MEMBRANE POTENTIALS 125 



ions in the outside solution and y + z the concentration of Cl in 

 the gelatin solution (as found by titration) and let us assume that 

 this difference of concentration determines the P.D. observed 

 between the gelatin chloride solution and the outside solution, 

 then we should expect that at 24C. the observed P.D. = .059 



lo S ly~+~ z volts - 



We shall see later in this chapter that the observed P.D. in 

 millivolts is actually equal to 59 log ^ millivolts, and this 



makes it very probable that the P.D. between a gelatin chloride 

 solution and the outside watery solution across a collodion 

 membrane is caused exclusively by the Donnan equilibrium. 



We have a second check since it follows also that we must be 

 able to calculate our observed P.D. on the basis of the difference 

 in the concentration of hydrogen ions on the opposite sides of the. 

 membrane with the aid of Nernst's formula. Donnan's equilib- 

 rium equation 



z 2 = y(y + z) 

 can be written in the form 



y = x 



x y + z 



where y is the concentration of the hydrogen ions inside the 

 gelatin solution and x the concentration of the hydrogen ions 

 in the outside solution. Hence, if the Donnan equilibrium is 

 responsible for the observed P.D. between the gelatin chloride 

 solution and the watery solution, it must also be possible to 

 show that 



Observed P.D. = 59 log | millivolts 



We intend to show that this is actually the case. Instead of 

 measuring the concentration of the hydrogen ions inside (i.e., 

 in the gelatin solution) and outside (i.e., in the aqueous solution) 

 by titration, we measure these concentrations with the hydrogen 

 electrode. Since log y is the value pH inside and log x the value 

 pH outside, the value 59 (pH inside minus pH outside) millivolts 

 must (within the limits of accuracy of measurement) be equal to 



