346 JOHN W. SHIVE 



252 solutions, these being monopotassium phosphate, potassium 

 nitrate, calcium nitrate and magnesium sulphate. The three 

 series were calculated to have diffusion tensions, or osmotic 

 concentrations, of 0.05, 2.50 and 8.15 atmospheres, respectively. 



For the weakest of these series of solutions there can be little 

 doubt that the method of calculation used by Tottingham must 

 give calculated values very close to those of the actual diffusion 

 tensions. For the remaining two series the method of calcula- 

 tion becomes somewhat more questionable, and it seems probable 

 that the error introduced in the case of the strongest medium 

 may be considerable. It is therefore desirable, as was indeed 

 indicated by Tottingham, that the diffusion tensions of his 

 numerous solutions be determined experimentally. With this 

 determination the present paper has to deal. 



The simplest method available for determining the diffusion 

 tensions or osmotic concentrations of such solutions as these, 

 and the one generally used in such cases, is that of cryoscopy, 

 and this was here employed. By this method the diffusion ten- 

 sion is derived from the observed depression of the freezing point 



/22.4\ 

 of the solution by use of the formula,^ Pf = A i^-^^j = 12.06 A, 



where P/ denotes the diffusion tension (in atmospheres) of the 

 solution at 0°C., and A stands for the depression of the freezing 

 point (in degrees Centigrade) below that of the pure solvent. 

 The freezing points of the solutions were determined by means 

 of the Beckmann apparatus, accounts of which are to be found 

 in text books of physical Chemistry. Since the values given by 

 the application of the formula are for 0°C., and since Totting- 

 ham's calculations refer to a temperature of 25°C., it is neces- 

 sary to apply a temperature correction to the value Pf. This 

 was accomplished in the usual manner, by using the formula 

 for Gay Lussac's principle, P25 = P/ (1 + 0.00366 X 25), where 

 P25 denotes the diffusion tension at 25°C. 



Of course, the temperature just prior to the formation of ice in 

 • an aqueous solution is usually several degrees lower than the 



* Jones, H. C, Elemeats of physical chemistry. New York, 1910, p. 256. 



