3 02 SCIENCE PROGRESS. 



the conductivity must, on this hypothesis, vary as the cube 

 of the concentration. 



The ordinary laws of chemical equilibrium have been 

 applied to the case of the dissociation of a substance into 

 its ions. 1 As this application is of fundamental importance, 

 a short investigation must be here introduced. Let c be 

 the number of molecules which dissociate per second when 

 the number of undissociated molecules in unit volume is unity; 

 then cp is the number when the concentration is p. Re- 

 combination can only occur when two ions meet, and, since 

 the frequency with which this will happen is proportional 

 to the square of the ionic concentration, we shall get for 

 the number of molecules re-formed in one second 



cq , 

 where q is the number of dissociated molecules in one 

 cubic centimetre. When there is equilibrium 



cp = cq 2 , 

 If fi be the molecular conductivity, and ^ its value at 

 infinite dilution, the fractional number of molecules dis- 

 sociated is /i/^oo , and the number undissociated i - fijfi^ , 

 so that, if v is the volume of the solution containing one 

 gram-molecule of the dissolved substance, we get 



v Voo / »' V Moo / •' V /*oo ' v 2 f* 



2 



'°°V Moo ; 



Let us put ft/fin = a ; then a, which we have called the 

 coefficient of ionisation, measures both the molecular con- 

 ductivity referred to its limiting value as unity, and also 

 the fractional number of molecules dissociated. 



The equation then becomes 



3 



a C 



= -, = constant 



y(l - a) C 



Thus the value of this expression for solutions of binary 

 electrolytes should be constant, and it has been confirmed 

 by Ostwald and others for an enormous number of weak 

 acids. In the case of solutions of strono- acids and salt 



o 



1 Ostwald's Lehrbuch der AI/g. Chemie. 



