Debye-Huckel theory quantitative

Then, about 1904, it was pointed out by A. A. Noyes in this country and Sutherland in England that many properties of solutions of salts and strong acids (such as their color) suggest that most salts and strong acids are completely ionized in dilute solution. This view has been generally accepted since 1923, when a quantitative theory of the interactions of ions in solution was developed by Debye and Hiickel. This theory is called the Debye-Huckel theory of electrolytes. 

Debye-Huckel theory. A theory advanced in 1923 for quantitatively predicting the deviations from ideality of dilute electrolytic solutions. It involves the assumption that every ion in a solution is surrounded by an ion atmosphere of opposite charge. Results deduced from this theory have been verified for dilute solutions of strong electrolytes, and it provides a means of extrapolating the thermodynamic properties of electrolytic solutions to infinite dilution. 

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 7l 1. It is also not unreasonable to expect 7 ML 7m,/+ in these dilute solutions, since ions with the same charge behave in a somewhat similar manner, as suggested by the Debye-Huckel theory. Hence, Jy 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 Jy. 

The activity is related to the concentration (moles/ liter) of the compound (X) by Eq. 5.13, where y is the activity coefficient. Gamma is always less than one, and is an empirically determined factor that mediates the concentration of the compound to reflect the amount of compound free in the solution. The activity coefficient of ions can be estimated from Debye-Huckel theory. Consult any quantitative analysis textbook to get a thorough discussion of activities and activity coefficients. It is particularly important to use activities in place of concentrations for concentrated solutions in water, and for nonaqueous solvents, which are the next two topics. 

In dilute solutions it is possible to relate the activity coefficients of ionic species to the composition of the solution, its dielectric properties, the temperature, and certain fundamental constants. Theoretical approaches to the development of such relations trace their origins to classic papers by Debye and Huckel (6-8). For detailed treatments of this subject, refer to standard physical chemistry texts or to treatises on electrolyte solutions [e.g., that by Hamed and Owen (9)]. The Debye-Hiickel theory is useless for quantitative calculations in most of the reaction systems encountered in industrial practice because such systems normally employ concentrated solutions. However, it may be used together with transition state theory to predict the qualitative influence of ionic strength on reaction rate constants. 

It may be pointed out in conclusion that the conductance phenomena with very high frequency currents and at high potential gradients provide striking evidence for the theory of electrolytic conductance, based on the existence of an ionic atmosphere surrounding every ion, proposed by Debye and Huckel and described in this chapter. Not only does the theory account qualitatively for conductance results of all types, but it is also able to predict them quantitatively provided the solutions are not too concentrated. 

Going beyond solutions of electrolytes in water, several other possibilities need consideration electrolytes in nonaqueous solvents, nonelectrolytic behavior in solutions, and nonelectrolytes in nonaqueous solvents. None of the theories proposed for the quantitative prediction of solution behavior has been as successful as that of Debye and Huckel for dilute ionic aqueous solutions. Nevertheless, general trends can be predicted. 

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