ELECTROLYSIS AND ELECTRO-CHEMISTRY. 233 



The coefficient a is thus given by the ratio between the actual mole- 

 cular conductivity of the solution and its value at infinite dilution, and 

 can therefore be readily determined. 



The velocities of the ions may be reduced by an increase in frictional 

 resistance, by a diminution in the fraction of the dissolved substance 

 which is, at any moment, active, or by a combination of both these causes. 

 In dilute solutions the resistance offered by the liquid to the passage of 

 the ions through it is probably sensibly the same as in pure water ; but 

 when the proportion of non-ionised molecules becomes considerable, we 

 cannot assume that this is the case. Arrhenius' experiments on the con- 

 ductivity of jelly solutions,' while they certainly show that the ionic 

 friction does not depend on the molar viscosity of the medium, do not prove, 

 as usually seems to be assumed, that it is not affected by the addition of 

 more of the electrolyte, which would cause a molecular change. 



While the solution is dilute enough for the friction to be taken as 

 constant, however, the coefficient n can be given a very simple physical 

 meaning. The fraction which expresses the ratio of the actual to the 

 limiting velocity of the ions must then also express the fraction of 

 its time during which, on the average, any ion remains active ; that is, it 

 must express the fractional number of molecules which are, at any 

 moment, in a state of activity. This fractional number may be called the 

 coefficient of ionisation. 



Thus, although we can, if we like, always put Kohlrausch's theory iri 

 the form shown in our last equation, the constant « will only have a 

 definite physical meaning when the solution is so dilute that the ionic 

 viscosity keeps constant. This caution is necessary, for it seems to be 

 universally assumed that o, as deduced from the ratio of the actual to 

 the limiting conductivity, always expresses the ionisation of the solution, 

 whatever its concentration may be, although for fairly strong solutions no 

 convincing evidence has been adduced in favour of the assumption made. 

 It is possible that some of the discrepancies between the ionisation as 

 found from the conductivity and as deduced in other ways — as, for example, 

 from the depression of the freezing point — may be due to this cause. 



On the other hand, the equation given on p. 229, in which u and v 

 denote the actual velocities of the ions under the conditions of the experi- 

 ment, probably holds good whatever be the concentration of the solution, 

 and this gives the simplest and most certain form of Kohlrausch's theory. 



The fact that the molecular conductivity of aqueous solutions becomes, 

 in general, constant as the dilution gets very great shows that the veloci- 

 ties of the ions must then become independent of the concentration of the 

 solution. This seems to offer strong evidence in favour of the view that 

 the ions are free from each other, which is also indicated by the fact that 

 the specific velocity of an ion at great dilution comes out the same 

 whatever be the nature of the other ion present. 



If the ions are not free, the alternative is to suppose that they move- 

 forward by taking advantage of a collision between two solute molecules by- 

 means of which an interchange of ions may occur, and each makes a step 

 in advance. Now the frequency with which such collisions would happen, 

 must vary as the square of the concentration ; and, since the quantity of 

 electricity conveyed must also depend on the number of ions present, the 

 conductivity would vary as the cube of the concentration. The motion of 

 the ions cannot, therefore, depend on collisions between the molecules o£ 



' British Association Report, 1886, p. 344. 



