ACIDOSIS 59 



The form represented in Equation 6 was first introduced by Hassel- 

 balch(6)(1916). 



Expressing log K! as pKj the value of pK x for B 2 HPO 4 : BH 2 P0 4 

 mixtures was shown by Soerensen (1909) and by Clark and Lubs (1916) 

 to be approximately 6.8. For BHCO 3 : H 2 CO 3 solution in the con- 

 centrations normally found in blood plasma Hasselbalch (1916) found 

 pK x at body temperature to have a value of 6.1. His results indicated 

 in fact that by determination of the ratio BHCO 3 : H 2 CO 3 the pH of a 

 blood sample could be estimated with Equation 6 as accurately as by the 

 standard electrometric method. 



The figure for pK t actually given by Hasselbalch is 6.4, because he 

 used the equivalent concentration of H 2 CO 3 , which is twice the molecular, 



BHPO 

 in calculating the ' ration. When used with the molecular ratio 



adopted by L. J. Henderson and, so far as we have observed, all other 

 authors except Hasselbalch, the value of pK^ must, therefore, be reduced 

 by log 2, or 0.3, giving pKj the value 6.1. 



BA K, 



2. Maximum Efficiency of Buffer Action When = 1, H + = -^ 



xiA A 



and pH^pK^ The identity of these three expressions is shown as 



HA 



follows: If in Equation 3 above, is replaced by 1, the equation be- 



comes H + = y . Similarly if in Equation 6, =- is replaced by 1, 

 A. -tLA 



BA 



log :pp becomes O, and the equation becomes pH = pKi- 

 HA 



The fact that a buffer mixture of a weak acid and its salt has its 



BA 



maximum efficiency, when ==-r 1, in diminishing changes in reaction 



HA 



caused by adding either base or acid, has its basis in the general proposition, 

 that in the ratio a given change in a produces the least percentage 



change in the ratio when a = 0.5 and the ratio is consequently unity. 

 The relationship is exemplified graphically by a curve expressing as 



BA 



ordinates values of the ratio -, as abscissa? values of pH. For 



bicarbonate at approximately normal blood plasma (0.03 M) concen- 

 tration, the curve indicated by figure 1 is obtained. The curve is 



BHOO 



calculated from the approximate equation pH = 6.1 -J- log ', the, 



for the present purposes, insignificant variations in pK x from the value 

 6.1 being neglected. It is evident from inspection that the curve is 



