Natural independent variables for a given state function are those, which permit

derivatives of that state function with respect to those variables to be

expressed as simple thermodynamic functions.

For example, the natural independent variables of H are S and P, which leads

to partial derivative H with respect to S at constant pressure equals temperature.

And, the partial derivative of H with respect to pressure at constant entropy

is equal to volume. So, there you see these simple,

thermodynamic variables. The Gibbs free energy of an ideal gas as

a function of temperature and pressure can be related to the pressure and the

standard molar Gibbs free energy at one bar.

Using G over bar at a given temperature and pressure is equal to G superscript 0

at temperature. This is the standard molar Gibbs free

energy at a given temperature and it is defined as the standard molar Gibbs free

energy at 1 bar plus RT log P. So, I only know what pressure I'm going

to in order to know what the new free pressure will be, given a tabulated

standard molar free energy. The temperature dependence of the Gibbs

free energy can be expressed through the Gibbs Helmholtz equation.

And that is the partial derivative with respect to T of G over T, holding

pressure constant is minus H over T squared, the Gibbs-Helmhotz equation.

And then finally, the Gibbs free energy as a function of temperature can also be

assembled from the enthalpy at a given temperature.

Which is evaluated relative to enthalpy at 0 kelvin, by doing measurements of

heat capacities. Minus T times the third law entropy at a

given temperature. And again, that is evaluated from

measurements of heat capacities at various temperatures.

Except what's being integrated is CP over T, instead of just CP, as is true for

enthalpy. So, given those enthalpy and entropy

quantities, we can always determine a free energy.