Thermodynamic functions mixing ideal gases

The thermodynamic functions for the gas phase are more easily developed than for the liquid or solid phases, because the temperature-pressure-volume relations can be expressed, at least for low pressures, by an algebraic equation of state. For this reason the thermodynamic functions for the gas phase are developed in this chapter before discussing those for the liquid and solid phases in Chapter 8. First the equation of state for pure ideal gases and for mixtures of ideal gases is discussed. Then various equations of state for real gases, both pure and mixed, are outlined. Finally, the more general thermodynamic functions for the gas phase are developed in terms of the experimentally observable quantities the pressure, the volume, the temperature, and the mole numbers. Emphasis is placed on the virial equation of state accurate to the second virial coefficient. However, the methods used are applicable to any equation of state, and the development of the thermodynamic functions for any given equation of state should present no difficulty. 

As mentioned before, Approach A (also called supercritical compounds can be handled easily and that besides the phase equilibrium behavior various other properties such as densities, enthalpies including enthalpies of vaporization, heat capacities and a large number of other important thermodynamic properties can be calculated via residual functions for the pure compounds and their mbctures. For the calculation besides the critical data and the acentric factor for the equation of state and reliable mixing rules, only the ideal gas heat capacities of the pure compounds as a function of temperature are additionally required. A perfect equation of state with perfect mixing rules would provide perfect results. This is the reason why after the development of the van der Waals equation of state in 1873 an enormous number of different equations of state have been suggested. 

Most of the species are only partially liquefied. The ratio between the occurrence of a species in the liquid and gaseous phases can be approximated by simplified thermodynamic calculations. For a first approximation, an ideal gas state and an ideal mixing behavior are assumed. The condensed hydrocarbons are assumed to be immiscible in the aqueous phase and to form a second liquid organic phase. A gas-liquid equilibrium describes the ratio between the concentrations in the gaseous phase ycqHp and the liquid phase xcqHp- Boiling pressures are calculated as a function of the temperature Pc Hp [1, 18] ... 

The act or process by which a compound such as oxygen is molecularly mixed with a liquid (such as water) or a solid (such as a polymer) is called dissolution, and the result of the mixing is a solution. If a solution is very dilute, as is commonly found in packaging, it behaves as an ideal solution, and again the activity coefficient is approximately 1, so concentration can be substituted for activity in thermodynamic relationships. In order to describe the solubility of a compound present in a gas phase that is in contact with a solid phase, as may be the case of oxygen in air contacting a polymer, we need a relationship between the concentration in the liquid (or solid) phase and the concentration (or partial pressure) in the gas phase. In other words, we need an expression for the solubility of the substance at equilibrium, as a function of the partial pressure of the gas or vapor in the contacting gas phase. 

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