ELECTROLYSIS AND ELECTRO-CHEMISTRY, 229 



second, viz. m u. But, since the chlorine ions move also, a further 

 separation occurs, and m v hydrogen ions are left without partners. The 

 total number of gram -equivalents liberated is therefore m{u4-v). This 

 must, by Faraday's law, be equal to r]C, where rj denotes the electro-chemical 

 equivalent of hydrogen. Thus we get 



m{u + v)=rjC=ri m q(u-\-v), 

 and it follows that the charge, q, on one gram-equivalent of each kind of 

 ion is equal to 1 /r]. 



We know that Ohm's law holds good for electrolytes, so that the 

 current C is also given by k. dF/dx, where k denotes the conductivity of 

 the solution, and d'Pjdx the potential gradient, i.e. the fall in potential 

 per unit length along the lines of current flow. 



Thus -(u + v)=k. dP/dx ; 



V 



k (fP 



m ax 

 Now t] is 1-0352 + 10"*, and the concentration of a solution is usually 

 expressed in terms of the number, «, of gram-equivalents per litre instead 

 of per cubic centimetre. 



Therefore M + i;=l-0352 xlQ-^ - • 5^- 



n ax 



When the potential gradient is one volt (10* C.G.S. units) per centi- 

 metre, this becomes 



w + t;=l-0352xlO'x~. 



n 



Thus, by measuring in C.G.S. units the conductivity of a solution of known 

 concentration, the relative velocity of its ions can a1» once be deduced. It 

 is true that, in this investigation, we have assumed that all the contents 

 of the solution are actively concerned in the electrolysis — an idea which 

 seems to be disproved by the diminution in the molecular conductivity 

 with increasing concentration. But although, at any instant, only a part 

 of the electrolyte is active, we must imagine that each portion will become 

 active in turn, two given ions of opposite kinds being sometimes free 

 {i.e. active) and sometimes paired (i.e. inactive). The immediate effect, 

 therefore, of the decrease in ionisation, with increasing concentration, is 

 to diminish the relative velocity of the ions, and this diminution will 

 reduce the molecular conductivity in accordance with the equation. 



Since Hittorf's numbers give us the ratio of the ionic velocities, we 

 can deduce the absolute values of u and v from this theory. Thus, for 

 instance, the molecular conductivity of a solution of potassium chloride 

 containing one-tenth of a gram-equivalent per litre is 1113 x lO"'"* C.G.S. 

 units at 18° C. 



.-. M-ft;=l-0352x 10' X 1113x10-", 



= 1-153 X 10-^=0-001153 cm. per sec. 



Hittorf's experiments show us that the ratio of the velocity of the 

 anion to that of the kation in this solution is -51 : -49. The absolute 

 velocity of the chlorine ion under unit potential gradient is therefore 

 0-000589 cm. per sec, and that of the potassium ion 0-000564 cm. 

 per sec. Similar calculations can be made for solutions of other con- 



