ELECTROLYTES AND THEIR ACTION 



179 



One only need be mentioned now. As we shall see, the " acidity " of a solution is readily 

 expressed on our theory by the number expressing its concentration in H' ions. The difficulty 

 found by those who do not accept the theory is seen on p. 576 of the paper by E. F. and 

 H. E. Armstrong (1913), where mixtures of acid and alkaline phosphates in certain proportions 

 have to be used, giving a set of numbers, having only a meaning relative to one another. 



Some of the difficulties may be referred to, chiefly for the purpose of keeping 

 in mind where further research is needed, but also on account of their instructive 

 nature. 



At the time of the first publication of the theory, objection was made to it 

 on the ground that, in the case of ammonium chloride, it was possible to separate 

 by diffusion the products of dissociation, NH 3 and HC1, whereas this could not be 

 done in the case of Na and Cl ions in water. Although, at the present time, the 

 explanation given by Arrhenius (1901, p. 176) is generally accepted, it is 

 instructive to refer to it on account of the fact that it turns up in various forms. 

 This explanation rests on the existence of the electric charge on the ions, whereas 

 the products of ordinary dissociation are devoid of charge. This charge is the 

 very large one of 96,500 coulombs per equivalent. 

 Suppose, then, that we have in a tube a stratum of 

 water lying over one of a solution of sodium chloride. 

 If the Na and Cl had no charge, the latter, which 

 diffuses much more rapidly than Na (in the ratio of 

 68 to 45), would be found in excess in the water 

 layer after a short time. But when only 10 ~ 13 gram- 

 equivalents of Cl in excess of Na ions have passed 

 to the upper layer, this layer would have a negative 

 charge of 96,500 x 10~ 13 coulombs or 96,500 x lO" 13 

 x3xlO' = 290 electrostatic units, a quantity of 

 electricity which would, on a sphere of 10 cm. radius, 

 give a spark of 0'3 cm. Now it is easy to calculate 

 that the electrical forces produced by the undetectable 

 amount of 10 ~ 13 gram-equivalents of Cl far exceed any 

 possible osmotic force which would cause unequal 

 diffusion of the two ions. The electrostatic unit of 

 electromotive force is about 300 volts, so that the 

 above-mentioned 290 units would give a potential of 



= 8,700 volts, on a sphere of 10 cm. radius, 



FIG. 54. DIAGRAM 

 CALCULATION OF 



FOR 

 THE 



10 



ELECTROSTATIC ATTRACTION 

 BETWEEN OPPOSITELY 

 CHARGED IONS. 



in round numbers say 10 4 volts. This would be about 



the same if the charge were given to a cube of liquid (Arrhenius.) 



of 10 cm. side in a diffusion vessel. 



Let us take now a stratum of half normal sodium chloride solution one centi- 

 metre high and one square centimetre in section, and imagine a potential of 10 4 

 volts at the end A and zero potential at B (Fig. 54). 



The sodium chloride is further supposed to be distributed in such a manner 

 that its concentration at A is zero and at B normal, half normal midway. It 

 is assumed to be completely dissociated for sake of simplicity. On the Cl ions 



V V 



there is acting an electrical force of 7X6, where 7- is the fall of potential per 



V V 



centimetre, i.e., 10 4 volts, and e is the amount of charge on the ions, i.e., 



na tzr)Q 



=r = 48*2 coulombs, since the solution contains per cubic centimetre 



2000 

 0-5 



gram ions. The total force acting is 



1000 l 



48'2 x 10 4 volt-coulombs per centimetre (Arrhenius, 1901, p. 6) = 48'2 x 10 11 dynes. 

 The osmotic force, on the other hand, which acts on the same Cl ions is given by 

 the difference between the osmotic pressures of the normal solution at B and 



273 + 18 

 that of zero concentration at A, i.e., at 18, 22'4 x 273 =24'2 atmospheres, or 



