Hydrochloric acid, activity coefficient concentration cells

The e.m.p. s of the cell with transference Ag, AgCl(s) 0.1 N HCl HCl(c) AgCl(5), Ag at 25 C and the transference numbers of the hydrogen ion in the hydrochloric acid solution of concentration c mole liter , are given below [Shed-lovsky and Macinnes, J. Am. Chem. Soc., 58, 1970 (1935) Longsworth, ibid. 54, 2741 (1932)]. Utilize the data to calculate the activity coefficients of hydrochloric acid at the various concentrations. 

Since the hydrochloric acid may be regarded as being completely ionized, ch+ and Ccr may each be taken as equal to chci, the concentration of this acid in the cell further, the product of/h+ and/cr is equal to/nci, where /hci is the mean activity coefficient of the hydrochloric acid. It follows, therefore, that the quantity aH+Ocr, which is equal to (cH ccr)/iV/cr, may be replaced by chci/hci/h" upon inserting this result in equation (9) and rearranging, it is found that... 

A plot of some typical activity coefficient ratios as a function of the square root of the concentration is shown in Fig. 1. The emf data for hydrochloric acid are from the work of Harned and Ehlers10 on cells of the type represented by equation (21). The mean activity coefficient ratios were computed by arbitrarily assuming that the most dilute solution, 0.003205 normal (which is the most nearly ideal) has the activity coefficient of unity. It will be observed that as the concentration increases the mean activity coefficient, on this arbitrary basis, steadily decreases whereas, if the ions were perfect solutes the activity coefficient ratios would be unity throughout the concentration range. The shift of activity coefficient ratios in the range of concentration included in this plot is roughly typical of the behavior of uni-univalent electrolytes. Fig. 1 also shows the activity coefficient ratios of zinc sulphate from the work of Cowperthwaite and LaMer,11 based on emf measurements at 25°, of the cell... 

The computation of activity coefficients from A log j values will be illustrated for hydrochloric acid since in that case direct comparison can be made with the results of measurements on concentration cells without transference of the type described in Chapter 6. The relevant data are given in Table II and are from the work of Shedlovsky and Maclnnes.18 The emf data in the second column were obtained from a cell of the type illustrated in Fig. 4. The transference numbers in the third column were interpolated from the measurements of Longs-worth given in Table IV of Chapter 4. The A log f values in the fourth column were computed as described in the last paragraph. 

In addition to hydrochloric acid, the results for which have just been described in detail, the method utilizing concentration cells with transference has been used in obtaining the activity coefficients of potassium chloride,17 sodium chloride,18 silver nitrate,10 and calcium chloride.17 The resulting activity coefficients, /, and comparisons with equation (45), Chapter 7, of the Debye-Hiickel theory,... 

Values at other temperatures are given in Table V, Knowing Eq it is evidently possible to compute the activity coefficients, 7, of hydrochloric acid at the molality, m, from the potential E of the cell of equation (11). Such activity coefficients, as a matter of fact, agree very closely with those obtained from concentration cells with transference. This is indicated indirectly by Fig. 5, Chapter 8. 

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