ}{{V }}$

or more conveniently as its chemical potential:

$\frac{G}{N} = \mu = \mu^\circ + kT\ln \frac{p}{{p^\circ }}$

In non-ideal systems, fugacity comes into play. These four properties that constitute an ideal gas can be easily remembered by the acronym RIPE which stands for - R andom Motion (molecules are in constant random motion The Gibbs–Helmholtz equation is a thermodynamic Equation useful for calculating changes in the Gibbs energy of a system as a function of temperature In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical Fugacity is a measure of a Chemical potential in the form of 'adjusted pressure

Derivation

The Gibbs free energy total differential in terms of its natural variables may be derived via Legendre transforms of the internal energy. In the mathematical field of Differential calculus, the term total derivative has a number of closely related meanings A thermodynamic potential is a Scalar potential function used to represent the Thermodynamic state of a system. In Mathematics, it is often desirable to express a functional relationship f(x\ as a different function whose argument is the derivative of f rather In Thermodynamics, the internal energy of a Thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes For a system undergoing an internally reversible process that is allowed to exchange matter, heat and work with its surroundings, the differential of the internal energy is given from the first law of thermodynamics as

$\mathrm{d}U = T\mathrm{d}S - p \,\mathrm{d}V + \sum_i \mu_i \,\mathrm{d} N_i\,$ . In Thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the Conservation of energy.

Because $S$ , $V$ , and ${N i}$ are extensive variables, Euler's homogeneous function theorem allows easy integration of $d U$ :^[5]

$U = T S - p V + \sum_i \mu_i N_i\,$ . In the Physical sciences an intensive property (also called a bulk property) is a Physical property of a system that does not depend on the In Mathematics, a homogeneous function is a function with multiplicative scaling behaviour if the argument is multiplied by a factor then the result is multiplied by some power

The definition of $G$ from above is

$G = U + p V - T S\,$ .

Taking the total differential, we have

$\mathrm{d} G = \mathrm{d}U + p\,\mathrm{d}V + V\mathrm{d}p - T\mathrm{d}S - S\mathrm{d}T\,$ .

Replacing $d U$ with the result from the first law gives^[5]

$\mathrm{d} G = T\mathrm{d}S - p\,\mathrm{d}V + \sum_i \mu_i \,\mathrm{d} N_i + p \,\mathrm{d}V + V\mathrm{d}p - T\mathrm{d}S - S\mathrm{d}T\,$

$\mathrm{d} G = V\mathrm{d}p - S\mathrm{d}T + \sum_i \mu_i \,\mathrm{d} N_i \,$ .

The natural variables of $G$ are then $p$ , $T$ , and $\left \{ N_i \right \}$ . Because some of the natural variables are intensive, $d G$ may not be integrated using Euler integrals as is the case with internal energy. However, simply substituting the result for $U$ into the definition of $G$ gives a standard expression for G:^[5]

$G = T S - p V + \sum_i \mu_i N_i + p V - T S\,$

$G = \sum_i \mu_i N_i\,$ .

Overview

In a simple manner, with respect to STP reacting systems, a general rule of thumb is:

“

Every system seeks to achieve a minimum of free energy. In Physical sciences standard conditions for temperature and pressure are Standard sets of conditions for experimental measurements to allow comparisons to be made A rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation

”

Hence, out of this general natural tendency, a quantitative measure as to how near or far a potential reaction is from this minimum is when the calculated energetics of the process indicate that the change in Gibbs free energy ΔG is negative. Essentially, this means that such a reaction will be favored and will release energy. The energy released equals the maximum amount of work that can be performed as a result of the chemical reaction. Conversely, if conditions indicated a positive ΔG, then energy--in the form of work--would have to be added to the reacting system to make the reaction go.

History

The quantity called "free energy" is essentially a more advanced and accurate replacement for the outdated term “affinity”, which was used by chemists in previous years to describe the “force” that caused chemical reactions. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called The term affinity, as used in chemical relation, dates back to at least the time of Albertus Magnus in 1250.

From the 1998 textbook Modern Thermodynamics by Nobel Laureate and chemical engineering professor Ilya Prigogine we find: "As motion was explained by the Newtonian concept of force, chemists wanted a similar concept of ‘driving force’ for chemical change? Why do chemical reactions occur, and why do they stop at certain points? Chemists called the ‘force’ that caused chemical reactions affinity, but it lacked a clear definition. Ilya Viscount Prigogine (Илья́ Рома́нович Приго́жин ( January 25, 1917 &ndash May 28, 2003) was a Russian "

During the entire 18th century, the dominant view in regards to heat and light was that put forward by Isaac Newton, called the “Newtonian hypothesis”, which stated that light and heat are forms of matter attracted or repelled by other forms of matter, with forces analogous to gravitation or to chemical affinity. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements

In the 19th century, the French chemist Marcellin Berthelot and the Danish chemist Julius Thomsen had attempted to quantify affinity using heats of reaction. Marcellin (or Marcelin Pierre Eugène Berthelot ( October 25, 1827 - March 18, 1907) was a French Chemist and Politician Hans Peter Jørgen Julius Thomsen ( February 16, 1826 &ndash February 13, 1909) was a Danish Chemist noted in Thermochemistry The standard enthalpy change of reaction (denoted ΔH ° or ΔH o is the Enthalpy change that occurs in a system when one mole of matter In 1875, after quantifying the heats of reaction for a large number of compounds, Berthelot proposed the “principle of maximum work” in which all chemical changes occurring without intervention of outside energy tend toward the production of bodies or of a system of bodies which liberate heat. In the History of science, the principle of maximum work was a postulate concerning the relationship between Chemical reactions Heat evolution and the In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature

In addition to this, in 1780 Antoine Lavoisier and Pierre-Simon Laplace laid the foundations of thermochemistry by showing that the heat given out in a reaction is equal to the heat absorbed in the reverse reaction. In Thermodynamics and Physical chemistry, thermochemistry is the study of the Heat evolved or absorbed in Chemical reactions Thermochemistry They also investigated the specific heat and latent heat of a number of substances, and amounts of heat given out in combustion. Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity In Thermochemistry, latent heat is the amount of Energy in the form of Heat released or absorbed by a substance during a change of phase Similarly, in 1840 Swiss chemist Germain Hess formulated the principle that the evolution of heat in a reaction is the same whether the process is accomplished in one-step or in a number of stages. Germain Henri Hess (Герман Иванович Гесс German Ivanovich Gess, August 7, 1802 &ndash November 30, 1850) was a This is known as Hess' law. Hess's law is a law of Physical chemistry named for Germain Hess 's expansion of the Hess Cycle and used to predict the enthalpy change and conservation of energy (denoted With the advent of the mechanical theory of heat in the early 19th century, Hess’s law came to be viewed as a consequence of the law of conservation of energy. In the history of Science, the theory of heat or mechanical theory of heat was a theory introduced predominantly in 1824 by the French physicist Sadi Carnot In Physics, the law of conservation of energy states that the total amount of Energy in an isolated system remains constant and cannot be created although it may

Based on these and other ideas, Berthelot and Thomsen, as well as others, considered the heat given out in the formation of a compound as a measure of the affinity, or the work done by the chemical forces. This view, however, was not entirely correct. In 1847, the English physicist James Joule showed that he could raise the temperature of water by turning a paddle wheel in it, thus showing that heat and mechanical work were equivalent or proportional to each other, i. James Prescott Joule FRS (ˈdʒuːl December 24, 1818 &ndash October 11, 1889) was an English Physicist e. approximately, $dW \propto dQ$ . This statement came to be known as the mechanical equivalent of heat and was a precursory form of the first law of thermodynamics. In the History of science, the mechanical equivalent of heat was a Concept that played an important part in the development and acceptance of the Conservation In Thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the Conservation of energy.

By 1865 the German physicist Rudolf Clausius had shown that this equivalence principle needed amendment. Rudolf Julius Emanuel Clausius (Born Rudolf Gottlieb, January 2, 1822 &ndash August 24, 1888) was a German Physicist That is, one can use the heat derived from a combustion reaction in a coal furnace to boil water, and use this heat to vaporize steam, and then use the enhanced high pressure energy of the vaporized steam to push a piston. Combustion or burning is a complex sequence of Exothermic chemical reactions between a Fuel and an Oxidant accompanied by the production of Thus, we might naively reason that one can entirely convert the initial combustion heat of the chemical reaction into the work of pushing the piston. Clausius showed, however, that we need to take into account the work that the molecules of the working body, i. e. the water molecules in the cylinder, do on each other as they pass or transform from one step of or state of the engine cycle to the next, e. A thermodynamic state is the macroscopic condition of a Thermodynamic system as described by its particular thermodynamic parameters. The Carnot cycle is a particular Thermodynamic cycle, modeled on the hypothetical Carnot heat engine, proposed by Nicolas Léonard Sadi Carnot in 1824 and g. from (P1,V1) to (P2,V2). Clausius originally called this the “transformation content” of the body, and then later changed the name to entropy. In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy Thus, the heat used to transform the working body of molecules from one state to the next cannot be used to do external work, e. g. to push the piston. Clausius defined this transformation heat as dQ = TdS.

In 1873, Willard Gibbs published A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces in which he introduced the preliminary outline of the principles of his new equation able to predict or estimate the tendencies of various natural processes to ensue when bodies or systems are brought into contact. Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist By studying the interactions of homogeneous substances in contact, i. e. bodies, being in composition 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. The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy In Thermodynamics, the internal energy of a Thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes e. "necessarily stable", "neutral", and "unstable", and whether or not changes will ensue. In 1876, Gibbs built on this framework by introducing the concept of chemical potential so to take into account chemical reactions and states of bodies which are chemically different from each other. In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical In his own words, to summarize his results in 1873, Gibbs states:

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 p and temperature T, this equation may be written:

δ(ε - T η + p ν) = 0

when $δ$ refers 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. In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature A thermodynamic state is the macroscopic condition of a Thermodynamic system as described by its particular thermodynamic parameters. 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. In Thermodynamics, the internal energy of a Thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically

Hence, in 1882, after the introduction of these arguments by Clausius and Gibbs, the German scientist Hermann von Helmholtz stated, in opposition to Berthelot and Thomas’ hypothesis that chemical affinity is a measure of the heat of reaction of chemical reaction as based on the principle of maximal work, that affinity is not the heat given out in the formation of a compound but rather it is 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). In Thermodynamics, the internal energy of a Thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes Thus, G or F is the amount of energy “free” for work under the given conditions.

Up 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 Reactions 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. Gilbert Newton Lewis ( October 23, 1875 - March 23, 1946) was a famous American physical chemist known for the discovery Merle Randall (1888-1950 was an American Physical chemist famous for his work over the period of 25 years in measuring free energy calculations of compounds with

What does the term ‘free’ mean?

In the 18th and 19th centuries, the theory of heat, i. In the history of Science, the theory of heat or mechanical theory of heat was a theory introduced predominantly in 1824 by the French physicist Sadi Carnot e. that heat is a form of energy having relation to vibratory motion, was beginning to supplant both the caloric theory, i. e. that heat is a fluid, and the four element theory in which heat was the lightest of the four elements. Many ancient philosophies used a set of archetypal classical "elements" to explain patterns in Nature. Many textbooks and teaching articles during these centuries presented these theories side by side. Similarly, during these years, heat was beginning to be distinguished into different classification categories, such as “free heat”, “combined heat”, “radiant heat”, specific heat, heat capacity, “absolute heat”, “latent caloric”, “free” or “perceptible” caloric (calorique sensible), among others. In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity

In 1780, for example, Laplace and Lavoisier stated: “In general, one can change the first hypothesis into the second by changing the words ‘free heat, combined heat, and heat released’ into ‘vis viva, loss of vis viva, and increase of vis viva. In the history of Science, vis viva (from the Latin for living force) is an Obsolete scientific theory that served as an elementary ’” In this manner, the total mass of caloric in a body, called absolute heat, was regarded as a mixture of two components; the free or perceptible caloric could affect a thermometer while the other component, the latent caloric, could not. ^[6] The use of the words “latent heat” implied a similarity to latent heat in the more usual sense; it was regarded as chemically bound to the molecules of the body. In the adiabatic compression of a gas the absolute heat remained constant by the observed rise of temperature, indicating that some latent caloric had become “free” or perceptible.

During the early 19th century, the concept of perceptible or free caloric began to be referred to as “free heat” or heat set free. In 1824, for example, the French physicist Sadi Carnot, in his famous “Reflections on the Motive Power of Fire”, speaks of quantities of heat ‘absorbed or set free’ in different transformations. Sadi Carnot may refer to Nicolas Léonard Sadi Carnot (1796-1832 French physicist Marie François Sadi Carnot (1837-1894 president In 1882, the German physicist and physiologist Hermann von Helmholtz coined the phrase ‘free energy’ for the expression E – TS, in which the change in F (or G) determines the amount of energy ‘free’ for work under the given conditions. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός In Thermodynamics, work is the quantity of Energy transferred from one system to another without an accompanying transfer of Entropy. ^[7]

Thus, in traditional use, the term “free” was attached to Gibbs free energy, i. e. for systems at constant pressure and temperature, or to Helmholtz free energy, i. e. for systems at constant volume and temperature, to mean ‘available in the form of useful work. ’^[1] With reference to the Gibbs free energy, we add the qualification that it is the energy free for non-volume work. ^[8]

An increasing number of books and journal articles do not include the attachment “free”, referring to G as simply Gibbs energy (and likewise for the Helmholtz energy). In Thermodynamics, the Helmholtz free energy is a Thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic 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. The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization ^[9] This standard, however, has not yet been universally adopted, and many published articles and books still include the descriptive ‘free’.

Free energy of reactions

To derive the Gibbs free energy equation for an isolated system, let S_tot be the total entropy of the isolated system, that is, a system which cannot exchange heat or mass with its surroundings. In the Natural sciences an isolated system, as contrasted with a open system, is a Physical system that does not interact with its Surroundings In the Natural sciences an isolated system, as contrasted with a open system, is a Physical system that does not interact with its Surroundings According to the second law of thermodynamics:

$\Delta S_{tot} \ge 0 \,$

and if $\Delta S_{tot} = 0 \,$ then the process is reversible. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which The heat transfer $Δ Q$ vanishes for an adiabatic system. Any adiabatic process that is also reversible is called an isentropic $\left( {\Delta Q\over T} = \Delta S = 0 \right) \,$ process. In Thermodynamics, an isentropic process ( iso = "equal" (Greek Entropy = "disorder" is one during which the entropy of the system

Now consider diabatic systems, having internal entropy S_int. Such a system is thermally connected to its surroundings, which have entropy S_ext. The entropy form of the second law does not apply directly to the diabatic system, it only applies to the closed system formed by both the system and its surroundings. Therefore a process is possible if

$\Delta S_{int} + \Delta S_{ext} \ge 0 \,$ .

We will try to express the left side of this equation entirely in terms of state functions. ΔS_ext is defined as:

$\Delta S_{ext} = - {\Delta Q\over T} \,$

Temperature T is the same for two systems in thermal equilibrium. By the zeroth law of thermodynamics, if a system is in thermal equilibrium with a second and a third system, the latter two are in equilibrium as well. The zeroth law of thermodynamics is a generalized statement about thermal Equilibrium between bodies in contact Also, $Δ Q$ is heat transferred to the system, so $- Δ Q$ is heat transferred to the surroundings, and −ΔQ/T is entropy gained by the surroundings. We now have:

$\Delta S_{int} - {\Delta Q\over T} \ge 0 \,$

Multiply both sides by T:

$T \Delta S_{int} - \Delta Q\ge 0 \,$

ΔQ is heat transferred to the system; if the process is now assumed to be isobaric, then ΔQ_p = ΔH:

$T \Delta S_{int} - \Delta H \ge 0\,$

ΔH is the enthalpy change of reaction (for a chemical reaction at constant pressure and temperature). An isobaric process is a Thermodynamic process in which the pressure stays constant \Delta p = 0 The term derives from the Greek isos "equal" Then

$\Delta H - T \Delta S_{int} \le 0 \,$

for a possible process. Let the change ΔG in Gibbs free energy be defined as

$\Delta G = \Delta H - T \Delta S_{int} \,$ (eq. 1)

Notice that it is not defined in terms of any external state functions, such as ΔS_ext or ΔS_tot. Then the second law becomes, which also tells us about the spontaneity of the reaction:

$\Delta G < 0 \,$ favored reaction (Spontaneous)

$\Delta G = 0 \,$ Neither the forward nor the reverse reaction prevails (Equilibrium)

$\Delta G > 0 \,$ disfavored reaction (Nonspontaneous)

Gibbs free energy G itself is defined as

$G = H - T S_{int} \,$ (eq. In a Chemical process, chemical equilibrium is the state in which the chemical activities or Concentrations of the reactants and products have no net change 2)

but notice that to obtain equation (2) from equation (1) we must assume that T is constant. Thus, Gibbs free energy is most useful for thermochemical processes at constant temperature and pressure: both isothermal and isobaric. Such processes don't move on a P-T diagram, such as phase change of a pure substance, which takes place at the saturation pressure and temperature. Chemical reactions, however, do undergo changes in chemical potential, which is a state function. In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical Thus, thermodynamic processes are not confined to the two dimensional P-V diagram. There is a third dimension for n, the quantity of gas. Naturally for the study of explosive chemicals, the processes are not necessarily isothermal and isobaric. For these studies, Helmholtz free energy is used. In Thermodynamics, the Helmholtz free energy is a Thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic

If a closed system (ΔQ = 0) is at constant pressure (ΔQ = ΔH), then

$\Delta H = 0 \,$

Therefore the Gibbs free energy of a closed system is:

$\Delta G = -T \Delta S \,$

and if $\Delta G \le 0 \,$ then this implies that $\Delta S \ge 0 \,$ , back to where we started the derivation of ΔG.

Useful identities

$\Delta G = \Delta H - T \Delta S \,$ for constant temperature

$\Delta G^\circ = -R T \ln K \,$

$\Delta G = \Delta G^\circ + R T \ln Q \,$

$\Delta G = -nF \Delta E \,$

and rearranging gives

$nF\Delta E^\circ = RT \ln K \,$

$nF\Delta E = nF\Delta E^\circ - R T \ln Q \, \,$

$\Delta E = \Delta E^\circ - \frac{R T}{n F} \ln Q \, \,$

which relates the electrical potential of a reaction to the equilibrium coefficient for that reaction.

where

ΔG = change in Gibbs free energy, ΔH = change in enthalpy, T = absolute temperature, ΔS = change in entropy, R = gas constant, ln = natural logarithm, K = equilibrium constant, Q = reaction quotient, n = number of electrons per mole product, F = Faraday constant (coulombs per mole), and ΔE = electrical potential of the reaction. In Thermodynamics and molecular chemistry, the enthalpy (denoted as H, h, or rarely as χ) is a quotient or description of Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working The natural logarithm, formerly known as the Hyperbolic logarithm is the Logarithm to the base e, where e is an irrational For a general Chemical reaction \alpha A +\beta B. \rightleftharpoons \sigma S+\tau T. In Chemistry, reaction quotient is a quantitative measure of the extent of reaction the relative proportion of products and reactants present in the reaction mixture at some The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this In Physics and Chemistry, the Faraday constant (named after Michael Faraday) is the magnitude of Electric charge per mole of The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb. The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this The Galvanic cell, named after Luigi Galvani, consists of two different metals connected by a Salt bridge or a porous disk between the individual half-cells Moreover, we also have:

$K_{eq}=e^{- \frac{\Delta G^\circ}{RT}}$

$\Delta G^\circ = -RT(\ln K_{eq}) = -2.303RT(\log K_{eq})$

which relates the equilibrium constant with Gibbs free energy.

Standard change of formation

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 degrees Celsius and 100 kilopascals). The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this In Chemistry, the standard state of a material is its state at 1 bar (100 Kilopascals exactly The Celsius Temperature scale was previously known as the centigrade scale. Its symbol is ΔG_f^O.

All elements in their standard states (oxygen gas, graphite, etc. Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the The Mineral graphite, as with Diamond and Fullerene, is one of the Allotropes of carbon. ) have 0 standard Gibbs free energy change of formation, as there is no change involved.

ΔG = ΔG˚ + RT ln Q

At equilibrium, ΔG=0 and Q = K so the equation becomes ΔG˚= −RT ln K

Table of Selected Substances

Substance	State	ΔG˚ (cal/mol)
NH₃	g	-3. This article is about the unit of energy For its use in Nutrition and Food labelling regulations, see the article on Food energy. The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this 976
H₂O	lq	-56. 69
H₂O	g	-54. 64
CO₂	g	-94. 26
CO	g	-32. 81
CH₄	g	-12. 14
C₂H₆	g	-7. 86
C₃H₈	g	-5. 614
C₈H₁₈	g	4. 14
C₁₀H₂₂	g	8. 23

^[10]

References

^ ^a ^b ^c Perrot, Pierre (1998). In Thermodynamics and molecular chemistry, the enthalpy (denoted as H, h, or rarely as χ) is a quotient or description of In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy In Thermodynamics, the term thermodynamic free energy refers to the amount of work that can be extracted from a System, and is helpful in Engineering In Thermodynamics, the Helmholtz free energy is a Thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic A Thermodynamic free entropy is an entropic Thermodynamic potential analogous to the free energy. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist The grand potential is a quantity used in Statistical mechanics, especially for Irreversible processes in Open systems Grand potential is defined by A to Z of Thermodynamics. Oxford University Press. ISBN 0-19-856552-6.
^ 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.
^ ^a ^b ^c Salzman, William R. (2001-08-21). Year 2001 ( MMI) was a Common year starting on Monday according to the Gregorian calendar. Events 1192 - Minamoto Yoritomo becomes Seii Tai Shōgun and the De facto ruler of Japan. Open Systems (English). Chemical Thermodynamics. University of Arizona. Archived from the original on 2007-07-07. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1456 - A retrial verdict acquits Joan of Arc of heresy 25 years after her death Retrieved on 2007-10-11. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1138 - A massive earthquake struck Aleppo, Syria. 1531 - Huldrych Zwingli is killed
^ Mendoza, E. (1988). Reflections on the Motive Power of Fire – and other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Carnot. Dover Publications, Inc. . ISBN 0-486-44641-7.
^ Baierlein, Ralph (2003). Thermal Physics. Cambridge University Press. ISBN 0-521-65838-1.
^ Reiss, Howard (1965). Methods of Thermodynamics. Dover Publications. ISBN 0-486-69445-3.
^ International Union of Pure and Applied Chemistry Commission on Atomspheric Chemistry (1990). The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization "Glossary of Atmospheric Chemistry Terms (Recommendations 1990)". Pure Appl. Chem. 62: 2167–2219. Pure and Applied Chemistry (abb Pure Appl Chem) is the official journal for the International Union of Pure and Applied Chemistry. International Union of Pure and Applied Chemistry Commission on Physicochemical Symbols Terminology and Units (1993). The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization Quantities, Units and Symbols in Physical Chemistry (2nd Edition). Oxford: Blackwell Scientific Publications, 48. ISBN 0-632-03583-8. Retrieved on 2006-12-28. Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Events 1065 - Westminster Abbey is Consecrated. 1308 - The reign of Emperor Hanazono, Emperor of International Union of Pure and Applied Chemistry Commission on Quantities and Units in Clinical Chemistry; International Federation of Clinical Chemistry Committee on Quantities and Units (1996). The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization "Glossary of Terms in Quantities and Units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)". Pure Appl. Chem. 68: 957–1000. Pure and Applied Chemistry (abb Pure Appl Chem) is the official journal for the International Union of Pure and Applied Chemistry.
^ Handbook of chemistry and physics, 1960, p. 1882-1915, p. 1919-1921, 42nd ed. , Harrison

External links

IUPAC definition (Gibbs energy)
Gibbs energy - Florida State University
Gibbs Free Energy - Eric Weissteins World of Physics
Gibbs Free Energy - Chemistry Gateway
Entropy and Gibbs Free Energy - www. 2ndlaw. com
Gibbs Free Energy - Georgia State University
Gibbs Free Energy Java Applet - University of California, Berkeley
Gibbs Free Energy - Illinois State University

Dictionary

-noun

(physics) The difference between the enthalpy of a system and the product of its entropy and absolute temperature

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