190 PROTOPLASM 



osmometer, and the pressure read from the manometer scale. 

 By such methods, Pfeffer obtained osmotic vahies for many- 

 concentrations of sugar. 



Indirect methods of measuring osmotic pressure have to do 

 with the depression of the freezing point, elevation of the boiling 

 point, and lowering of the vapor pressure. Osmotic pressure is 

 proportional to these properties. Vapor pressure varies inversely 

 as the concentration of a solution while osmotic pressure is 

 directly proportional to concentration ; consequently, if the one is 

 known, the other can be calculated. Indeed, we have defined 

 the one, osmotic pressure, in terms of the other, vapor pressure. 



Osmosis and the Theory of Solutions. — That solutions and 

 gases are subject to the same laws was first set forth in the year 

 1885 by van't Hoff. The gas law of Boyle states that volume 

 and pressure vary inversely if the temperature remains constant. 

 The law of Gay-Lussac (or Charles) states that volume varies 

 directly as temperature if pressure remains constant. From 

 these two laws it follows that pressure varies directly as tem- 

 perature if volume remains constant. The third gas law is 

 the hypothesis of Avogadro. It states that equal volumes of 

 all gases at the same pressure and temperature contain the same 

 number of molecules. Our present purpose is to investigate these 

 laws as applied to solutions in relation to osmotic pressure. The 

 first gas law, therefore, may be reworded as follows: Osmotic 

 pressure is proportional to concentration if the temperature 

 remains constant. Qualitatively this has already been shown 

 to be true in our visualization of osmosis. The more molecules 

 of sugar there are, i.e., the higher the concentration, the greater 

 is the excess of inwardly diffusing water molecules over those 

 diffusing outward. Quantitative proof is more convincing. 

 At zero temperature (0°C.) and atmospheric pressure (76 cm. of 

 mercury), a gram-molecular weight or ''mole," of a gas {i.e., 

 the molecular weight in grams, e.g., 44 grams of CO2) occupies a 

 volume of 22.4 1. (this is true by experiment). If, as van't Hoff 

 states, the pressure developed by a substance in solution is the 

 same as that which it would exert if converted into a gas of the 

 same volume and temperature, then one mole of a substance 

 dissolved in 22.4 1, of water should give an osmotic pressure 

 of 1 atmosphere. One mole (the molecular weight in grams) of 

 every substance has the same number of molecules because, if a 



