# Si Unit For Gibbs Energy

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 G \displaystyle G is necessary for a reaction to be spontaneous under these conditions.

## Si Unit For Gibbs Energy

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.

If two chemical reactions are coupled, then an otherwise endergonic reaction (one with positive Î”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 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.

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The quantity called "free energy" is a more advanced and accurate replacement for the outdated term affinity, which was used by chemists in the earlier years of physical chemistry to describe the force that caused chemical reactions.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

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.

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:

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 Ni are changing. For a closed, non-reacting system, this term may be dropped.

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.

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. 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 i \displaystyle i is its (partial) mol(ecul)ar Gibbs free energy. It applies to homogeneous, macroscopic systems, but not to all thermodynamic systems.[14]

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.

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 Î”fG.

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.

That said, however, almost everywhere they are specified in terms of $\pukJ/mol$ because that makes the comparison across different substances easier. Since $G$ is an extensive function, its value can vary even with the amount of substance. Your calculated $\Delta G_\mathrm f^\circ$ can differ from mine even if we take the same substance, just because we had the amounts different. Hence, to ease comparison and computations, they are "specified" in terms of $\pukJ/mol$, although their correct SI unit is Joule.

Free energy change criteria for predicting spontaneity is better than entropy change criteria because the former requires free energy change of system only whereas the latter requires entropy change of system and surroundings.Standard Energy Change of FormationWe can say that the standard Gibbs free energy of formation of a compound is basically the change of Gibbs free energy that is followed by the formation of 1 mole of that substance from its component element available at their standard states or the most stable form of the element which is at 25 C and 100 kPa. Its symbol is Î”fG.

The change in the free energy of the system that occurs during a reaction measures the balance between the two driving forces that determine whether a reaction is spontaneous. As we have seen, the enthalpy and entropy terms have different sign conventions.

The free energy change of the reaction in any state, Î”G (when equilibrium has not been attained) is related to the standard free energy change of the reaction, Î”G (which is equal to the difference in the free energies of formation of the products and reactants both in their standard states) according to the equation.

If Q is greater than K, the reaction has exceeded the equilibrium state. It will proceed non-spontaneously (since equilibrium has already been reached), and this must mean that the Î”G (Gibbs free energy) must be positive, or greater than zero.

We must take care when using mathematical expressions that include both energy and entropy. Chemists normally measure energy (both enthalpy and Gibbs free energy) in kJ mol-1 (kilojoules per mole) but measure entropy in J K-1 mol-1 (joules per kelvin per mole). So it is necessary to convert the units, usually by dividing the entropy values by 1000 so that they are measured in kJ K-1 mol-1.

Notice that if Î”G is negative, the reaction is feasible. Notice also that all the terms in the expression relate to the system rather than the surroundings. This is what makes this quantity so useful to chemists. It is also an energy term, which is a concept more familiar to most chemists than entropy. 041b061a72