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. R. H. FOWLER 443 NOTE ON THE INTERIONIC ATTRACTION THEORY OF DEBYE AND HUCKEL. BY D. L. CHAPMAN. Received 30th ,‘March, I 9 2 7. Attempts have from time to time been made to explain the divergence of the properties of strong electrolytes from the laws which approximately hold in the case of slightly ionised substances.The latest theory is that of Debye and Hiicke1.l The theory is simple and the assumed postulates few in number. To quote the words of A. A. Noyes who has given an account of the theory.2 ‘(The fundamental idea underlying the treatment of Debye and Hiickel is that owing to the electrical attraction between the positive and negative ions, there are on an average in the neighbourhood of any ion more ions of unlike sign than of like sign ; and that consequently when a solution is diluted, the separation of the ions involves doing internal work against this electrical attraction and a corresponding increase in the energy content of the solution.” I have found a difficulty in understanding that part of the theory which relates to ions of small dimension.To explain this difficulty it will be sufficient only to consider the case of a uni-univalent electrolyte. Debye and Hiickel determine the mean distribution of the ions surrounding a selected ion by the application of the so-called Boltzmann principle and Poisson’s equation. If I) is the mean potential at a point distant, r, from a central positive ion, then by the Boltzmann principle the number of positive and negative ions respectively present in an element of volume, dv, at the point will be ne- k t d ~ and nektdv, where n is the number of ions in unit volume of the solution, E the magnitude of the charge in electrostatic units of an ion, R Boltzmann’s constant, and t the absolute temperature.The density p of the charge at the point is obviously 2 9 PhySik. Z., 1923, 24, I8 j. ”. Amer. Chem. SOC., 1924, 46, 1080.444 INTERIONIC ATTRACTION THEORY 4 alG- n r ( e - h - ex). Substituting this value of p in Poisson’s equation, w e obtain - J2# ~ Y Z + Y a* a r I 4 y 3 D - e5?) . ’ (1) where D is the dielectric constant of the solvent. the exponential terms of the above equation, we obtain If we neglect all terms of higher order than the first in the expansion of - (4 a2# 2 3# 8rrnc2$ -+--=- a+ Y d~ Dkt The authors state in a footnote : “ We have investigated the influence - 6lG- kt and have thereby been For the I t is however difficult to see how the approximation can be justified in To ( 2 ) there is a simple general solution, namely, - of the higher terms in the expansion of ez - e able to show that this influence on the final result is very small.sake of brevity these calculations are omitted from this communication.” the case of very small ions. where C’ is zero since otherwise the potential would be infinity at an infinite distance, and the constant C has the value 5 because (as the authors state) the potential must reduce to that caused by the central ion when the concentration is infinitesimal and k = 0. Therefore for the particular case under consideration the solution becomes D’ From this result the potenti-a1 due to the atmosphere of ions surrounding the selected ion is found by subtracting from the potential due to the whole system that due to the central ion. We thus obtain - K Y -(e - I) DT which becomes when Y is small - E K D ’ and this is the potential due to the atmosphere of ions at the point occupied by the central ion.Then from the theory of potential the work required to 2 K remove all the ions in the solution to infinity is @-- Under the heading DY’ ‘‘ Ionendurchmesser verschwindend ” the authors gave the above result as the solution of the problem. Nevertheless if the ions are point charges they cannot (under the joint operation of the Boltzmann principle and of electrostatic forces only) be distributed in the manner portrayed. For con- sider two ions of opposite sign. The probability that the negative ion willD. L. CHAPMAN 445 be found at a distance between r and Y + dr from the positive ion is qxr2Ceymdr, and therefore the probability that it will be found in a sphere of radius Y having its centre at the positive ion is 4mC o r 2 e m L d ~ .The probability that it will be found in the shell of radii Y and R is ea 5' 62 R e2 r2eymdr. But 5 7 From which it follows that the ions cannot separate after having once united. Furthermore if the ions are not actually dimensionless but very small, the ratio of the probability that the negative ion would be found in the small sphere of radius Y to the probability that it would be found in the shell of radii Y and R would be given by the quotient obtained by changing the limits of the numerator of (5) from o and Y to c and Y where E is a very small distance, and this quotient would be a large quantity provided that R was of moderate dimensions. Therefore the time during which the ions are united would be very large in comparison with the time during which they are dissociated. Such a distribution could not result in potentials given by equation (4) or to the densities of the two classes of ions calculated from these potentials. The inconsistency of the conclusion expressed by equation ( 5 ) with the result of Debye and Huckel can be accounted for by the fact that they made the assumption that d! 9 k t kt A 2 4 . e - e -__ K t