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XXIII. Intelligence and Miscellaneous Articles. 



ON THE KINETICS OF BODIES IN SOLUTION. BY W. NERNST. 



QINCE Van t'Hoff disclosed the great analogy of the constitution 

 ^ of dissolved bodies in dilute solution with the gaseous state, it 

 becomes possible, as the author shows, to explain diffusion on purely 

 mechanical principles. The most essential difference from gaseous 

 diffusion lies in the much smaller velocity of diffusiou of solutions, 

 which justifies the inference that the solvent offers an enormous 

 resistance to the moving molecules. 



The author investigates in the first place the diffusion of non- 

 electrolytes. Here the driving force is solely the alteration of 

 osmotic pressure p with the locality x. Since p is proportional to 

 the concentration c (number of (/-molecules in 1 cub. centim.), and 

 thus p =p c, we get for the quantity of substance in g molecules, 

 which travels through the section q of a cylinder in the time z : — . 



qzp> Q dc 

 " K dec' 



K is the force which imparts unit velocity to a molecule in solution. 

 This law, which is of the same form as the well-known one stated 

 by Fick, renders it possible to calculate K in absolute measure, as 

 the author shows by a few examples. 



Still more interesting is the calculation of the diffusion for 

 solutions of electrolytes ; for the coefficient of diffusion may here 

 be calculated in absolute measure, on the basis of the hypothesis of 

 dissociation propounded by Arrhenius and others. By means of 

 Ohm's law, Kohlrausch, as is well known, has calculated from the 

 galvanic migration of the ions, which is solely due to electrostatic 

 forces, the force which imparts to a g-ion in aqueous solution unit 

 velocity of migration. If now, in the diffusion of an electrolyte 

 the inequality of osmotic pressure were the only driving force, then, 

 from the different mobility of the positive and the negative ions 

 (e. g. H and 01), free electricity would at once form in the solution. 

 This is prevented by the establishment of an electrostatic force, the 

 action of which has just the result that the ions in the solution 

 are present in equivalent ratios. From this condition the magni- 

 tude of that force may be calculated, and retaining the same nomen- 

 clature as above, we get for the actual quantity of the anion or 

 kation diffusing in unit time : — 



S = -M21.1(f%? Po J^r.fk 



* r ° u + v dx 



u and v are the molecular conductivities in mercury units. From 

 this formula we have for the centimetre, the day, and 18° : — ■ 



K- -^-004768. 10 7 . 

 u-\-v 



