ENZYME RliACTIONS AT SURFACES 25 



He intrpduccs the assuiiiplion that the adchtional lowering of l.T. helow the I.T. 

 given by the undissociatetl acid is exactly proportional to the fractional dissociation 

 (a) in the surface phase, 



^ [As-] . . 



" [HA,] + [A,-]' ^^ 



The sum | HAs | + | As" | was calculated from a knowledge ot the surface area 

 per polar group at an interface and an assumed value of 8. Although one arrives 

 at [As~] from ajuation j, [ Hs' ] cannot he evaluated from equation 2 since Ks 

 may not be assumed to be ec]ual to the dissociation constant (Ki,) in bulk phase. 

 Instead [H^ ] is obtained from equation i by further assuming that | Ms^] 

 = [As~] + [B"J, which is a reasonable assumption near neutrality. An example is 

 the following: 



PH VALLKS FOR \[\ PALMITIC ACID IN A BROMOBENZENE-WATER SYSTEM 



(buffer 0.02 m in cation) 



pHi, 7 8 9 10 II 



pHb-(pH), 1-4 2.1 2.5 2.7 2.7 



The values of ApH are significant (about i pH unit) even in 0.4 m butters. 



Danielli pointed out that his approach fell short of providing a theoretical re- 

 lationship between K^ and Kb- This problem has since been reexamined by 

 Hartley and Roe (20). They suggested that the electrokinetic potential {'Q) of the 

 colloidal chemist can be identified with the potential t// in the neighborhood of a 

 simple ion at the distance of closest approach of another ion. as considered by 

 Debye and Hiickel. In this sense the ^-potential detennines the local concentra- 

 tion of ions near the surface of a particle. The potential near the surface of a 

 particle with ionized acidic groups is greater than the average for the bulk solu- 

 tion by an amount t, and the hydrogen ion concentration near the surface will be 

 g-ef/kT fij-,-,es the H^ concentration in bulk. The effective dissociation constant 

 according to Hartley and Roe becomes 



Ks = Ke-^f/'^'^'-Ke-Ff/^''^ {4) 



where K is the thermodynamic dissociation constant in bulk, e is the electronic 

 charge, F is the faraday, T the absolute temperature, and k the Boltzmann 

 constant. 



At 25°, equation 4 may be rewritten as 



pH« = pH„ + C/6o (5) 



The difficulties in defining pHs in a suitable manner in order to be consistent 

 with pH], in the usual sense has been thought through by Craxtord et al.(6). 

 We will use the Gibbs-Guggenheim approach to show that at a charged interlace 



