Chapter 8: Thermodynamic Behavior of Gases

The differences arise primarily because real gas particles occupy a finite volume and exhibit inherent atomic or molecular interaction forces, unlike the non-interacting, volume-less particles of an ideal gas. The thermodynamic properties of ideal gases are explored, showing that the molar Gibbs free energy increases logarithmically as pressure rises. This leads to the definition of a conventional standard state as one mole of pure gas at a pressure of one atmosphere at the temperature of interest. When studying gas mixtures, composition is defined using mole fraction (X i​ ), and the specific pressure contribution of each component is its partial pressure (p i​ ); Dalton’s law of partial pressures relates the partial pressure of a component to its mole fraction and the total pressure. The chapter introduces partial molar quantities, specifying that the partial molar Gibbs free energy is the same as the chemical potential (μ i ) of that component in the solution. Analysis of the mixing of ideal gases shows that the internal energy change and the enthalpy of mixing are zero because there are no interactions. The mixing process is spontaneous solely due to a negative Gibbs free energy of mixing, which is driven by a positive entropy of mixing. Real gas deviations are numerically quantified using the compressibility factor (Z), defined as the ratio of Pressure times Volume to R times Temperature, which is 1 for a perfect gas. Isothermal compression paths for real gases reveal distinct P-V isotherms, showcasing liquid-vapor coexistence below the critical temperature. The critical point is the specific state where the liquid and vapor molar volumes become identical. Furthermore, when pressure, temperature, and volume are expressed relative to their critical parameters (reduced variables), all gases adhere to a unified relationship known as the Law of Corresponding States. The semi-empirical van der Waals equation models real gases by adding terms to the ideal gas law to correct for attractive forces and finite particle volume, correctly predicting the critical point, the existence of the vapor-to-liquid phase transition, and the intrinsic stability limits known as spinodal points. For precise thermodynamic treatment of highly nonideal gases, the concept of fugacity (f) is introduced to replace pressure in the ideal Gibbs free energy relationship, defining the standard state as where the fugacity is unity. Other empirical models include the Virial equation of state, which expresses the compressibility factor as a power series of pressure or reciprocal volume.