Debye-Htickel equation

With the Debye-Htickel equation (7.44), we can complete Example 9.4 and calculate the solubility of AgCl in (b) 0.010m KNOj and (c) 0.010m KC1. 

Statistical thermodynamics takes into account the microscopic structure of matter and how it is constituted. According to - Boltzmann the entropy can be correlated with the microscopic disorder of the system. Beside the Boltzmann distribution formula (- Debye-Htickel equation) other statistics (e.g., - Fermi-Dirac statistics) are of importance in electrochemistry (- semiconductors, -> BCS theory). 

For incompletely dissociated electrolytes this involves a knowledge of the degree of dissociation, which may not always be available with sufficient accuracy. It is for this reason that the Debye-Htickel equations are generally tested by means of data obtained with strong electrolytes, since they can be assumed to be completely dissociated. It is probable that some of the discrepancies observed with certain electrolytes of high valence types are due to incomplete dissociation for which adequate allowance has not been made. 

Although the structure of the transition state is not given, it must have a charge of + Zg. Using the Debye-Htickel equation in Equation (2.3.18) gives ... 

For solutions dilute enough for the Debye-Htickel equation to be applicable, the plot of log (t /7r) + A c against Qog 7r + log (t /7r)]Vc should be a straight line, the intercept for c equal zero giving the required value of -- log 7r, by equation (39.68). The values of log (y /yB,) are obtained from equation (39.67), and log yr, which is required for the purpose of the plot, is obtained by a short series of approximations. Once log yn has been determined, it is possible to derive log 7db for oy solution from the known value of log (y /yn)> The mean ionic activity coefficient of the given electrolyte can thus be evaluated from the e.m.f. s of concentration cells with transference, provided the required transference number information is available. ... 

Use the Debye-Htickel equation (for A, see Exercise 5), in conjunction with a graphical procedure, to evaluate the true dissociation constant from the K values. (The result is 1.845 X lO"". )... 

In sufficiently dilute solutions, the activity of a nonelectrolyte is directly proportional to its concentration, whereas, according to the DEBYE-HtiCKEL equation (1), the activity of ions in electrolyte solutions is an exponential function of the ionic strength. This proportionality factor, which is different for each substance and ion, changes also with the solvent. The state of a solute (ion or nonelectrolyte molecule) is different in each solvent. A reaction with the solvent takes place, this change usually being termed solvation (or hydration in aqueous medium). The term solvation has no stoichiometric significance, but rather indicates a physical process (polarization). 

Thus the Debye-Htickel equation for multivalent ions becomes... 

The Debye-Htickel equation logjo y, = —Az v7/(1 + /7) holds for moderate concentra-... 

For higher concentrations, Aiassoc will have to be corrected for non-ideality by including activity coefficients calculated from the Debye-Htickel equation. 

Prankerd RJ, Determination of Bie pXa of phenylbutazone, 4Bi Year Undergraduate Research Project, Department of Pharmacy, University of Otago, Dimedin, New Zealand, 1973. NB The Guggenheim modification of Bie Debye-Htickel equation was used to account for ionic strengBi effects by extrapolating to / = 0.00. 

Data compilation, pKa values and, 26-28 Davies modification, 21-22 Debye-Htickel equation, 8,11 Davies modification of, 21-22 Guggenheim modification of, 10, 21 Dielectric constant (s), 20... 

The model relates the excess total Gibbs energy of a system to an equation similar in principle to the virial equation we saw for gases in 13.5, in which the first term is not the ideal gas expression, but a simplified form of the Debye-Htickel equation. The general equation used by Pitzer (from which many others are derived by differentiation) is... 

The first virial coefficient /(/) is some function of the ionic strength and is not 0 as it would be for an ideal solution, but is in fact a version of the Debye-Htickel equation, which represents departure from ideality in very dilute solutions. The following term is a function of the interactions of all pairs of ions, and the third term a function of the interactions of ions taken three at a time. The second coefficient. Ay, is a function of ionic strength, but the third coefficient ju-y - is considered to be independent of ionic strength and equals zero if /, j, and k are all anions or cations. Later extensions to the model published by Pitzer and co-workers allow for an ionic strength dependence to the third coefficient. Pitzer (1987) and Harvie and Weare (1980) note that higher virial coefficients are required only for extremely concentrated solutions, so the series is stopped at the third coefficient. 

For ionic strengths up to about 0.01, activity coefficients from the Debye-Htickel equation lead to results from equilibrium calculations that agree closely with experiment even at ionic strengths of 0.1, major discrepancies are generally not encountered. At higher... 

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