CONDUCTIVITY OF SODIUM HYDROXIDE IN AQUEOUS SOLUTION. 289 



PART VI. THE VISCOSITY AND INTRINSIC CONDUCTIVITY OF AQUEOUS 

 SOLUTIONS OF SODIUM HYDROXIDE. 



Reference has been made in the earlier parts of the paper to the great viscosity of 

 concentrated solutions of sodium hydroxide, which indeed manifests itself even in so 

 simple an operation as filling and emptying a pipette. As this was likely to have 

 a great effect upon the ionic mobility, a series of measurements of viscosity was made, 

 with the help of which it was hoped that it might be possible to correct the observed 

 conductivities for the influence of viscosity. 



Relation bettveen Conductivity, lonisation and Ionic Mobility. The usual mode of 

 expressing the relationship between conductivity and ionic velocities is derived from 

 the consideration of the flow of electricity from side to side of a unit cube of the 

 electrolyte under a potential gradient of 1 volt per centim. Thus if U and V are 

 the ionic velocities under such a potential gradient, m the concentration of the solute 

 in gramme equivalents per litre (and therefore m/1000 the number of gramme 

 equivalents in the unit cube), a the fraction of the solute that is in the ionised or 

 current-carrying state, and q the quantity of electricity of either sign liberated 

 by 1 gramme equivalent of any monad (q = 98360 coulombs), then the 

 current = amfl 000. ^(U+V). Since the potential difference between the sides of 

 the cube is unity, the current (by OHM'S law) is equal to the conductivity K. Hence 

 K = am/lOOO . q (U+ V), or since A = K . lOOO/m, we have, writing u = ^U, v = qV, 

 the equation A = a(w+). Whilst U and V are the absolute velocities of the 

 ions expressed in centims. per second, u and v are what are known as the " ionic 

 mobilities " and are of the same dimensions as A. 



The ionic velocities, and therefore also the ionic mobilities, are determined, not 

 alone by the nature of the ion, but also by the solvent, the temperature, and the 

 concentration of the solution. In considering the theory of ionisation it is customary 

 to deal exclusively with the case of " dilute solutions " for which the values of the 

 ionic mobilities do not differ appreciably from the values at infinite dilution, so that 



u = tt, v = v. and - - = a approximately. 

 A 



This is the relation from^which the coefficient of ionisation is usually deduced, but 

 recent observations have shown that whilst the relation A = a.(u+v) is universally 

 true, the relation A = a A. is only valid for solutions of concentrations below about 

 N/100. At concentrations up to about decinormal it is probably legitimate to 

 deduce the coefficient of ionisation from the osmotic constants of the solution or 

 from the electromotive force of concentration cells (JAHN), but it is clear that, except 

 in dilute solutions, the coefficients of ionisation and the ionic mobilities are altogether 

 unknown quantities, and much confusion has arisen from the general tendency to 



VOL. cciv. A. 2 P 



