192 SURFACES AND MEMBRANES 



after osmotic equilibrium had been attained the pressure was read on the 

 manometer. 



Using dilute solutions of cane sugar, Pfeffer discovered that the os- 

 motic pressures developed by them were proportional to their concentra- 

 tions and that the osmotic pressure increased with rise in temperature. 

 He found that the osmotic forces developed by his solutions were aston- 

 ishingly large. A 10 per cent sugar solution, for instance, actually 

 developed an osmotic pressure of nearly 7 atmospheres, or a force of 

 more than 100 lb/in. 2 



Van't Hoff's Discovery 



Ten years later van't Hoff pointed out the remarkable parallelism 

 between the properties of gases and the osmotic behavior of dilute solu- 

 tions. The experimental evidence showed that the osmotic pressure of a 

 dilute solution was directly proportional (1) to the concentration of the 

 solute and (2) to the absolute temperature. 



If it could be proved that the ultimate material particles in the solvent 

 behave as if they were entities having the properties of gas molecules, 

 the application of the general gas law to osmotic-pressure phenomena 

 would be justified. Or, conversely, if the general gas law could be 

 used to predict the osmotic pressure of a solution, the conclusion is that, 

 to the first approximation, the entities in the solvent of a dilute solution 

 had properties analogous to those of gas molecules. 



The first step is the justification of Boyle's law. In order to apply it 

 the pressure must be shown to be inversely proportional to the volume, 

 provided that the temperature is kept constant. Since the measured 

 hydrostatic pressure P = hdg and the density of this column of liquid 

 d = m/V, it follows that PV = hmg. When the osmotic pressure 

 developed by sucrose, as indicated in Table V-4, is examined, it can be 

 seen that a 0.2 M concentration develops a pressure of 5.11 atmospheres 

 at 20° C. It should follow that a 0.4 M concentration must develop a 

 pressure of 10.22 atmospheres, and 0.6 M concentration, a pressure of 

 15.33 atmospheres. The corresponding experimental values are 10.22 

 and 15.52 atmospheres, respectively. The agreement is surprisingly 

 good. The conclusion is that the osmotic pressure is proportional to the 

 concentration expressed in gram-molecular weights per 1000 grams of 

 water; i.e., P is proportional to mg/V. 



The gram-molecular weight is the weight of a substance in grams 

 numerically equal to its molecular weight. A gram-molecular weight of 

 any substance contains the same number of molecules (6.064 X 10 23 ) 

 as a gram-molecular weight of any other substance. The concentration 



