Dilute solution nonelectrolyte solutes

For dilute solutions, solute-solute interactions are unimportant (i.e., Henry s law will hold), and the variation of surface tension with concentration will be linear (at least for nonelectrolytes). Thus... 

A logical division is made for the adsorption of nonelectrolytes according to whether they are in dilute or concentrated solution. In dilute solutions, the treatment is very similar to that for gas adsorption, whereas in concentrated binary mixtures the role of the solvent becomes more explicit. An important class of adsorbed materials, self-assembling monolayers, are briefly reviewed along with an overview of the essential features of polymer adsorption. The adsorption of electrolytes is treated briefly, mainly in terms of the exchange of components in an electrical double layer. 

Here, i, the van t Hoff i factor, is determined experimentally. In a very dilute solution (less than about 10 3 mol-I. ), when all ions are independent, i = 2 for MX salts such as NaCl, i = 3 for MX2 salts such as CaCl2, and so on. For dilute nonelectrolyte solutions, i =l. The i factor is so unreliable, however that it is best to confine quantitative calculations of freezing-point depression to nonelectrolyte solutions. Even these solutions must be dilute enough to be approximately ideal. 

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). 

The value for the van t Hoff factor, i, for strong electrolytes in dilute solution approximates the total number of ions present in a formula unit. So, / = 2 for KC103 and / = 3 for CaCl2. The value of / for the weak electrolyte such as CH3COOH is between 1 and 2. The value of / for a nonelectrolyte such as CH3OH is 1. 

In moderately dilute solution, with a salt concentration e8 and a nonelectrolyte of concentration (the solubility), the following expressions have been experimentally justified ... 

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. 

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. 

According to modem theory, many strong electrolytes are completely dissociated in dilute solutions. The freezing-point lowering, however, does not indicate complete dissociation. For NaCl, the depression is not quite twice the amount calculated on the basis of the number of moles of NaCl added. In the solution, the ions attract one another to some extent therefore they do not behave as completely independent particles, as they would if they were nonelectrolytes. From the colligative properties, therefore, we can compute only the "apparent degree of dissociation" of a strong electrolyte in solution. 

In the following sections we discuss some aspects of solute-solvent interactions. This discussion is not a complete, current survey but rather an attempt to bring together some divergent experimental facets of water-solute interactions which often are not discussed by either theoreticians or experimentalists. For more detailed, general information see Refs. 18, 19, 20, and 73. The two essential points we wish to make are (1) even in moderately concentrated solutions, there is evidence for the persistence of structural elements of the type found in pure water and especially in dilute solutions (2) there is evidence for what appears to be discrete changes with concentration in the behavior of some aqueous solutions of both electrolytes and nonelectrolytes, and for nonelectrolytes this may be caused by the existence of discrete sites available to the solute molecules. Unfortunately, we shall be able to discuss only electrolyte-water interactions to any extent the often more interesting nonelectrolyte-water interactions will be discussed in a later paper. This is all the more... 

Reaction (15.37) is usually studied in dilute solution (ionic strength <0.1). If, as in our examples, the ligand is a nonelectrolyte, then it is a reasonable approximation to assume that tl 1. It is also not unreasonable to expect 7 mlj 7m v+ in these dilute solutions, since ions with the same charge behave in a somewhat similar manner, as suggested by the Debye-Htickel theory. Hence, /7 1 and K = Kc. Because we will not be overly concerned with quantitative results of high accuracy in this discussion, we will assume this approximation is sufficient and use K for Kc. It is not absolutely necessary that we do so, however, since corrections can be made for /7. 

Solutions are usually classified as nonelectrolyte or electrolyte depending upon whether one or more of the components dissociates in the mixture. The two types of solutions are often treated differently. In electrolyte solutions properties like the activity coefficients and the osmotic coefficients are emphasized, with the dilute solution standard state chosen for the solute.c With nonelectrolyte solutions we often choose a Raoult s law standard state for both components, and we are more interested in the changes in the thermodynamic properties with mixing, AmjxZ. In this chapter, we will restrict our discussion to nonelectrolyte mixtures and use the change AmjxZ to help us understand the nature of the interactions that are occurring in the mixture. In the next chapter, we will describe the properties of electrolyte solutions. 

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,... 

The osmotic pressure n of a dilute solution of a nonelectrolyte is given by an equation formally equivalent to the ideal gas law ... 

The vapor pressure of the solvent reduces as the concentration of the solute increases (inverse relationship). Generally, the discussions of vapor pressure are with reference to the concentration of nonvolatile solutes and, therefore, we are dealing with the tendency of only the solvent to leave the solution. Experimentation has determined that dilute solutions of equal molality, using the same solvent and different nonelectrolytes (no dissociation) as solutes, show the same amount of vapor pressure lowering (depression) in every case. 

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. 

For any dilute solution, whether electrolyte or nonelectrolyte, the deviations from any one of the laws of the dilute solution are equal to the deviations from any of the others on a fractional or percentage basis. That is,... 

On the other hand the standard state of a dissolved substance, which behaves in the solvent as a nonelectrolyte, is defined as its state in a hypothetical ideal solution containing one mole of the substance in 1000 grams of solvent (i. e. with a concentration in terms of molality, to = 1). In this solution some properties of the dissolved substance are the same as in an infinitely diluted solution In other cases the hypothetical standard state of the dissolved substance is used in which 1 mole of the substance is contained in one liter of the ideal solution (i. o. the concentration is expressed in terms of molarity, c — 1). 

Osmotic pressure may be considerable for even highly dilute solutions for example, for an aqueous nonelectrolyte solution with x2 = 0.001 at 200 K, we have... 

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. 

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