II. OSMOTIC PRESSURE MEASUREMENTS 43 



slant, T is the absolute temperature, and 1' is a summolion sjnnbol 

 that indicates that the vahie of Wmin reefers to the concentration work 

 for all components of the solutions, algebraic signs being taken into 

 consideration. Osmotic work is that part of the total concentration 

 work that involves changes in solvent concentration alone and is re- 

 lated to the observed osmotic pressure difference, tto, between the 

 solutions b}' the relationship : 



woV, = RT In (Na/Nb) 



where Vi is the partial molar volume of the solvent and A^'a and A^b 

 refer to the mole fraction of solvent in solutions A and B, respectively. 

 Osmotic pressure, therefore, will give information concerning the 

 concentration work done on the solvent alone by a tissue membrane, 

 but will tell nothing about the concentration work performed by the 

 membrane on the various solutes that may be present. It would be 

 erroneous to assume, in a system containing a tissue membrane across 

 which there exists no osmotic pressure difference, that no concentra- 

 tion work is being performed by the membrane. 



The second realm of usefulness of osmotic pressure measurements 

 in biophysics, and one that usually makes use of the direct measure- 

 ment of the quantity, is in the determination of number average 

 molecular weights of the naturally occurring high molecular sub- 

 stances, such as proteins, gums, etc. With such solutes, because of 

 their relatively huge molecular dimensions, it is quite easy to obtain 

 membranes completely impermeable to these particles while easily 

 permeable to the molecules of a solvent. It is also readily apparent 

 that, because of their high molecular weights, these substances must 

 show only small effects upon the coUigative properties of their solu- 

 tions. An examjile will illustrate why osmotic pressure measurements 

 are resorted to in preference to those of the other colligative proper- 

 ties. One gram molecular weight of any solute dissolved in 1000 

 g. of water will, for dilute solutions obeying the ideal solution laws, 

 depress the freezing point of the water 1.86 °C., elevate the boiling 

 point 0.54 °C., and depress the relative vapor pressure of the water 

 by 0.018. The osmotic pressure for such a solution would amount to 

 22.4 atmospheres (about 1700 cm. of mercury or 23,150 cm. of water) 

 at 0°C. For a protein of a molecular weight of 45,000 dissolved in 

 water to make an approximately 1% solution (1 g. of protein to 100 

 g. of water) the freezing point depression would amount to 0.00041 °C., 

 the relative vapor pressure lowering would be only 4 parts in a mil- 



