G. S. ADAIR 



A number of salts or non-ionized substances may be present in 

 buffer mixtures. An equation (1) applicable to solutions containing a 

 mixture of salts, acids or bases was derived by G. S. Adair 5 



dlna p = (v s /RT)dn - b a d\na° a - b b d\na° b - ^dlnn?. . . .(1) 

 a p == activity or ' effective concentration of protein ' 

 v s = volume of solvent per mol of protein 

 n = osmotic pressure 



b a = ' excess coefficient ' for substance a, referred to later 

 a° a = activity of substance a in the dialysate 

 Similar terms, with subscripts b, c, i may be applied to the substances 

 b, c and i. 



If substance a be a strong electrolyte with two ions, it may be con- 

 venient to introduce the mean activity of the ions a ± 

 b a d log a° a = 2 b a d log a° ± 

 The ' excess coefficient ' is defined by Formula 2. 



b a = (m a -m:)(l/m p ) ....(2) 



m a = molality of substance a in the protein solution L 

 m° = molality of substance a in the dialysate L° 

 TOp = molality of protein in L 

 It may be noted that the activities of salts, acids or bases in L° can 

 be measured or calculated from molalities by a number of methods 

 that are not applicable to protein solutions. 



If we are considering a series of dilute phosphate buffers, with pYL 

 values close to the isoelectric point of the protein, the activities of the 

 individual ions in L and L° are nearly equal, and it may be possible to 

 apply a simplified form of equation 1 expressed in terms of ionic 

 activities instead of mean activities. 



d log y p = - b H d log a° H - b t d log a) ... .(3) 



y p = activity coefficient = ajm p for solutions where m p is constant. 

 b H — hydrogen ions combined with protein. 

 a° H = activity of hydrogen ions in L° 

 b t — corrected total excess coefficient for all ions excluding hydrogen 



ions. 

 a — sum of activities of all ions excluding hydrogen ions. 



b t = (m t - m° - *,) (l//w,) ....(4) 



m t and m° = sums of molalities of diffusible ions excluding hydrogen 



ions in L and L° 

 The term e ( is a correction for the osmotic effects of the excess of 

 ions inside the membrane, calculated in accordance with Donnan's 

 theory. This correction is extremely small in the region of the iso- 

 electric point. 



184 



