42 ENERGY OF SUBSTANCE IN SOLUTION 



pressure than the solution. When, then, will the pressure inside 

 become equal to the pressure outside that is, when will the 

 hydrostatic pressure developed become great enough to balance 

 the reduction of pressure to the solute ? Experiment has shown 

 that the maximal rise of hydrostatic pressure is reached when its 

 value is equal to the difference in vapour pressures between the 

 solvent and the solution. Vapour pressure, as we have seen, 

 depends on the kinetic energy of the molecules in a liquid. Ex- 

 periment has further shown that for simple dilute solutions the 

 magnitude of the osmotic pressure depends on the molecular 

 weight of the substance dissolved, the amount of substance in 

 the solute per unit volume and on the temperature of the solution. 

 That is, osmotic pressure is controlled by just those factors which 

 control gaseous pressure. Suppose the gram-molecular weight 

 of the (undissociated) substance to be taken as m grams, dis- 

 solved in V litres of water, at the absolute temperature T. The 



n 

 concentration, i.e. the number of mols. (n) per litre would be ^ 



Now, we may consider that dilute solutions obey the gas laws, 

 and therefore 



We have seen that of the kinetic energy of a gas is manifested 

 as gaseous pressure, and so we may state that 



2 \nmv z 

 = 3 ~F~- 



That is, osmotic pressure is equivalent to f of the total kinetic 

 energy of the particles in solution. Put in another way, it might 

 be stated that in a simple solution the osmotic pressure of a sub- 

 stance would be numerically equal to the gaseous pressure which 

 the substance would exert were it a gas occupying the same volume 

 as the solution. 



Now we have seen that the variables connected with gaseous 

 pressure are T and V . As, according to Avogadro's hypothesis, 

 equal volumes of gases under equal T and P contain the same 

 number of molecules, we may state that, if T is kept constant, 

 P varies as the number of molecules. De Vries (1884) found that 

 one gram-molecule of sugar dissolved in water to make up a 

 litre, has at C. an osmotic pressure of 22-4 atmos. (Prac- 

 tically all gases at C. and 760 mm. pressure have a gram 



