## Minimize Gibbs Free Energy

## Gibbs Free Energy

In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system. 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. Every system seeks to achieve a minimum of free energy. 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 is negative. In essence, this means that such a reaction will be favoured and will release energy. The energy released equals the maximum amount of work that can be performed as a result of the chemical reaction. In contrast, if conditions indicated a positive change in Gibbs free energy, then energy, in the form of work, would have to be added to the reacting system to make the reaction go.

The equation can also be seen from the perspective of both the system and its surroundings (the universe). For the purposes of calculation, we assume the reaction is the only reaction going on in the universe. Thus the entropy released or absorbed by the system is actually the entropy that the environment must absorb or release respectively. Thus the reaction will only be allowed if the total entropy change of the universe is equal to zero (an equilibrium process) or positive. The input of heat into an "endothermic" chemical reaction (e.g. the elimination of cyclohexanol to cyclohexene) can be seen as coupling an inherently unfavourable reaction (elimination) to a favourable one (burning of coal or the energy source of a heat source) such that the total entropy change of the universe is more than or equal to zero, making the Gibbs free energy of the coupled reaction negative.

This optimization problem determines the mole fractions of a mixture of common combustion species at equilibrium by minimizing the Gibbs Energy.

Name |
Lower |
Value |
Upper |

gibbs.t | --- | 1.0000E+03 | --- |

gibbs.p | --- | 2.0000E+00 | --- |

gibbs.x[1] | 1.0000E-04 | 3.9421E-01 | --- |

gibbs.x[2] | 1.0000E-04 | 1.0316E+00 | --- |

gibbs.x[3] | 1.0000E-04 | 1.2432E+00 | --- |

gibbs.x[4] | 1.0000E-04 | 3.6261E-01 | --- |

gibbs.x[5] | 1.0000E-04 | 5.1800E+00 | --- |

gibbs.z | 1.0000E-01 | 9.9953E-01 | --- |

gibbs.y[1] | --- | 4.8007E-02 | --- |

gibbs.y[2] | --- | 1.2563E-01 | --- |

gibbs.y[3] | --- | 1.5139E-01 | --- |

gibbs.y[4] | --- | 4.4158E-02 | --- |

gibbs.y[5] | --- | 6.3081E-01 | --- |

### References

Lwin, Y., Chemical Equilibrium by Gibbs Energy Minimization on Spreadsheets, Int. J. Engng Ed. Vol. 16, No. 4, pp. 335-339, 2000.