DILUTE SOLUTIONS OF NONELECTROLYTES

We will proceed in our discussion of solutions from ideal to nonideal solutions, limiting ourselves at first to nonelectrolytes. For dilute solutions of nonelectrolyte, several limiting laws have been found to describe the behavior of these systems with increasing precision as infinite dilution is approached. If we take any one of them as an empirical mle, we can derive the others from it on the basis of thermodynamic principles. 

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Van t Hoff introduced the correction factor i for electrolyte solutions the measured quantity (e.g. the osmotic pressure, Jt) must be divided by this factor to obtain agreement with the theory of dilute solutions of nonelectrolytes (jt/i = RTc). For the dilute solutions of some electrolytes (now called strong), this factor approaches small integers. Thus, for a dilute sodium chloride solution with concentration c, an osmotic pressure of 2RTc was always measured, which could readily be explained by the fact that the solution, in fact, actually contains twice the number of species corresponding to concentration c calculated in the usual manner from the weighed amount of substance dissolved in the solution. Small deviations from integral numbers were attributed to experimental errors (they are now attributed to the effect of the activity coefficient). 

In the preceding chapters we considered Raoult s law and Henry s law, which are laws that describe the thermodynamic behavior of dilute solutions of nonelectrolytes these laws are strictly valid only in the limit of infinite dilution. They led to a simple linear dependence of the chemical potential on the logarithm of the mole fraction of solvent and solute, as in Equations (14.6) (Raoult s law) and (15.5) (Heiuy s law) or on the logarithm of the molality of the solute, as in Equation (15.11) (Hemy s law). These equations are of the same form as the equation derived for the dependence of the chemical potential of an ideal gas on the pressure [Equation (10.15)]. 

We shall see in Chapter 17 that it is frequently difficult to obtain reliable data at very low concentrations to demonstrate experimentally that Henry s law is followed in dilute solutions of nonelectrolytes. 

The activity coefficients of solute and solvent are of comparable magnitudes in dilute solutions of nonelectrolytes, so that Equation (17.33) is a useful relationship. But the activity coefficients of an electrolyte solute differ substantially from unity even in very dilute solutions in which the activity coefficient of the solvent differs from unity by less than 1 x 10 . The data in the first three columns of Table 19.3 illustrate the situation. It can be observed that the calculation of the activity coefficient of solute from the activity coefficient of water would be imprecise at best. 

Oiffusivity The kinetic theory of liquids is much less advanced than that of gases. Therefore, the correlation for diffusivities in liquids is not as reliable as that for gases. Among several correlations reported, the Wilke-Chang correlation (Wilke and Chang, 1955) is the most widely used for dilute solutions of nonelectrolytes,... 

All the laws discussed so far are valid for dilute solutions of nonelectrolytes. If there is a solute that is an electrolyte, the ions contribute independently to the effective molal (or molar) concentration. The ions interact and, therefore, the effects are not as large as predicted by the mathematical equations. 

Notwithstanding the considerations of Section 2.12.1, the use of the bulk dielectric constant of water for dilute solutions of nonelectrolyte is not very inaccurate in the region outside the primary solvation sheath. The point is that in this region (i.e., at distances > 500 to 1000 pm from the ion s center), there is neghgible structure breaking and therefore a neghgible decrease in dielectric constant from the bulk value. 

The above laws are valid only for dilute solutions of nonelectrolytes. For electrolyte solutions each ion contributes independently to the effective molality or molar concentration. On account of the electrical interactions between ions, however, none of the effects is as large as would be predicted on the basis of simple counting of ions. 

At this stage it is worthwhile to describe the constitution of ionic solutions in some detail. The solute in dilute solutions of nonelectrolytes is adequately described thermo-... 

Fig. 5.2. Diffusivity correlation for dilute solutions of nonelectrolytes. C. R. Wilke [Chem. Eng. Progress 46, 218 (1949). Reproduced with the permission of the American Institute of Chemical Engineers.]...

Wilhelm, W. (1992) Thermodynamics of Solutions, Especially Dilute Solutions of Nonelectrolytes. In Molecular Liquids New Perspectives in Physics and Chemistry, J. J. C. Teixeira-Dias, Ed. Kluwer Academic Publishers pp 175-206. 

Thus, in an ideal-dilute solution of nonelectrolytes each solute obeys Henry s law and the solvent obeys Raoult s law. 

Consider the following expressions for chemical potentials in ideal mixtures and ideal-dilute solutions of nonelectrolytes. The first equation is a rearrangement of Eq. 9.5.3, and the others are from earUer sections of this chapter. ... 

His measurements with dilute solutions of nonelectrolyte solutes in various other solvents, including benzene, ethanol, and water, gave the same results. He was pleased that his measurements confirmed the theory of solutions being developed by J. H. van t Hoff. 

The ratio n jn n has the form of an equilibrium constant for formation of activated complex. For systems in which the activity of the various species equals their concentration (dilute gases, dilute solutions of nonelectrolytes) (9.41) defines a totally empirical function, the activation equilibrium constant K iT),... 

Estimates of the diffusivity in the absence of data cannot be made with anything like the accuracy with which they can be made for gases because no sound theory of the structure of liquids has been developed. For dilute solutions of nonelectrolytes, the empirical correlation of Wilke and Chang [23, 24] is recommended. ... 

Molar mass determination by freezing-point depression or boiling-point elevation has its limitations. Equations (14.5) and (14.6) apply only to dilute solutions of nonelectrolytes, usually much less than 1 mol kg . This requires the use of special thermometers so that temperatures can be measured very precisely, say to 0.001 °C. Because boiling points depend on barometric pressure, precise measurements require that pressure be held constant. As a consequence, boiling-point elevation is not much used. The precision of the freezing-point depression method can be improved by using a solvent... 

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