OSMOTIC PRESSURE AND GAS PRESSURE loi 



sidered by van't Hoff to be one in which the volume of solute was small in 

 proportion to the volume of solvent.^ For example, if we could imagine the 

 complete and instantaneous removal of all of the water in a sucrose solution 

 without any change in the spatial relations of the solute molecules, the residual 

 sucrose molecules would be in a gaseous state. According to van't Hoff the 

 osmotic pressure of this solution would be equal to the gas pressure which 

 would be exerted by such a hypothetical "sucrose gas." Furthermore, he 

 showed that the osmotic pressures of dilute solutions obey laws analogous 

 to those which describe the relations of gases to variations in temperature, 

 volume and pressure. The analogies will now be briefly summarized: 



( 1 ) According to Boyle's Law the pressure exerted by a gas varies in- 

 versely as its volume, temperature remaining constant. In other words the 

 pressure of a gas varies directly with its concentration, since the smaller the 

 volume which contains a given number of gas molecules, the greater the 

 concentration of the gas. A similar principle holds for osmotic pressures. 

 A molar weight of an undissociated solute dissolved in lOOO g. of water, 

 for example, results in a solution with twice the osmotic pressure possessed 

 by a solution prepared by dissolving half the molar weight of the same solute 

 in lOOO g. of water. The third column of Table 13 shows the calculated 

 pressures which a "sucrose gas" would exert if dispersed in the same volume 

 and at the same temperatures as the dissolved sucrose. The correspondence 

 of these hypothetical "sucrose gas" pressures with the osmotic pressures of 

 the sucrose solutions is evident from the last column of this table. 



(2) According to the law of Gay-Lussac the pressure exerted by a gas 

 varies directly with the absolute temperature, if the volume of the gas re- 

 mains constant. From the data presented in the last two columns of Table 14 

 we see that the osmotic pressure of a sucrose solution shows approximately 

 the same variation with temperature that the gas pressure of a correspondmg 

 hypothetical "sucrose gas" would show. The osmotic pressure of a solution 

 is therefore proportional to the absolute temperature. 



(3) According to Avogadro's Hypothesis equal volumes of all gases under 

 identical conditions of temperature and pressure contain equal numbers of 

 molecules and hence exert equal pressures. One mol of any gas at standard 

 conditions (0° C. ; i atmos. pressure) occupies 22.4 liters. If this gas be com- 

 pressed to a volume of i liter, it will exert a pressure of 22.4 atmos. (Boyle's 

 Law). Similarly one mol of any undissociated solute dissolved in a liter of 

 water exerts an osmotic pressure of approximately 22.4 atmos. at 0° C. 



2 Actually the analogies between gas pressures and osmotic pressures as dis- 

 cussed by van't Hoff hold with a fair degree of approximation for solutions up to 

 concentrations of at least one molar. 



