The quantum casino: tutorials |

We can use ∆*S*_{total }to predict the direction of a reaction, but largely for historical reasons chemists prefer to think in terms of energy.

A note on units. 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}. |

∆*S*_{total} = ∆*S*_{system} + ∆*S*_{surroundings}

but remember ∆S_{surroundings} = –∆*H* / *T*

so

∆*S*_{total} = ∆*S*_{system} + (* –∆ H / T)*

If we multiply through by –*T*, we get

–*T*∆S_{total} = ∆*H* – *T*∆*S*_{system}

Since entropy has units of J K^{-1} mol^{-1}, *T *x ∆*S* has units of J mol^{-1} and is a measure of energy. We call the term ‘–*T*∆S_{total}’ the Gibbs free energy after the American chemist Josiah Willard Gibbs. It is given the symbol ∆*G* so

∆*G* = ∆H – *T*∆*S*_{system}

Notice that if it 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.

The Gibbs free energy |