Change in Gibbs energy of ideal gas associated with pressure change

The total derivative of Gibbs energy under equilibrium conditions is written as follows:

(1)

The equation of state of an one-mole ideal gas, PV = RT, leads to change in Gibbs energy from pressure Pi to Pf:

(2)

where Vm is the molar volume.

Molar Gibbs energy of this ideal gas at a temperature T and standard pressure of P is written by Gm (T). Then, molar Gibbs energy Gm of this gas at this T and a given pressure of P is obtained as:

(3)

Namely, Gibbs energy of an ideal gas increases as a function of logarithmic pressure. Note that the symbol “∅” indicates that it is at standard pressure.