Free energy of an ideal gas

The Gibbs free energy of a liquid is almost independent of pressure, and so we can replace Gm(l) by its standard value (its value at 1 bar), Gm°(l). The Gibbs free energy of an ideal gas does vary with pressure, and thermodynamics can be used to show that, for an ideal gas,... 

FIGURE 8.4 The variation of the molar Gibbs free energy of an ideal gas with pressure. The Gibbs free energy has its standard value when the pressure of the gas is 1 bar. The value of the Gibbs free energy approaches minus infinity as the pressure falls to zero. 

To find how AG changes with composition, we need to know how the molar Gibbs free energy of each substance varies with its partial pressure, if it is a gas, or with its concentration, if it is a solute. We have already seen (in Section 8.3) that the molar Gibbs free energy of an ideal gas J is related to its partial pressure, P(, by... 

Where G° is molar free energy of an ideal gas in its standard state and G is molar free energy of an ideal gas in the state of interest. 

We have shown qualitatively that the entropy and therefore the free energy of an ideal gas depend on its pressure. From a more detailed argument, which we will not consider here, one can show that... 

These equations permit the calculation of the molar free energy of an ideal gas, with reference to the value in the lowest energy state, i.e., at 0° K they will be used in Chapter XIII in connection with the determination of equilibrium constants and the free energy changes accompanying chemical reactions. 

Based on the observation that the free energy of an ideal gas is dependent on its pressure (concentration) and that the state function G can be manipulated in the same way as the state function H, the following equation was derived ... 

The contribution Foand can be written as the free energy of an ideal gas of counterions ... 

Obtain an explicit expression for the Helmholz free energy of an ideal gas as a function of T, V and N. 

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