22 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



underlying these concentration changes is that, within the solution, the 

 electric current is carried by positive and negative carriers which move 

 with velocities proportional to the potential gradient existing in the 

 solution. Within the body of the electrolyte itself, Ohm's law is obeyed. 

 The observed concentration change at an electrode is thus the resultant 

 of two effects; namely, loss or gain due to the reaction at the electrode 

 and loss or gain due to the motion of the positively and negatively 

 charged carriers. The simplest case is that in which precipitation of 

 the ions takes place at the electrodes. Let us assume that the charge u 

 is transported through the solution by the cation and the charge v by 



the anion. Then will be the fraction of the charge carried by the 



positive ion and -p the fraction of the charge carried by the negative 



ion. If one equivalent of material is precipitated at the cathode, then 

 u and v will represent the number of equivalents of matter carried up 

 to the electrodes as cation and anion respectively. The concentration 

 change in the neighborhood of the cathode will correspond to a loss of 

 one equivalent of the electrolyte due to precipitation at the electrode and 



to a gain of -:- equivalents carried up to the electrode by the cations. 

 The total observed concentration change, therefore, will be equal to the 

 difference of these two or to a loss of -r - equivalents. Similarly, 



at the anode, the change will correspond to equivalents. It is 



evident that, if the concentration change due to the passage of a given 

 charge is known and if the nature of the electrode reactions is known, 



? J ?/ 



then the ratios and may be determined. These ratios, 



which Hittorf termed the "transference numbers" of the cation and anion, 

 respectively, we shall denote by the symbols n and 1 n. 



In determining the transference numbers of an electrolyte by the 

 method of Hittorf, the concentration changes are measured with respect 

 to water. In other words, the determination of these numbers is based 

 upon the assumption that water itself remains at rest, and is in no wise 

 concerned in the process of the transfer of electricity through the solution. 

 We now know that this condition is not strictly fulfilled and that water 

 plays a part in the conduction process. When a current of electricity 

 passes through an aqueous solution, the solvent itself is transferred to 

 some extent along with the ions. Obviously, this will affect the concen- 



