Mixing, entropy, gases solids

In crystals for which n0 is large, such as iodine, the lowest symmetric and the lowest antisymmetric state have practically the same energy and properties, and each corresponds to one eigenfunction only. As a result a mixture of symmetric and antisymmetric molecules at low temperatures will behave as a perfect solid solution, each molecule having just its spin quantum weight, and the entropy of the solid will be the translational entropy plus the same entropy of mixing and spin entropy as that of the gas. This has been verified for I2 by Giauque.17 Only at extremely low temperatures will these entropy quantities be lost. 

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. 

The final colligative property, osmotic pressure,24-29 is different from the others and is illustrated in Figure 2.2. In the case of vapor-pressure lowering and boiling-point elevation, a natural boundary separates the liquid and gas phases that are in equilibrium. A similar boundary exists between the solid and liquid phases in equilibrium with each other in melting-point-depression measurements. However, to establish a similar equilibrium between a solution and the pure solvent requires their separation by a semi-permeable membrane, as illustrated in the figure. Such membranes, typically cellulosic, permit transport of solvent but not solute. Furthermore, the flow of solvent is from the solvent compartment into the solution compartment. The simplest explanation of this is the increased entropy or disorder that accompanies the mixing of the transported solvent molecules with the polymer on the solution side of the membrane. Flow of liquid up the capillary on the left causes the solution to be at a hydrostatic pressure... 

The entropy of mixing is generated not only in the gas state (gas mixtures) but also in the states of liquids (liquid solutions) and solids (solid solutions). 

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. 

It is of interest to note that since the mole fraction n of any gas in a mixture must be less than unity, its logarithm is negative hence ASm as defined by equation (19.32) is always positive. In other words, the mixing of two or more gases, e.g., by diffusion, is accompanied by an increase of entropy. Although equation (19.32) has been derived here for a mixture of ideal gases, it can be shown that it applies equally to an ideal mixture of liquids or an ideal solid solution. 

The standard state for a pure liquid or solid is taken to be the substance in that state of aggregation at a pressure of 1 bar. This same standard state is also used for liquid mixtures of those components that exist as a liquid at the conditions of the mixture. Such substances are sometimes referred to as liquids that may act as a solvent. For substances that exist only as a solid or a gas in the pure component state at the temperature of the mixture, sometimes referred to as substances that can act only as a solute, the situation is more complicated, and standard states based on Henry s law may be used. In this case the pressure is again fixed at 1 bar, and thermal properties such as the standard-state enthalpy and heat capacity are based on the properties of the substance in the solvent at infinite dilution, but the standard-state Gibbs energy and entropy are based on a hypothetical state.of unit concentration (either unit molality or unit mole fraction, depending on the form of Henry s law used), with the standard-state fugacity at these conditions extrapolated from infinite-dilution behavior in the solvent, as shown in Fig. 9.1-3a and b. Therefore just as for a gas where the ideal gas state at 1 bar is a hypothetical state, the standard state of a substance that can only behave as a solute is a hypothetical state. However, one important characteristic of the solute standard state is that the properties depend strongly upon the solvent. used. Therefore, the standard-state properties are a function of the temperature, the solute, and the solvent. This can lead to difficulties when a mixed solvent is used. 

Dissolving a gas. The particles in a gas already have so much freedom of motion and such highly dispersed energy that they always lose freedom when they dissolve in a liquid or solid. Therefore, the entropy of a solution of a gas in a liquid or a solid is always less than the entropy of the gas. For instance, when gaseous O2 [5°(g) = 205.0 J/moFK] dissolves in water, its entropy decreases dramatically [5°(flr/) = 110.9 J/mohK] (Figure 20.7). When a gas dissolves in another gas, however, the entropy increases from the mixing of the molecules. 

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