Activity coefficients Debye-Huckel value

How Well Does the Debye-Huckel Theoretical Expression for Activity Coefficients Predict Experimental Values ... 

This relation has been demonstrated in the case of very dilute electrolytes (where the Debye-Huckel theory applies) by replacing the individual activity coefficients by their value as given by the limiting law of Debye, we obtain... 

At moderate ionic strengths a considerable improvement is effected by subtracting a term bl from the Debye-Huckel expression b is an adjustable parameter which is 0.2 for water at 25°C. Table 8.4 gives the values of the ionic activity coefficients (for z, from 1 to 6) with a taken to be 4.6A. 

While this relationship is simple, it introduces more errors because the activity coefficient (or more normally, the mean ionic activity coefficient y ) is wholly unknown. While y can sometimes be calculated (e.g. via the Debye-Huckel relationships described in Section 3.4), such calculated values often differ quite significantly from experimental values, particularly when working at higher ionic strengths. In addition, ionic strength adjusters and TISABs are recommended in conjunction with calibration curves. 

The activity a and concentration c are related by a = (c/c ) x y (equation (3.12)), where y is the mean ionic activity coefficient, itself a function of the ionic strength /. Approximate values of y can be calculated for solution-phase analytes by using the Debye-Huckel relationships (equations (3.14) and (3.15)). The change of y with ionic strength can be a major cause of error in electroanalytical measurements, so it is advisable to buffer the ionic strength (preferably at a high value), e.g. with a total ionic strength adjustment buffer (TISAB). 

Figure 22. Mean ionic activity coefficients, y , for various salts in water, mj = 0-2 at 298 K the dotted line indicates the value required by the Debye-Huckel limiting law (Desnoyers and Jolicoeur, 1969).

Measurements of emf (electromotive force) are to be made with this cell under reversible conditions at a number of concentrations c of HCl. From these measurements relative values of activity coefficients at different concentrations can be derived. To obtain the activity coefficients on such a scale that the activity coefficient is unity for the reference state of zero concentration, an extrapolation procedure based on the Debye-Huckel limiting law is used. By this means, the standard electrode emf of the silver-silver chloride electrode is determined, and activity coefficients are determined for all concentrations studied. 

Utilize the known values of the Debye-Huckel constants A and B for water to calculate the mean activity coefficients for 1 1, 1 2, and 2 2-valent electrolytes in water at the ionic strengths 0.1 and 0.01 at 25 °C. The mean distance of closest approach of the ions a may be taken as 300 pm in each case. (Constantinescu)... 

Cupric ion activities and cupric ion concentrations were determined using the Nernst equation from the differences in potential between the test solutions and a standard solution consisting of 10-5 M CUSO4 and 0.01 M KNO3 at pH 5.4 + 0.3. Values of cupric ion activity in test solutions were based on a cupric ion activity coefficient of 0.68 in the standard solution as calculated from the extended Debye-Huckel equation. For measurements in defined solutions containing 0.01 M KNO3 or 0.01 M NaHC03 cupric ion concentrations could be directly computed via the Nernst equation because activity coefficients were the same in both test and standard solutions. 

Values of K, the thermodynamic association constants are given at 25°. The concentrations of ionic species in the solutions at any time can be determined from mass balance, electroneutrality, and the appropriate equilibrium constants as described previously (19, p, 85-92) by successive approximations for the ionic strength. The activity coefficients of Z-valent ionic species may be calculated from an extended form of the Debye-Huckel equation such as that proposed by Davies (20, p. 34-53). 

Calculate the activity coefficients of the silver iodate in the various solutions plot the values of — log / against Vv to see how far the results agree with the Debye-Huckel limiting law. Determine the mean ionic diameter required to account for the deviations from the law at appreciable concentrations. 

Table 3.4 lists some activity coefficients as calculated from the extended Debye-Huckel limiting law for various values of /. In dilute solutions, such calculated values agree well with experimental data for mean activity coefficients of simple electrolytes. At higher concentrations, the Davies equation usually represents the experimental data better. 

The effect of temperature on ion activity coefficients is largely predicted by changes in the value of A, which is proportional to - log y, in the Debye-Huckel equation. The value of A increases from 0.492 to 0.534 between 0 and 50°C. Thus, activity coefficients become smaller with increasing temperature. Because A is multiplied by z in the Debye-Hiickel equation, the effect of temperature on activity coefficients is greatest for multivalent ions. 

HA-, and A=. The pKa values of the buffer species, H2A, HA-, and A-, could be adjusted to represent any appropriate buffer. Activity coefficients were calculated from a modified Debye-Huckel limiting law (26). 

The Debye-Huckel theory gives a calculation of the activity coefficients of individual ions. However, although the individual concentrations of the ions of an electrolyte solution can be measured, experiment cannot measme the individual activity coefficients. It does, however, furnish a sort of average value of the activity coefficient, called the mean activity coefficient, for the electrolyte as a whole. The term mean is not used in its common sense of an average quantity, but is used in a different sense which reflects the number of ions which result from each given formula. Such mean activity coefficients are related to the individual activity coefficients in a manner dictated by the stoichiometry of the electrolyte. 

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