Bronsted-Guggenheim equation

Equation 1 is differentiated to calculate the ionic activity coefficients using the same technique as for non-electrolytes. Combining these ionic activity coefficients to form the mean ionic activity coefficients, y., we obtain the Bronsted-Guggenheim equations for two 1-1 electrolytes with a common ion ... 

For dilute solutions, Equations 4 and 5 reduce to the Bronsted-Guggenheim equations, and the parameters a23 and cu2 can be expressed in terms of the interaction parameters of tne Bronsted-Guggenheim theory. For concentrated solutions, Harned s rule is a simple empirical extension of the Brb nsted-Guggenheim theory. Thus, 1t 1s surprising how well the rule describes activity coefficients 1n highly concentrated solutions. 

The Bronsted-Guggenheim equations provide a highly satisfactory description of the activity coefficients in dilute solutions however, their empirical extension to concentrated solutions (Harned s rule) introduces several serious problems. 

A further approach is to consider a more specific form of ion interaction and replace Eq. (5.80) with die Bronsted-Guggenheim equation (Guggenheim and Turgeon 1955)... 

As our basis we chose the Bronsted-Guggenheim (6) equation for the mean activity coefficient YR x t ie electrolyte in a solution of several electrolytes having cation R and anion X. The mean activity coefficient Y R>x is given by... 

Bronsted-Guggenheim approach to multicomponent equations are only exact if pR,x is constant, the basic equations are reasonable exact if 3r,x is a slowly varying function of concentration and Harned s Rule (7) for mixed electrolytes through an empirical correlation does show such of an effect. 

The Bronsted-Guggenheim-Scatchard approach (abbreviated B-G-S equation in this document), (see section 6.1). 

The Harned coefficient, a12, is related to the Bronsted-Guggenheim parameters by means of the following equation ... 

Bronsted-Guggenheim-Scatchard specific ion interaction theory (SIT) (cf. Grenthe and Wanner 1989 Giridhar and Langmuir 1991 Nordstrom and Munoz 1994) is an ion- and electrolyte-specific approach to activity coefficients, which is, therefore, theoretically capable of greater accuracy than the Davies equation. The general SIT equation for a single ion, i, can be written... 

Figure 1.7 Activities coefficients of ions Na+ and Ch vs. concentration of NaCl calculated using various equations. Equation 1 - Debye-Huckel (1.76), 2 - Bronsted-Guggenheim-Scatchard (1.78), 3 - Pitzer (1.79) 4 - experimental values (Geological evolution..., 2005).

Lowry and co workers141,222 studied the mutarotation of tetra-O-methyl-a-D-glucopyranose, and found that the rate of reaction is low in dry pyridine or in dry cresol, but high in a mixture of the two solvents or in either solvent when moist. Lowry and Smith57 concluded that the mutarotation requires an acid catalyst and a base catalyst, and that amphoteric solvents are complete catalysts for the process, whereas aprotic solvents are not. They also showed that molecules of undissociated acids, cations of weak bases, and anions of weak acids have catalytic properties. Much the same concept was developed independently by Bronsted and Guggenheim,189,223 and came to be known as generalized acid and base catalysis. It was found that the rate of mutarotation of a sugar in the presence of a mixture of several catalysts may be represented by an equation of the type ... 

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