Gibbs Free Energy - Definitions

Definitions

The Gibbs free energy is defined as:

G(p,T) = U + pVTS

which is the same as:

G(p,T) = HTS

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 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 magnetical) 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:




where:

  • μi is the chemical potential of the ith chemical component. (SI unit: joules per particle or joules per mole)
  • Ni is the number of particles (or number of moles) composing the ith chemical component.

This is one form of Gibbs fundamental equation. 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.

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 −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.

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 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:

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

or more conveniently as its chemical potential:

In non-ideal systems, fugacity comes into play.

Read more about this topic:  Gibbs Free Energy

Famous quotes containing the word definitions:

    The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.
    Pamela Patrick Novotny (20th century)

    What I do not like about our definitions of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.
    —G.C. (Georg Christoph)

    Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?
    There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.
    Edmond De Goncourt (1822–1896)