Lewis introduced a concept by making use of free energy function G to represent the actual behavior of real gases which is very much different from the concept of ideal gases. This concept is known as concept of Fugacity.

We know that the variation of free energy change with change in pressure at constant temperature is given as:

(∂G / ∂P) _{T} = V ……………………………… (1)

This equation is applicable to all gases whether ideal or non-ideal.

If one mole of a pure gas is taken under consideration, then V refers to molar volume.

For an ideal gas, equation (1) can be given as:

(dG) _{T} = RT dP / P

And for ‘n’ moles will be:

(dG) _{T} = nRT dP / P = nRT d (ln P) ………………………. (2)

Integrating both sides we will get:

G = G^{*} + nRT ln P ………………………………. (3)

Where G^{*} represents the integration constant, which is the free energy of n moles of the ideal gas at temperature T when pressure P is unity. This equation represents the free energy of an ideal gas at temperature T and pressure P.

Integrating equation (2) between the pressures P_{1} and P_{2}, at constant temperature T, will give:

∆G = G_{2} – G_{1} = nRT (P^{2}∫ P_{1}) dP / P

= nRT ln (P^{2}/ P_{1}) ……………….. (4)

For one mole of an ideal gas the free energy will be:

∆G = G_{2} – G_{1} = RT ln (P^{2}/ P_{1}) ……………………… (5)

The above equations (4) and (5) are not valid for real gases

since V is not exactly equal to RT / P

For making applicable to real gases, the equations are simplified by Lewis. He introduced a new function f, known as Fugacity function which can be represented as:

(dG) _{T} = nRT d (ln f)

And

G = G^{*} + nRT ln f

Where G^{*} represents the free energy of n moles of a real gas when its fugacity is equal to unity.