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What is the significance of Gibbs free energy?

What is the significance of Gibbs Free Energy?

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    http://en.wikipedia.org/wiki/Gibbs_free_energy is a measure of the amount of energy available to do work in an isothermal and isobaric (constant temperature and pressure) thermodynamic system. This is where the term "free" comes from; it refers to the amount of energy in a system that is easily available for usage. This insight gives a good intuition for its mathematical definition: G=H−TSG=H−TSG=H-TS The Gibbs energy is thus the http://en.wikipedia.org/wiki/Enthalpy (essentially the total energy of the system) minus the http://en.wikipedia.org/wiki/Entropy times the temperature (a measure of the amount of energy that is unavailable). While there are many uses for Gibbs free energy, its most well-known application, and indeed, the one in which most students are introduced to it, is in determining the spontaneity of a chemical process. Essentially if a process results in a negative change in the amount of Gibbs free energy, then it is said to occur spontaneously. Note, however, that this does not imply anything about the time it takes for the reaction to occur; it only states that given enough time in the absence of other forces, the process will eventually occur. As a classic example, consider that under standard atmospheric conditions, the reaction of diamonds decaying into graphite is spontaneous, but it occurs so slowly that it is not observed.

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Maxwell labelled the Free energy as avaliable energy (1871) and it is only in recent times the definition changed to honour Gibb's achievement in Statistical Mechanics. It is the useful work done in a system with a constant pressure and temperature (or isothermal).  Whilst 's definition is absolutely correct, the derivation is not so obvious. It is at first defined as: [math] G = F + PV = E - TS + PV [/math] In a reversible isothermal system, this becomes: [math] \Delta{G} = \Delta{F} + {P}\Delta{V}[/math] In a reversible isothermal process, the change in free energy is also defined as: [math] w_{T} = -\Delta{F}[/math] Whilst the [math] {P}\Delta{V} [/math] can be written as [math]w_{v} [/math], the work done due to volume change. Hence, the [math]\Delta{G}[/math] can be defined as: [math] -\Delta{G} = w_{t} - w_{v}[/math] Rather than [math]\Delta[/math] - if you have a infinitesimal ([math]d[/math]) amount of change, you can write the change in the Gibbs Free Energy/Avaliable Energy as: [math] dG = dF +PdV + VdP [/math]= [math](dE - TdS - SdT) + PdV + VdP[/math] [math]       = (dE - TdS + pdV) - SdT + VdP  [/math] As we are only dealing with volume change, we know that: [math] dE = TdS - pdV [/math] Hence, the [math] dE [/math] can be substituted, meaning the term in the bracket will become zero. This means that the definition for a infinitesimal small change in the Gibbs Free Energy is now: [math]dG = -SdT + VdP [/math] This gives rise to the following partial diffrentials, with constant P and T: [math] (\frac{dG}{dT})_{P} = -S[/math] and: [math]   (\frac{dG}{dP})_{T} = V [/math] The heat content (or enthalpy) is defined as: [math] H = E + PV [/math] This means that the enthalpy can be defined as: [math] H = F  + TS + PV = G + TS [/math]  The change in H can therefore be written; the S term can now be substituted with the diffrential written above to show that [math] {\Delta}H = \Delta{G} + T{\Delta}S = \Delta{G}- T(\frac{dG}{dT})_{P}[/math]

Sang Young Noh

The trouble with Wikipedia is that when it spouts misleading nonsense, that can be spread all over the Internet. Free enegy does not have a direct microscopic interpretation, it is a bookkeeping equation. Analogous to the accounting equation.

Keith Allpress

Wikipedia’s https://en.wikipedia.org/wiki/Gibbs_free_energy page gives a pretty good explanation.

Jess H. Brewer

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