Mixtures solutions, nonideal

Those involving solution nonideality. This is the most serious approximation in polymer applications. As we have already seen, the large differences in molecular volume between polymeric solutes and low molecular weight solvents is a source of nonideality even for athermal mixtures. 

The examples tested by Taylor et al. (80) for the efficiency homotopy were for moderate- or narrow-boiling mixtures. No wide-boiling mixtures were tested. Since the temperature profiles at the intermediate values of E yy will be flat and not broad, the homotopy may be best for the moderate- and narrow-boiling systems. Most of the mixtures were nonideal and the efficiency homotopy should lessen the effect of nonideal If-values where E yy acts as a damper on the if-values. The efficiency homotopy does not work for purity specifications because the purity will not be satisfied in solutions of early values of E yy-Vickery and Taylor (81) presented a thermodynamic homotopy where ideal If-values and enthalpies were used for the initial solution of the global Newton method and then slowly converted to the actual If-values and enthalpies using the homotopy parameter t, The homotopy functions were embedded in the If-value and enthalpy routines, freeing from having to modify the MESH equations. The If-values and enthalpies used are the homotopy functions ... 

Mixtures of nonpolar solvents are normally characterized by the term solubility parameter (5). The difference in solubility parameters of mixture components provides a measure of solution nonideality.Mixtures of aliphatic hydrocarbons are nearly ideal, whereas mixtures of aliphatic hydrocarbon with aromatics show appreciable nonideality. Sometimes, it is difficult to predict the behavior of highly nonideal mixtures. Thermodynamic properties of binary and multicomponent mixtures have been dealt with extensively in the literature. " ... 

In the remainder of this section we examine several EOS-G models using three prototype binary mixtures that form sti ongly nonideal solutions. For comparison, we also include the predictions of the UNIFAC model used directly in the y-(p method wherever applicable. The systems considered are the methanol and benzene (Butcher and Medani 1968), the acetone and water (Gmehling and Onken 1977), and the 2-propanol and water (Barr-David and Dodge 1959) binary mixtures. Note that there are many systems with small to moderate solution nonideality for which all or most of the methods mentioned above work reasonably well. We are not concerned with such systems here because the method selection would not be a problem in such cases. Rather we consider only those systems that are more nonideal and for which the differences between the models discussed here are clearly evident. 

Mixtures exhibiting nonideal solution behavior present both challenges and opportunities in connection with separation processes. Azeotropes cannot be separated by ordinary distillation, yet the formation of azeotropes itself may be used as a means for carrying out certain separations. The formation of two liquid phases in a column may complicate the separation process however, the coexistence of liquid phases with distinct compositions provides one more separation tool. Chemical reactions concurrent with distillation may be used either to enhance the separation or to perform both the reaction and the separation in one process. 

Flash points of mixtures of oxygenated and hydrocarbon solvents cannot be predicted simply. A computer based method is proposed which exhibits satisfactory prediction of such Tag Open Cup flash points. Individual solvent flash point indexes are defined as an inverse function of the component s heat of combustion and vapor pressure at its flash point. Mixture flash points are then computed by trial and error as the temperature at which the sum of weighted component indexes equals 1.0. Solution nonidealities are accounted for by component activity coefficients calculated by a multicomponent extension of the Van Laar equations. Flash points predicted by the proposed method are compared with experimental data for 60 solvent mixtures. Confidence limits of 95% for differences between experimental and predicted flash points are +8.0-+3.0°F. 

SYSTEMS OF COLUMNS IN THE SERVICE OF SEPARATING MIXTURES OF NONIDEAL SOLUTIONS... 

Polar molecules interact more strongly at large distances than do nonpolar molecules, and generally form nonideal solutions. One model for solution nonidealities in a binary mixture consisting of a nonpolar species, which we denote by A, and a polar substance, designated by the symbol B, is based on the supposition that the polar substance partially dimerizes,... 

For a liquid mixture, and again neglecting solution nonidealities, U H and Cv Cp, so that this equation can be rewritten as... 

The calculation of the pH of a mixture of a weak acid and a strong base is considered next, and is slightly more complicated. (The development of the equations for a weak base and a strong acid is left for the reader as Problem 15.5.) For simplicity of presentation, we will neglect the ionization of water, except at the neutral point (pH = 7) or when there is an excess of base, and also neglect solution nonidealities. Of course, electrolyte solution nonideality can be included following a procedure such as that in the illustration above. The dissociation reactions of a weak acid and a strong base are... 

In the foregoing sections, the mixtures (solutions) were assumed to behave ideally. This implies that the molecules of solute i interact with the solvent but not with each other. As a consequence, p,(X is determined by the dependence of the molar configuration entropy of i on resulting in Equation 3.30 (see Section 3.5). A mixture behaves ideally only when X, is sufficiently small. At higher mole fractions of i, deviation from ideality occurs due to excluded volume effects and/or interactions between the dissolved components (e.g., ions). Hence, the mole fraction of i, where nonideal behavior sets off, depends on the size and charge of the dissolved component(s). 

The dipole-induced dipole forces between acetone and carbon disulfide molecules are weaker than the dipole-dipole interactions among acetone molecules, causing the acetone molecules to be relatively less stable in their solutions with carbon disulfide than they are in pure acetone. As a result, acetone-carbon disulfide mixtures are nonideal solutions. 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

Physical Equilibria and Solvent Selection. In order for two separate Hquid phases to exist in equiHbrium, there must be a considerable degree of thermodynamically nonideal behavior. If the Gibbs free energy, G, of a mixture of two solutions exceeds the energies of the initial solutions, mixing does not occur and the system remains in two phases. Eor the binary system containing only components A and B, the condition (22) for the formation of two phases is... 

Salting-out crystalli tion operates through the addition of a nonsolvent to the magma ia a crystallizer. The selection of the nonsolvent is based on the effect of the solvent on solubiHty, cost, properties that affect handling, iateraction with product requirements, and ease of recovery. The effect of a dding a nonsolvent can be quite complex as it iacreases the volume required for a given residence time and may produce a highly nonideal mixture of solvent, nonsolvent, and solute from which the solvent is difficult to separate. 

Perhaps the most significant of the partial molar properties, because of its appHcation to equiHbrium thermodynamics, is the chemical potential, ]1. This fundamental property, and related properties such as fugacity and activity, are essential to mathematical solutions of phase equihbrium problems. The natural logarithm of the Hquid-phase activity coefficient, Iny, is also defined as a partial molar quantity. For Hquid mixtures, the activity coefficient, y, describes nonideal Hquid-phase behavior. 

Density and Specific Gravity For binary or pseudobinary mixtures of hquids or gases or a solution of a solid or gas in a solvent, the density is a funcrion of the composition at a given temperature and pressure. Specific gravity is the ratio of the density of a noncompress-ible substance to the density of water at the same physical conditions. For nonideal solutions, empirical calibration will give the relationship between density and composition. Several types of measuring devices are described below. 

This approach to solution chemistry was largely developed by Hildebrand in his regular solution theory. A regular solution is one whose entropy of mixing is ideal and whose enthalpy of mixing is nonideal. Consider a binary solvent of components 1 and 2. Let i and 2 be numbers of moles of 1 and 2, 4>, and 4>2 their volume fractions in the mixture, and Vi, V2 their molar volumes. This treatment follows Shinoda. ... 

SOLUTION Reaction will take place in the direction that reduces the increase in pressure. (a) In the forward reaction, two N02 molecules combine to form one N204 molecule. Hence, compression favors the formation of N204. (b) Because neither direction corresponds to a reduction of gas-phase molecules, compressing the mixture should have no effect on the composition of the equilibrium mixture. (In practice, there will be a small effect due to the nonideality of the gases.)... 

The chloroform/polystyrene solution exhibits highly nonideal behavior. As shown by curve C in Figure 4, the x parameter for this solution rises from a low value to a high value as solvent concentration increases. However, as shown in Figure 5, the partial pressure of chloroform above a mixture of... 

The behavioural pattern of two immiscible solvents, say a and ib is essentially nonideal with respect to one another. Now, if a third substance is made to dissolve in a two-phase mixture of the solvents (i.e., a and 3 ), it may behave ideally in either phases provided its concentration in each individual phase is approximately small. Therefore, under these prevailing experimental parameters the ratio of the mole fractions of the solute in the two respective immiscible phases ( a and A) is found to be a constant which is absolutely independent of the quantity of solute present. It is termed as the Nernst Distribution Law or the Partition Law and may be expressed as follows ... 

The thermodynamic development above has been strictly limited to the case of ideal gases and mixtures of ideal gases. As pressure increases, corrections for vapor nonideality become increasingly important. They cannot be neglected at elevated pressures (particularly in the critical region). Similar corrections are necessary in the condensed phase for solutions which show marked departures from Raoult s or Henry s laws which are the common ideal reference solutions of choice. For nonideal solutions, in both gas and condensed phases, there is no longer any direct... 

We will see that the relationships that are derived for mixtures of ideal gases will form convenient bases for the treatment of nonideal gases and solutions. 

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