December 29, 1922] 



SCIENCE 



737 



cent, solution of originally isoelectric gelatin 

 and we consider ithe distribution of ions inside 

 the protein solution and in 'tihe acjueous solu- 

 tion outside the collodion bag containing the 

 protein solution at osmoitie equilibrimn. We 

 also assume complete electrolytic dissociation 

 of gelatin chloride as 'well as HCl. Let 

 a be (tJie molar concentration of the pro- 

 tein molecules and ions, let z he the molar 

 concentration of the 'CI ions in combina- 

 tion with the ionized protein, let y be the molar 

 concentration of the hydrogen ions of the free 

 HCI inside the protein solutiom ; itthe molar con- 

 centration of the CI ions of this HCl is also y. 

 In that ease the osmoitie isressure of the pratein 

 solution is determineid by 



a -f 21/ + £• 

 From this must be deducted the osmotic pres- 

 sure of the HCl of the outside aqueous solu- 

 tion. If X is the molar concentration of the H 

 ions of the outside solution, it is also the molar 

 concentration of the CI ions. Hence the oib- 

 served osmotic pressure of a protein solution 

 is 'determined by the following molar concen- 

 tration, 



o -I- 2j/ + — 2a; 

 Fig. 2 shows how this value varies with the 

 Pjj of the protein soluition (». e., y). In order 

 to arrive at a theory concerning the influence 

 of HCl on the osmotic pressure of protean solu- 

 tions it is necessary to calculate ithte va;lue of 

 2y + z — 2x and to deduct it from the ob- 

 served osmotic pressure of the p.ix>tein solution. 

 The term 2y + z — 2,x we will call the Donnan 

 correction. In ithis term y and x can be calcu- 

 lated from the measurements of the Pn, Pn 

 inside being — log y and pn outside 'being 

 — log X. z can be calculated from x 'and y 

 with the aid of the Donnaii equatio'n (1) 



{x + y){x — y) 



n =1 



y 



since we now know that x and y are deter- 

 mined by the Donnan equilibrium. If the value 

 of 2y -\- z — 2a! is calculated for different Pu 

 of a gelatin chloride solution (of -the same con- 

 centration of ori'ginally isoelectric gelatin which 

 in th,is ease was 1 per cent. ) ; and if from this 

 value is calculated 'the osmotic pressure due to 

 this excess of the molar concentration of 



orystalloidal ions inside the protein solution 

 over that outside, it is found that the curve for 

 the Donnan correction is almost identical with 

 'the curve for the observed osmotic pressui-e. 

 In other words, it turns lOut that 'the increase 

 in 'Osmotic pressure of a 1 per cent, solution 

 of originaly isoelectric 'gelatin upon the addi- 

 tion of little acid until 'a maximum is reached, 

 and the diminution of osmotic pressure upon 

 the addi'tion of further acid are not 'due to -any 

 variation in the 'state of 'disipersion of 'the pro- 

 tein, or any other real or imaginary "coUoidal" 

 property of the protein, ibut purely to the fact 

 that protein 'ions can not diffuse 'through the 

 collodion memhrane which is easily permeable 

 to ciystalloidal ions; as a consequence of which 

 the molar concentration of the crystalloidal 

 ions must always he greater inside the protein 

 solution than outside. What varies with the 

 Pjj of the gelatin solution is 'the quantity of 

 the excess of. 2y -\- z pver 2x. This follows 

 from the Donnan equation (1) according to 

 which 



while 



V2/2 + yz or 



y4i/2 _)- iys 



Now it is obvious that 



^^iy■i Jf- iyz + z^ ^ ^iy- + 41/3 

 i. e., the concentration of the crystalloidal ions 

 inside the protein solution 2y + z is alwaj-s 

 greater than the concentration of the crystal- 

 loidal ions 2x outside, when z is not or oo. 



If we substitute for the term 2y + z — 2a: of 

 the Donnan correction the identical term 



y4i/2 _|_ iyz 4-s'2 _ yiyi _|- 4i/s 

 we can visualize why the osmotic -pressure is a 

 minimum at 'the isoelectric point, why it 

 increases with the addition of little acid, reach- 

 ing a masimimi, and why it diminishes again 

 with the addition of more acid. 



At the isoelectric point no protein is ionized 

 and z ibeing zero, the whclle term 



Y4J/2 4- iyz + ^2 _ y4i/2 + 4i/2 

 becomes zero. Hence at the isoelectric point 

 the observed osmotic pressure is purely 'that 

 due to the protein, which is very low on ac- 

 count of the high molecular weight of gelatin. 



