Gibbs free energy

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.

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.

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.

ΔG 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 ΔG 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 ΔG to be smaller than the non-pV work and make it possible for the reaction to occur.

The input of heat into an inherently endergonic reaction, such as the elimination of cyclohexanol to cyclohexene, can be seen as coupling an unfavorable reaction (elimination) to a favorable 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.

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.

[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.

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.

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) Xi, which cause the external parameters of the system ai to change by an amount dai, can be derived as follows from the first law for reversible processes:

[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.

[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 definition of G from above is Taking the total differential, we have Replacing dU with the result from the first law gives[13] The natural variables of G are then p, T, and {Ni}.

Because S, V, and Ni are extensive variables, an Euler relation allows easy integration of dU:[13] Because some of the natural variables of G are intensive, dG may not be integrated using Euler relations as is the case with internal energy.

Then 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),

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 dQele is passed between the electrodes of an electrochemical cell generating an emf

At constant pressure the above equation 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.

Assuming constant pressure and volume, the thermodynamic properties of the cell are related strictly to the behavior of its emf by where ΔH is the enthalpy of reaction.

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

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).

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.

The reaction C (s) diamond → C (s) graphite has a negative change in Gibbs free energy and is therefore thermodynamically favorable at 25 °C and 1 atm. However, the reaction is too slow to be observed, because of its very high activation energy . Whether a reaction is thermodynamically favorable does not determine its rate.
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. MN is the section of the surface of dissipated energy . Q ε and Q η are sections of the planes η = 0 and ε = 0, and therefore parallel to the axes of ε ( internal energy ) and η ( entropy ), respectively. 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.
Relation to other relevant parameters
American scientist Willard Gibbs ' 1873 figures two and three (above left and middle) used by Scottish physicist James Clerk Maxwell in 1874 to create a three-dimensional entropy , volume , energy thermodynamic surface diagram for a fictitious water-like substance, transposed the two figures of Gibbs (above right) onto the volume-entropy coordinates (transposed to bottom of cube) and energy-entropy coordinates (flipped upside down and transposed to back of cube), respectively, of a three-dimensional Cartesian coordinates ; the region AB being the first-ever three-dimensional representation of Gibbs free energy, or what Gibbs called "available energy"; the region AC being its capacity for entropy , what Gibbs defined as "the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume.