ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 211 
with, or numerically expressed by, the ratio of the molecular conductivity 
of the solution to the molecular conductivity of an infinitely dilute solution 
of the same compound, in which all molecules are probably dissociated. 
The explanation of chemical phenomena thus given is sufficiently well 
established to indicate some relation, at any rate, between conductivity 
and chemical activity, but a more direct comparison may be made between 
conductivity and dissociation as measured indirectly on the basis of 
Van ’t Hoft’s theory of the effects of osmotic pressure.! On Van’t Hoff’s 
theory the osmotic pressure of a salt in solution at a given temperature 
depends upon the number of molecules contained in a given volume 
irrespective of the weight of the individual molecules; so that if the 
osmotic pressure be regarded as corresponding to gaseous pressure, 
Avogadro’s law holds for salts in solution as well as gases. Van’t Hoff 
verified this law for a number of bodies, leaving, however, a number of 
exceptions, and Arrhenius has shown that the exceptions may in general 
be quite satisfactorily explained by supposing that the effective number 
of the molecules is increased by the dissociation of some into ions, and 
the fraction of the whole number that must be supposed dissociated in 
order to account for the exceptional osmotic pressure is, within very small 
limits of difference, the same as the dissociation ratio—that is, the frac- 
tion of the whole number required to be dissociated in order to account 
for the conductivity on the dissociation hypothesis; or, to express the 
fraction free from hypothesis, it is the fraction represented by the ratio of 
the molecular conductivity of a given salt-solution to the limiting value of 
the molecular conductivity of the salt when the dilution is indefinitely 
great. Let a represent this ‘ dissociation ratio,’ or coefficient of activity, 
as it is termed by Arrhenius, which can be determined from measure- 
ments of conductivity at different degrees of dilution.? Let m be the 
number of inactive, or undissociated, molecules in unit volume of solution, 
an the number of active molecules, each of which we may suppose dis- 
sociated into & ions (e.g., for KCl, s=2; for BaCl,, or K,SO,, k=3, and 
so on); then, assuming that each separate ion is as effective as regards 
osmotic pressure as each combined molecule, the osmotic pressure will be 
the same as if the whole number of molecules were m+n; the ratio 7 of 
this number to the whole number of original molecules is (m+n) /(m+n), 
whereas a=n/(m+n). Whence i=1+(k—L)a. On the other hand, the 
osmotic pressure, and consequently the number of effective molecules in 
unit volume, can be determined on Van’t Hoff’s theory by observing the 
depressions of the freezing-point of water, as Raoult has done in many 
cases, produced by the solution of one gramme-molecule of salt in a litre. 
Thus the normal ® depression of the freezing-point for one gramme-mole- 
eule of salt when there is no dissociation is 1°85° C., so that if ¢ be an 
observed depression of the freezing-point for a gramme-molecule of 
' Van ’t Hoff, Zeitschr. fiir ph. Ch. i. p. 481, 1887. ‘Trans.’ by Ramsay, in Phil. 
Mag. ser. 5, 26, p. 81,1888. Arrhenius, Zeitschr. fiir ph. Ch. i. p. 631, 1887. B.A. 
Rep. 1887. 
? The molecular conductivity for infinite dilution may be arrived at by plotting a 
curve with the number of gramme-molecules per litre of solutions of different con- 
centration as abscisse and the molecular conductivities (i.e. conductivity + number 
of gramme-molecules per litre) as ordinates, and continuing the curve until it meets 
the line of no concentration. (See Kohlrausch, Wied. Ann. vol. 26.) 
* For an account of the application of the depression of the freezing-point to the 
examination of the molecular constitution of dilute solutions, see also Planck, 
Leitschr. fiir phys. Chem. i. p. 577 (1887) ; Wied. Ann. vol. 32, p. 499. 
P2 
