102 OSMOTIC PRESSURE OF AQUEOUS SOLUTIONS. 



of the free space, instead of the total volume of the gas, the correction 

 term b in the equation of van der Waals would be automatically elim- 

 inated. Such a course is impracticable in the case of gases, but easy in 

 that of solutions. The obviously equivalent procedure in the case of 

 solutions was to compute the gas pressure of the solute — with which 

 osmotic pressure was to be compared — on the basis of the volume of 

 the solvent, which is known approximately wherever the weight-normal 

 system of solutions is employed. The correction for the volume of the 

 solute, which is effected by adopting the weight-normal system and by 

 the practice of referring the gas pressure of the solute to the volume of 

 the solvent, is, however, somewhat uncertain, because the volume of 

 the solvent in a solution is not exactly known. The volume of a solu- 

 tion is not equal to the sum of the volumes of the solvent and solute 

 in their separate states. Moreover, the volume of the free solvent is lia- 

 ble to diminution through combination of solvent with solute mole- 

 cules, as in hydration. When a weight-normal solution of cane sugar is 

 made up at 0° by dissolving a gram-molecular weight of the substance 

 in 1,000 grams of water, the volume of the solution is less than the sum 

 of the volumes of the separate components by about 6.7 cubic centi- 

 meters. The shrinkage in the case of glucose under identical conditions 

 is about 6 cubic centimeters. It is uncertain how much of this shrink- 

 age is to be ascribed to each of the apparently possible causes, i. e., to 

 change in the volume of the solvent itself, to change in the state of 

 aggregation of the solute, and to the formation of hydrates. It appears 

 probable, however, that the observed shrinkage in volume is principally 

 due to one or both of the last two causes; but only one of these, namely, 

 hydration, is known to affect the volume of the solvent. 



In regard to the adoption of the volume of the solvent at the tem- 

 perature of maximum density, as the standard for the computation of 

 the gas pressure of the solute, it can only be said that the practice is 

 based on the observation that the results appear to be slightly more 

 harmonious among themselves, when this is done, than when the gas 

 pressure is referred to the supposed volumes of the solvent at the tem- 

 perature at which the measurements of osmotic pressure are made. 



The most amazing judgment upon the work of the author and his 

 collaborators is that pronounced by Professor W. D. Bancroft,* who 

 says, in regard to the practices elaborated above : 



"Quite recentty Morse and Frazer have shown that their direct measure- 

 ments of osmotic pressure came out better when the concentrations are 

 referred to a constant volume of solvent. They consider this a discovery of 

 their own, quite overlooking the fact that they have simply gone back to 

 van't Hoff's original formulation. Having reached their conclusion empiric- 

 ally, Morse and Frazer have also overlooked that their method of expressing 

 concentration contains the tacit assumption that there is neither expansion 

 nor contraction when the two components are mixed." 



*Jour. Phys. Chem., x, 320. 



