Chapter VII — 93 — Osmotic Quantities of Cells 



Vapor pressure: temperature curves of dilute solutions are approxi- 

 mately parallel with those of pure water. Therefore, for dilute solutions 



rp ^^^ rp 



-^-—f = a constant (K) (5) 



where To and T are the freezing temperatures of pure solvent and solu- 

 tion. If — ^ — be substituted for po — p in Raoult's law, then 



To-T no (d) 



K Pq m + n2 



T„-T = Kp„ 



o 



or 

 n2 (7) 



ni + no 



For dilute aqueous solutions K has been determined to be 1.86° C. per 

 mol of undissociated solute. Where the solute is an electrolyte, dissocia- 

 tion into ions increases the total number of particles, each of which has 

 an equal effect in lowering the vapor pressure of the solvent. Since the 

 ratio of the number of solute particles to the number of solvent particles is 

 the important factor in determining the freezing point of the solution, 

 electrolytes are more effective than nonelectrolytes. It has been noted 

 earlier that a molal solution of KNO3 has a much lower freezing point 

 than has a molal sucrose solution ; if ionization were complete, and other 

 factors did not interfere, the lowering would be twice as great. Before 

 the introduction of the activity concept, freezing point determinations were 

 used to measure the so-called "degree of ionization." More recently they 

 are used to measure activities, the discrepancy between theoretical and 

 actual measured activity being ascribed to the influence of intermolecular 

 force fields upon the escaping tendency of the molecules. 



Conversion of the freezing-point lowering of a solution to osmotic 

 pressure values at 0° C. is easily accomplished by the following relation : 



0F=^- 22.4 (S) 



or 

 OP = 12.04 A (9) 



where A = freezing-point depression. 



Lewis (1908) offers the more accurate form of this equation 



OP = 12.06 A — 0.021 A- (10) 



which has been used by Harris and Gortner (1914) and Harris (1915) 

 to compile a table of values convenient for converting freezing point data 

 to osmotic pressures. In correcting for change in osmotic pressure from 

 0° to, for example, 20° C, the assumption is made that expressed tissue 

 saps, like sucrose solutions, obey the gas law for change in temperature. 

 The validity of this assumption is of special importance where the sap is 

 high in colloids. 



Freezing-Point Determination: — The procedure generally used for determining 

 the freezing point of expressed sap is as follows. The sap is placed in a small tube, 

 and a thermometer is inserted with the bulb immersed, together with a small wire 

 stirrer. This tube is placed within another larger tube, providing a dead air space 

 to preclude too rapid cooling. The jacket tube is now immersed in a freezing mixture, 

 usually ice and salt, and the temperature of the sample slowly falls; stirring is con- 

 tinuous. Upon crystallization, the mercury column rises abruptly, steadies, remains 

 constant for a short time, then falls slowly. The plateau, or highest temperature 

 reached is recorded as the observed freezing point. Crystallization at temperatures 

 below the freezing point can be readily induced by introducing the tip of a fine glass 

 capillary containing ice into the solution. 



