THE NEW THEORY OF SOLUTIONS. 



{Continued from p. 26.) 



THE well-known equation PV = RT which expresses 

 in the case of a gas both the laws of Boyle and 

 Guy Lussac may be made to include Avogadro's hypo- 

 thesis. As Horstmann first pointed out, if we decide that 

 in all cases our unit of weight shall be a number of grams 

 numerically equal to the molecular weight of the particular 

 gas with which we are dealing, the constant R will then 

 have the same value for all gases which conform to Avo- 

 gadro's hypothesis, for under the same conditions of tem- 

 perature and pressure the volume occupied by unit weight 

 will be the same for all. If the pressure P be measured 

 in atmospheres and the volume V in litres, and if T be 

 the absolute temperature, the volume energy of a gram- 

 molecular weight of an ideal gas is given by — 



PV=-o8iqT. 



The direct observations on osmotic pressure indicate that 

 precisely the same expression holds for a dilute aqueous 

 solution of an indifferent substance if P be now the osmotic 

 pressure, and V the volume of the solution which contains a 

 gram-molecular weight of dissolved substance. 1 



On account of the difficulties besetting the experimental 

 methods and from the fact that aqueous solutions alone have 

 at present been investigated, the support lent by direct ob- 

 servations on osmotic pressure to the validity of the above 

 expression in the case of solutions is not very extensive. 



1 Pfeffer's results expressing the relation between the osmotic pressure 

 P' measured in cm. of mercury, the ordinary temperature/, and C the num- 

 ber of grams of sugar in 100 gr. of water may be summarised by — 



P' = 49-27 C (1 + -00367/). 



On assuming the densities of the dilute solutions employed to be the same 

 as that of water and on calculating from this equation the pressure P in 

 atmospheres for V litres of solution containing a gram-molecular weight, 

 i.e., 342 gr. of sugar at the absolute temperature T, we obtain — 



P = 49*27 x 342 T/760 V x 273, 



which is PV = -0812 T. 



28 



