Debye-Hiickel extended equation, extrapolation

Fig. 2.3 was constructed using a K2-3 value at 250°C extrapolated from high-temperature data by Orville (1963), liyama (1965) and Hemley (1967). Ion activity coefficients were computed using the extended Debye-Hiickel equation of Helgeson (1969). The values of effective ionic radius were taken from Garrels and Christ (1965). In the calculation of ion activity coefficients, ionic strength is regarded as 0.5 im i ++mci-) (= mc -)- The activity ratio, an-f/aAb, is assumed to be unity. 

The standard emf E° of the cell was determined by means of an extrapolation technique involving a function of the measured emf E (which was measured experimentally), taken to the limit of zero ionic strength /. A linear function of I was observed when the Debye-Hiickel equation (in its extended form) (12) was introduced for the activity coefficient of hydrobromic acid over the experimental range of molalities m. With this type of mathematical treatment, the adjustable parameter became a0, the ion-size parameter, and a slope factor / . This procedure is essentially the same as that used in our earlier determinations (7,10) although no corrections of E° for ion association were taken into account (e = 49.5 at 298.15°K). 

Measurements of f are then taken for several HCl solutions at different molalities then a plot of vs. should yield a straight line in the range where the extended Debye-Hiickel equation holds. Extrapolation of this line to m = 0 yields and the slope is proportional to C. One then returns to Eq. (5) to find the r m) values for each set of measured f and m values. Very accurate measurements of the activity coefficient thus become available. 

However, it is recommended that one of the extended Debye-Hiickel equations (see Sections 10.10.1 and 10.10.2) should always be used if the ionic strength range is extended, and especially so when extrapolation of experimental data is needed. 

Wood, Smith and Jongenburger have suggested a method of extrapolation using an extended form of the Debye-Hiickel equation (see sect. 2.5.2 for discussion of forms of the Debye-Hiickel equation)... 

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