II. O S M O T I (: P R 10 S S TT R E M F. A S U K E M E N T S 53 



In an osmotic cell containing such a colloid electrolyte as solute 

 the small "counterions" will tend to reach a condition of equal con- 

 centration on either side of the membrane but fail to do so because of 

 the electrostatic attraction for the impermeable component from 

 which they are derived. This situation will, in turn, influence the 

 distribution of other small ions in the system. At equilibrium there 

 wall exist a difference in small ion distribution (as electrostatically 

 neutral electrolytes) on the two sides of the membrane that will re- 

 sult in an added increment of osmotic pressure over that due to the 

 nondiffusible (high molecular weight) ions alone. 



For illustrative purposes, let us consider a protein that has been 

 titrated with sodium hydroxide to some pH value alkaline to the iso- 

 electric point of the protein (i.e., at such a pR that H+ and OH" ions 

 are at insignificant concentrations). The protein salt in solution will 

 ionize to a protein ion bearing 22 negative charges per molecule and 

 to 22 Na+ ions per molecule (22 may be called the "valence" of the 

 protein). If this protein salt is dissolved, at a molar concentration 

 C2, in, say, an aqueous sodium chloride solution of molar concentra- 

 tion Cs, and placed in one compartment (1) of an osmotic cell and the 

 sodium chloride solution (concentration C3) placed in the other com- 

 partment (2) and a pressure is maintained in compartment 1 such 

 that no change in volume of the fluids in the two compartments 

 takes place up to the time when equilibrium is reached, it will be ob- 

 served that a concentration change will have occurred with respect 

 to the sodium chloride. The concentration of sodium chloride in 

 compartment 2 will be greater than at the beginning of the experi- 

 ment, while in compartment 1 it will be less than originally. Donnan 

 (11) was the first to point out that this phenomenon is the result of 

 the circumstance that the thermodjmamic condition for equilibrium 

 in such a system requires that the products of the activities of the dif- 

 fusible ions be the same on both sides of the membrane, that is : 



(aNa+)i («ci-)i = (aNa+)2 (ac\-)2 (11) 



At equilibrium, assuming the activity coefficients of the ions to be 

 unity, [Na+]i will be equal to the sum of that derived from the pro- 

 tein salt and from the sodium chloride present and will therefore 

 (electrical neutrality in each solution being maintained) be greater 

 than the [Cl~]i. In compartment 2, however, [Na+]2 = [Cl~]2. 

 From equation (11), the relationships [Na+]i > [Na+]2 and [Cl-]i < 

 [C1-J2 must hold at equilibrium so that [NaCl]2 > [NaClJi will also 



