192 PROTOPLASM 



parable to the osmotic pressure of a solution ( page 204). The 

 deviation between vapor pressure and osmotic pressure is seen 

 in the mathematical expression of the two — PV = RT for the 

 gas law and PV = KT for the osmotic law. The two are nearly 

 the same but not quite, because R is not the proper constant for 

 water vapor. The systems are not identical; there are variables 

 of which we are ignorant ; but the analogy is a very close one and 

 indicates a fundamental similarity. How close it is is not always 

 fully appreciated. Frazer has shown that with a substance such 

 as mannite, where there is little heat of solution, the agreement 

 of the gas laws is quite surprising, even up to as high as 20 atmos- 

 pheres pressures, and there are many gases which begin to 

 diverge from the so-called gas laws at or before pressures of this 

 magnitude are reached. 



Physicochemical Applications. — An interesting application of 

 osmosis to nonliving physical and chemical processes is that 

 of deVries. Chemists were considering the probable formula of 

 the sugar raffinose, a trisaccharose found in molasses. There 

 were three possibilities: Ci2H220ii-3H20, Ci8H320i6-5H20, and 

 C36H64O32. Sucrose and rafhnose may be compared by balancing 

 them on opposite sides of a membrane, then, when the two are 

 in osmotic equilibrium, each solution will contain the same num- 

 ber of molecules per unit volume. This is true of all (nonion- 

 izable) isotonic solutions. The total weight of the raffinose 

 (i.e., the concentration) which is isotonic with sucrose being 

 known, it is an easy matter to calculate the weight of one raffinose 

 molecule from the following simple proportion : 



Total weight of sucrose _ total weight of raffinose 

 Weight of one sucrose molecule ~ weight of one raffinose molecule 



If a sucrose solution of 3.42 per cent is chosen, 342 being the 

 molecular weight of cane sugar, then the calculations are simpli- 

 fied. That concentration of raffinose which is isotonic with 

 3.42 per cent sucrose is 5.96 per cent. The relationship then 

 becomes 



3.42 ^ 5^ 

 342 ~ M 



(M being the desired molecular weight of raffinose); therefore, 

 3.42 M = 342 X 5.96, and M = 596, the molecular weight of 



