736 



SCIENCE 



[Vol. LVI, No. 1461 



The wiiter "was able to ^ow that t-his is true 

 by making measurements of a property of pro- 

 teia solutions, which had roeeived little if any 

 attention in colloid chemistry, namely, the 

 measurements of the membrane potentials ex- 

 isting between a protein solution and ihe sur- 

 rounding aqueous solution at the (time of 

 osmotic equilibrium. 



Donnan's equilibrium formula can be written 

 in the form 



x_ _ y + z 

 y ~ X 



X 



where - is the ratio of the molar concerutration 



y 

 of the hydrogen ions outside to ithe concen- 

 tration of the hydrogen ions inside, while 



2/ -f- ^ 



is the ratio of the molar concentration 



X 



of the chlorine ions inside to that outside. 

 Donnan had shown that there should exist a 

 potential difference 'between the inside and out- 

 side solutions, which at 24° C. should he equal 



X y + 2 



to 59 X log - millivolts or 59 X log 



y « 



millivolts. Since pn inside is = ■ — log y and 



X 



Ph outside is — — ^log x, log - is equal to Ph 



inside minus pjj outside. Ph inside and pjj out- 

 side can be detennined directly with the aid of 



y -{- ^ . 

 the hydrogen electrode; log is equal to 



Pci outside minus pci inside and this quantity 

 ean be measured dureotly 'by titration or with 

 the silver chloride electrode. 



On the other hand, the P.D. between the pro- 

 tein solution and the surrounding aqueous solu- 

 tion across a collodion membrane can he 

 measured direetly with the aid of a Compton 

 electrometer and a pair of identical indifferent 

 calomel electrodes (and saturated KCl). If 

 the unequal distribution of diffusible «rystal- 

 loidal ions (e. g., H and €1 in the ease of gela- 

 tin chloride) on the opposite sides of the mem- 

 brane is really determined iby the Donnan 

 equilibrium, then the P.D. observed directly 

 with ithe pair of identical calomel electrodes 

 should 'be equal to 'the P.D. calculated in milli- 

 vfolts from the values 59 X (Ph inside minus 

 Ph outside) or from 59 X (Pci outside minus 



p inside), where p or pjj may be obtained 

 'by titration or by the silver chloride or hydro- 

 gen electrodes respectively. The writer has 

 made these measuremeents and found that when 

 various quantities of acid are added to solu- 

 tions of isoelectric protean — e. g., crystalline egg 

 albumin, or gelatin, or casein — the observed, 

 membrane potentials always agree with the 

 membrane potentials calculated on the basis of 

 Donnan's equation within one or itwo millivolts, 

 i. e., within the limits of accuracy of the meas- 

 urements. 



The net result of estensive measurements of 

 memhrane potentials was, first, that when a 

 protein solution, enclosed in a collodion bag 

 (impermeable to protein ions but permeable to 

 crystalloidal ions), is in osmotic equilibrium 

 with an outside aqueous solution, the concen- 

 trations of ci^stalloidal ions in (the protein 

 solution and in the outside aqueous solution 

 are not the same; and second, that the differ- 

 ence in (the two concentrations can be calcu- 

 lated from Donnan's equilibrium equation. 



We are now in a position to explain the 

 osmotic pressure curves in Fig. 2. The colloid 

 chemists would have taken it for granted that 

 such curves were due to an influence of the 

 acids on the state of dispersion or on some 

 other real or imaginary colloidal property of 

 proteins. Before we have a right to indulge in 

 such speculations we musit realize thait these 

 curves of observed osmotic pressui-e are not 

 exclusively the expression of the osmotic pres- 

 sui-e due to the protein particles, or protein 

 molecules, and protein ions alone, but are also 

 the result of the demonstrable unequal concen- 

 trations of 'the crystalloidal ions on the oppo- 

 site sides of the membrane, caused by the 

 establishment of a Donnan equilibrium. In 

 other words, the observed osmotic pressure of 

 a protein solution needs a corredtion due to the 

 Donnan equilibrium 'before we can begin to 

 speculate on the cause of the influence of acid 

 on these curves, and it is oui- purpose to calcu- 

 late the value of this corredtion. 



We begin with the curve expressing the influ- 

 ence of HCl on the osmotic pressure of a 1 per 



