54 DAVID R. BRIGGS 



be true. A concentration increment, x, of sodium chloride will have 

 moved from compartment 1 to compartment 2, as equilibrium is at- 

 tained. The final concentration of [Na+J2 = [Cl~]2 will be (C3 + 

 x), while the final concentration of [Cl~]i will be (C3 — x), and of 

 [Na+]i will be {C3 — x -\- Z2C2). From equation (11), letting activi- 

 ties equal concentrations, at equilibrium: 



(Cs- x + Z2C2)iCs - x) ^ [C3 + xY 

 and: 



X = z^C^Cz/i^ Cs + Z2C2) (12) 



The observed osmotic pressure at equilibrium, ttq, must be the sum 

 the osmotic pressure due to the protein ions, tt^, and that due to the 

 unequal distribution of diffusible ions, ttj. 



TTo = TT, + TT, = RTC2 + RT[Z2C2 + 2(C3 - x) - 2{C, ^ x)] = 



RTCi + RT{zoC2 - 4 a:) (13) 

 Combining equations (12) and (13) : 



TTo = RTC', + RT ,, Z^^'' ^, ^ RTC', + RT ""'"' 



(4 C3 + 22C2) " 4 C3 



Since Ci = W2/V0M2, where W2 — weight of protein in grams, ilf2 = 

 molecular weight of protein, and Vo = volume of 1 kg. of solution 

 when W2 = 0, we can write : 



_RTvh( zlw2 \ , ^. 



as the expression describing, for ideal solutions, the relationships be- 

 tween the osmotic pressure, the valence of the protein (22), and the 

 initial concentration of the salt {C3) (in solutions of uni-univalent 

 diffusible electrolytes). From this expression it is clear that, the 

 lower the value of 22 and the higher the value of C3, the less will be 

 the importance of tt^, the osmotic increment due to the unequal dis- 

 tribution of diffusible ions, relative to that due to the protein ion, 

 TTp. For this reason, it is the common practice, when the molecular 

 weight of a protein is to be calculated from osmotic pressure measure- 

 ments, to conduct the experiment at a pH value close to the isoelectric 



