Mixing, entropy, gases free energy

In most common chemical reactions, one or more of the reactants is in solution. Thus, an easy method to determine thermodynamic quantities of solution is desirable. Enthalpy of solution (heat of solution) is defined as the change in the quantity of heat which occurs due to a combination of a particular solute (gas, liquid, or solid) with a specified amount of solvent to form a solution. If the solution consists of two liquids, the enthalpy change upon mixing the separate liquids is called the heat of mixing. When additional solvent is added to the solution to form a solution of lower solute concentration, the heat effect is called the heat of dilution. The definitions of free energy of solution, entropy of solution, and so on follow the pattern of definitions above. 

System with random fluxes is defined as the nonequilibrium system where the fluxes of substance, heat, etc. change randomly. One can cite numerous examples of such systems turbulent gas-liquid systems with intensive heat/mass transfer, turbulent fluids containing dispersed solids, etc. In the case of pore formation, such situation is realized when the heat fluxes change randomly because of air fluidization or mechanical mixing. All macroscopic measured parameters of stationary turbulent flows, like their pressure, temperature, excess (free) energy, entropy, etc. do not change with time, while their values and directions in different spots of the flows can vary significantly. 

If we can write an equation for the chemical potential of a molecule as a function of pair potentials, p = /(p), and find the derivative of the chemical potential with the number density in terms of pair potential energies, we may solve the above integration. Since we know the p2 = P + kT nX2 expression per molecule from Equation (165), where X2 is usually expressed as the mole fraction or volume fraction, we need to relate the chemical potential of pure gas, p, to the molecular pair potentials and also the mole fraction, X2, to the gas number density, p. As the chemical potential, p2, is the total free energy per mole, it includes the interaction energy, p2, as well as enthalpy (kT) and entropy of mixing (kh X2) contributions. 

Calculate the Gibbs free energy and entropy due to mixing 2.5 moles of argon with 3.5 moles of oxygen, both at 1 bar and 25°C. Assume ideal gas behavior. 

For a solute dissolved in a solvent, the entropy of the solution becomes larger as the solute is diluted, an effect that lowers the overall Gibbs free energy of the solution. This is analogous to increasing the volume for a gas. The favorable entropy can be derived from the statistical mechanics of mixing. The solute has more ways to occupy the vessel when it is dilute. 

Example 1.4 Derive the following expressions for the entropy and Gibbs free energy of mixing at constant temperature and pressure for an ideal gas mixture ... 

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