Forces on the Osmotic Pressure of Electrolytes. 743 



none is wholly satisfactory*. Now both the formula o£ 

 Arrhenius, giving the dissociation in terms of the freezing- 

 point lowering, and the law of mass-action in its usual form 

 depend on the assumption that the osmotic pressure of the 

 ions, as well as that of the molecules, obeys the law for 

 perfect gases, and both will require modification in case any 

 deviation from the gas law is produced by the relatively 

 large electrical forces which exist between the ions. In a 

 previous paper | in this Magazine I have shown that a com- 

 pletely dissociated mixture of ions possesses a finite virial, 

 and have calculated its approximate value by what is I think 

 a strict mathematical method. In the application to solu- 

 tions it follows that the osmotic pressure of the ions of an 

 electrolyte differs from that of a perfect gas in a calculable 

 way. In the present paper the virial calculation is applied 

 to determine the theoretical osmotic pressure, and hence the 

 lowering of the freezing-point at different concentrations of 

 an assumed completely dissociated binary electrolyte. A 

 comparison of the result with experiment leads to the con- 

 clusion that the freezing-point lowering at all dilute concen- 

 trations in monovalent salts can be completely accounted for 

 by the effect of the interionic forces in reducing the osmotic 

 pressure below that given by the gas law on the assumption 

 that the dissociation is complete throughout. 



The view that so-called "strong" (or strongly dissociated) 

 electrolytes are completely dissociated at all concentrations 

 is not of course a new one. It has been proposed on other 

 grounds — in particular by Sutherland J — but the hypotheses 

 on which it has been based seem somewhat speculative, and 

 indeed the view is not one which is generally accepted. 

 The argument for the view which follows from the result of 

 this paper, however, seems to me to stand on a different 

 footing from any previously advanced. The interionic 

 forces certainly exist, and their effect on the osmotic pressure 

 and the freezing-point is a purely mathematical deduction 

 from the known facts. Further, the magnitude of the 

 theoretical effect is determined absolutely in terms of 

 known quantities, no arbitrary constants being involved. 

 The effect must thus be admitted, if the deduction is correct, 

 on the recognized theory of electrolytes, and allowed for 

 before any conclusion can be drawn from the freezing-point 



* A summary of the various explanations which have been suggested 

 up to J 910 is given by Partington, Journ. Chem. Soc. xcvii. p. 1158 

 (1910). 



t Phil. Mag. xxiii. p. 551 (1912). 



X Phil. Mag. iii. p. 1G1 (1902) ; xii. p. 1 (1906) 



3E 2 



