Debye-type extrapolation

Low-temperature adiabatic heat capacity (Cp) measurements then were carried out on microcrystalline BABI to look for evidence of ordering below 2K 190 The expected anomaly was somewhat broad but readily seen in the right-hand chart of Fig. 25, with a maximum at 2 K the shape was consistent with expectations for a low-dimensional antiferromagnet. After subtraction of molecular lattice contributions by a Debye-type extrapolation from the higher... 

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). 

In order to obtain activity coefficients or standard potentials from measurements on cells of the type shown in equation (1) it is necessary, as described in Chapters 8 and 10, to make some form of extrapolation. Furthermore in the test of the Debye-Huckel relations for these solutions it has been found that, because of the higher molecular weight of the non-aqueous solvents, the difference between the activity coefficient, f, and the rational coefficient, f, based on Raoult s law, cannot be neglected, even below a concentration of 0.1 normal, as it usually can with aqueous solutions. This difference was overlooked by the workers just mentioned, who found only partial agreement of their results with the Debye-Huckel theory. Their data have therefore been recomputed as follows. For the ethyl alcohol solutions, for instance, a reference solution with a molality, mu of 0.09501, was chosen. The relation... 

In this equation AE1 is the difference in the potentials of two cells of the type given in equation (1), containing hydrochloric acid at the molalities in and Wi, and m is the molecular weight of the solvent. Using A log f, obtained from equation (3), instead of A log f, in an extrapolation of the type described on page 161, and an example of which is plotted in Fig. 5 of Chapter 8, values of i may be obtained. It is of considerable interest that plots of this type for the data for methyl and ethyl alcohol solutions are straight lines, up to concentrations of 0.07 and 0.05 normal respectively, within the limits of the experimental error, indicating that the Debye-Hiickel relation... 

---