The chemical potential of a gas

Our starting point is eqn 3.3, G (pf) = G (pJ + RT ln(pflpj, which shows how the molar Gibbs energy of a perfect gas depends on pressure. First, we setpf=p, the pressure of interest, and pi = p, the standard pressure (1 bar). At the latter pressure, the molar Gibbs energy has its standard value, G, so we can write 

for a mixture of perfect gases, we interpret p as the partial pressure of the gas, and is the partial molar Gibbs energy, the chemical potential. Therefore, for a mixture of perfect gases, for each component J present at a partial pressure pj, 

In this expression, pf is the standard chemical potential of the gas J, which is identical to its standard molar Gibbs energy, the value of G for the pure gas at 1 bar. If we adopt the convention that, whenever pj appears in a formula, it is to be interpreted as pj/p (so, if the pressure is 2.0 bar,pj = 2.0), we can write eqn 3.10a more simply as 

Self-test 3.4 ) Suppose that the partial pressure of a perfect gas falls from 1.00 bar to 0.50 bar as it is consumed in a reaction at 25 C. What is the change in chemical potential of the substance  

---

The chemical potential of a gas depends on its partial pressnre p. When the gas obeys ideal gas laws, we have... 

The fugacity is defined in terms of the chemical potential of a gas, either pure or in a mixture, as... 

The calculation of the C02 solubility in aqueous solution was based upon the equations of Swope and Andersen [15]. When a chemical system is in equilibrium, the chemical potential of a gas phase particle and the particle in solution must be equal [16]. From this, we can show that the solubility of a gas particle in solution is given by ... 

Next we discuss the form of the pressure term in the chemical potential of a gas, where the assumption of incompressibility that we used for a liquid is not valid. Our point of departure is the perfect or ideal gas law ... 

The chemical potential of a gas therefore increases logarithmically with the pressure. Comparison of (10.8), (10.10) and (10.11) shows that, for a perfect gas,... 

Show that in its standard state the chemical potential of a gas is independent of the pressure. 

Dissolved Cases and Volatile Solutes. By analogy with equation 1.32, the chemical potential of a gas in a gas mixture is given by ... 

The chemical potential of a gas molecule (jigi) is expressed, setting the lowest energy state as energy zero... 

We need an explicit formula for the variation of the chemical potential of a substance with the composition of the mixture. Here we use the strategy mentioned at the start of the chapter we begin by considering the chemical potential of a gas, not because gases are particularly interesting in biology but because we can use the resulting expression to derive results for solutions. 

The standard chemical potential is then the molar free energy of the gas atunit pressure. The above equation subdivides the chemical potential of a gas into a temperature-dependent part, p,°i, and a concentration-dependent part, In(ai) -pressure is equivalent to concentration for a gas. 

This assumption allows the chemical potential of adsorbates to be related to the chemical potential of a gas-phase species. The gas-phase reference chemical... 

---