48 DAVID R. BRIGGS 



which upon expansion of the logarithm gives the relationship : 



ttFi = RTiN2 + }4 Nl + HNl^ ...) (5) 



In dilute solutions, higher terms than the first in A''2 may be ig- 

 nored and: 



ttFi = RTN2 



Furthermore, at high dilution. A''! becomes A'ery nearly unity, Vi can 

 be considered equal to the molar volume of the solution, V, and N2/V 

 is equal to the concentration, C2, of the solute in moles per unit vol- 

 ume of the solution. Under these conditions: 



TT - RTC2 - RTic/M^) (6) 



where c^ is the concentration of the solute in grams per unit volimie 

 of solution and 71/2 is the gram molecular weight of the solute. In 

 this equation, if C2 is expressed as grams per milliliter of solution, R 

 has the value of 82.07 milliliter atmospheres and ir is the osmotic 

 pressure in atmospheres. Equation (6) is a form of the van't Hoff 

 equation and is the limiting or ideal law describing the relationship 

 of the osmotic pressure of a solution to the molar concentration of the 

 solute. 



The other colligative properties of a solution can be utilized in 

 the calculation of the osmotic pressure as follows: 



From equation (2) it is seen that, in the "ideal" solution, P\/Pi° = 

 N-i, from which, by substitution in equation (4): 



RT ^ 1\ RT , Pi° 



Where water is the solvent, at 0°C., the osmotic pressure, in atmos- 

 pheres is: 



X = ^'^■^^^ ^^^ In ^ = 1245 X 2.313 log ^ = 2807 log ^ 

 18 /^i i 1 -t 1 



In a molar solution, the value for Pi°/Pi = 1.018, log 1.018 = 0.0078, 

 and: 



TT = 2807 X 0.0078 = 22.4 atmospheres 



In ideal solutions at high dilution it can be shown that the de- 

 pression of the freezing point, AT" = Tq - T, of the solvent in the solu- 

 tion is given by the equation : 



