118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 396 MOBILITIES OF IONS I N METHYL ALCOHOL NOTES ON THE DEBYE-HUCKEL THEORY. BY H. HARTLEY AND R. P. BELL. Eeceived 9th April, 1927. The Debye-Huckel theory of the conductivity of strong electrolytes postulates that the decrease in ionic mobility with increasin, 0 concentra- tion is due entirely to interionic forces and to cataphoresis of the solvent, the electrolyte being completely dissociated at all concentrations a t which the theory is applicable. In water it is probable that this latter condition is fulfilled for most salts in dilute solution, although certain salts of mercury and cadmium are exceptions; but in non-aqueous solvents the formation of complex ions or of undissociated molecules even in dilute solutions is a much more general phenomenon.ThusH. HARTLEY AND R. P. BELL 397 discrepancies between the Debye-Huckel theory and experimental results may mean Bther that the theory is incorrect, or that the electrolytes in question are not completely dissociated. I t is therefore a matter of great interest to see whether there is a substantial body of evidence in accord with the theory. If this is so, deviations from the theory might be ascribed to abnormal behaviour of the electrolyte and might even be used to detect lack of complete dissociation. Debye and Huckel have made a comprehensive survey of the con- ductivity data for dilute aqueous solutions, and have shown that they are in fair agreement with their theory.Similar comparisons for non- aqueous solvents are more difficult, as the experimental data are far less complete and homogeneous, but as such a comparison affords a more searching test of this general applicability of the theory in view of the large differences in properties between the solvents, we have examined a considerable number of the conductivity data for dilute salt solutions in thirteen different solvents, in order to see how far they are in agree- ment with the theory. Owing to the absence of reliable data for poly- valent ions the comparison is limited to uni-univalent salts. For elec- trolytes of this type Debye and Huclcel’s equation can be written in the form, where K, and K, are universal constants for all solvents varying only with the temperature, D is the dielectric constant of the solvent, 2, and I , being the mobilities of the cation and anion, b is the harmonic mean of the ionic radii and C is the molecular concentration. Obviously the first test of this equation is to see whether there is in all cases a linear relation between the equivalent conductivity and the square root of the concentration, corresponding to the empirical expression found by Kohlrausch to hold for dilute aqueous solutions :- - (2) A, = A, - ~ ~ ’ 1 2 .Hartley and Frazer have shown that this relation does hold for eighteen uni-univalent salts in methyl alcohol up to 0.002 N , and subsequent work has confirmed this for a large number of other salts. Walden, Ulich, and Busch have found the same relation for salts in acetone up to oaooj N! while Ulich has recently used the square root formula in recalcu- lating values of A,, in a number of solvents. We have examined a large number of experimental results in the thirteen non-aqueous solvents mentioned in Table I.by graphic methods, and we find that in general the more accurate and concordant are the data, the more closely do they confirm to the square root relation in dilute solution. In view of the wide range of solvents and the number of salts examined, it is a remark- able fact that the square root law was found to hold so generally. The dilution a t which the linear relationship ceases varies with the solvent, the solute and the temperature. It is interesting to note that in some non-aqueous solvents certain lithium salts do not obey this relation or do so only a t exceptionally high dilutions ; lithium iodide, however, shows no such abnormality, and there is little doubt that the exceptional behaviour of lithium salts is due to the formation of complex 2 7398 NOTES ON THE DEBYE-HUCKEL THEORY ions even in dilute solutions, as in non-aqucous solvents the tendency to form complexes appear t o be less with the iodine ion than with the other halogens or the nitrate ion.Comparatively little work has been done on conductivity in non- aqueous solvents over a wide range of temperature, but the measurements of Duperthuis in pyridine and various alcohols between o0 C. and 80" C. indicate that the range of applicability of the square root relation is diminished a t higher temperatures.However, it must be remembered that the difficulties in the way of accurate conductivity measurements in dilute solution are greatly increased when the temperature exceeds 25" C. Since it seems clear that the square root relation is obeyed a t high dilutions within the limits of experimental error, except where there is reason to suspect the absence of complete dissociation, it is possible to apply a further test t o the theory by considering the slope of the con- ductivity-concentration curve. This depends inter alia on '' b," the harmonic mean of the ionic radii, and by combining equations ( I ) and (2) we have for a uni-univalent electrolyte, b = (xo-- X K, D'io D81n w l ) * (3) I t is therefore possible to calculate values for b if A,, x, K,! K,, D and w1 are known.But Debye and Hucke! assume that a t infinite dilution the motion of the ions obeys Stokes' law, and therefore the radius of the ion Y can be calculated from the equation, where 7 is the viscosity of the solvent. If I, is the mobility of the ion a t infinite dilution, equation (4) becomes 8.15 x I O - ~ 1, = 7x5- ' or considering the sum of the mobilities so that from the known values of A, and 7, values of the harmonic mean of the ionic radii can be calculated and compared with the values of b obtained from the slope of the conductivity curve. The results of such calculations for potassium, sodium, and tetraethyl- ammonium iodides in fourteen solvents are given in Table I. Owing to lack of knowledge of the transport numbers in propyl, isobutyl, and isoamyl alcohol, in acetophenone, sulphur dioxide and ammonia, some uncertainty attaches to the values of b in these solvents.The transport number has been assumed to be 0.5 ; if the ions moved with unequal speeds the effect would be to reduce the value of b (Debye), but in isobutyl alcohol for example, even if one ion had three times the mobility of the other, the value of b for sodium iodide would only be reduced from 13.0 to 10.0. In Table I. the solvents are arranged in the order of their dielectric constants, which are given in column I ; column 2 gives their viscositiesTetraethylammonium Iodide. . . . . - . . . . . . . . . . . Potassium Iodide. 81 35 30 26 26 26 22 22 22 21 21 21 19 '9 I 8 16 16 15'5 13.6 12'3 12.3 Sodium Iodide. Solvent. __ b x id Debye 'I. bx 10s Debye I X I O R ;toke.X . 6 X 101 Debye ' X 108 #tokes. 1.19 2'34 2'55 2.92 - - - - 1-84 2.84 2.78 - - - 3'72 445 1.65 2.48 2'42 - - - 6.57 3.69 3'22 6.30 4.67 4.19 3'46 4'22 5'56 4'34 13.0 17.2 24.6 - 6.78 28-6 7-17 4'47 467 - __ - 2'44 3-07 3-08 2-53 3-30 3'27 2'05 2.86 2-84 2-80 3'34 3.64 2.78 4-60 3-70 2-62 2.82 - 2-2 I - Water . . . Acetonitrile . . Methyl alcohol . Ethyl alcohol . Benzonitrile . . Propyl alcohol . Ammonia . . Acetone . . ? 3 3 , > I 3 , 3, . . I , . . Isobutyl alcohol Me&yI ethyyketonc Isoamyl alcohol . Aretophenone . Sulphur dioxide . Pyridine . . 0.00893 0.00545 0~0109 0-0125 0.00256 000316 0.0035 I - 0-0222 - - - 0-0332 - 0.00402 0.0377 0'0 I80 000452 woo958 - - (a) Duperthuis (20°), Dissertation, Lausanne, ( e ) Gyr (~ 15"), Dissertation, Lausanne, 1907.(f) Kohlrausch (IS'), Sifzungsder. Preuss. Akad., (6) Dutoit and Levier ( 2s0), J. Chim. PAYS., 3, (g) Frankin and Kraus (- 33'5O), Am. ChePz.J., (A) Kraus and Bishop (18"), J. Am. Chem. Sor., (i) Morgan and Lammert (2so), 1. Am. Chem. 1908. 435, '905. 6, 545, Igo8. 109A, 351, 1925. 36, I , 1899. (66) Dutoit and Rappeport ( 2 s 0 ) , J . Cham. PAYS.. 23,277,1800 ; 2 4 , 8 3 , 1 9 ~ . (c) Frazer and Hartley (q0), Proc. Roy. Soc., (d) Gagnaux (2s0), Dissertafion, Lausanne, soc.. 46, 1117, 1924. 44, 2204, 1922. 1907. ( k ) Nicollier (2s0), Dissertation, Lausanne. (1) Ottiker (IS"), Dissertation, Lausanne. (m) Philip and Courtman ( z ~ " ) , J. Ckem. Soc. (0) Walden (25'7, Das Leitwermogen der &sun- ( p ) W'alden, Ulich and Busch (z~"), Z.physik. 97, 1268, 1910. gen, 11, 1924. Chern., 123,429, 1926.400 IONIEATION OF SOME TYPICAL STRONG ELECTROLYTES at 25’ or a t the highest temperature for which conductivity data are given. Under the heading of each salt the first column gives the value of A, a t the temperature shown in the reference to the author a t the foot of the table, the second column the value of x in equation (21, the third column the value of b calculated from the slope of the curve, the fourth column the value of b calculated by Stokes’ law. In some cases values are given for the same salt obtained by different observers in order to show the degree of concordance of independent determinations. The results in the table do not show any well-marked regularity, though it is clear that the values of b calculated from Stokes’ law rarely differ from one another by more than a factor of two, while the values from Debye’s equation show much larger variations, and in general show greater divergencies from the Stokes’ values in solvents of low dielcctric constant, although there are apparent exceptions to this in ammonia, methyl ethyl ketone, and for sodium iodide in pyridine.The contrast between the iodides of sodiuni and potassium in this solvent is curious. Likewise the difference between the behaviour of tetraethylammonium iodide and the two alkali metal iodides in aretonitrile. The table cer- tainly einphasises the need for further experimental work to confirm such differences and to make the data more complete. The rough correspondence between the two sets of values for h in all solvents with a dielectric constant greater than 20 is evidence of the essential correctness of Debye and Huckel’s theory. In view of the two methods of calciilation it is perhaps remarkable that they agree so well. The abnormally large values of b found in the higher alcohols, for instance, shows that conformity to the square root relation is no guarantee that the variation of the conductivity with concentration a41 be in accord- ance with Debye’s equation. The same point emerges from Walden, Ulich and Busch’s work in acetone, where in spite of the validity of the square root relation, the slopes of the curves vary to a much greater extent than could be accounted for by Debye’s theory, and indicate probably lack of complete ionization.