# The Gibbs free energy

We can use ∆Stotal  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.

Stotal = ∆Ssystem + ∆Ssurroundings

but remember ∆Ssurroundings = –∆H / T

so

Stotal = ∆Ssystem + ( –∆H / T)

If we multiply through by –T, we get

T∆Stotal =  ∆HTSsystem

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∆Stotal’ the Gibbs free energy after the American chemist Josiah Willard Gibbs. It is given the symbol ∆G so

G =  ∆H – TSsystem

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.

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