Simultaneous Determination of Precise Equivalence Points and pK Values from Potentiometric Data: Single pK Systems Sir: Briggs and Stuehr ( I ) recently proposed a procedure for detecting a strong acid H S present as an impurity in a weak one HW and for evaluating the mixed dissociation constant K ( = aH+Cw-/CHw) of the latter from data obtained in a potentiometric titration with strong base. It was based on the equations V + R - A V = -aH+(V + R - A V ) / K + V , (la)
1/K =
-l/aH+
+
v,/a~+[(vf
R - AV)]
+
[H+]=
+
V2CWo v2
+
- [H+]
Vbcb b'
v,o + v, +
(lb)
where V is the volume of base added at the point where the measured pH is -log aH+; V, and AV are the volumes of base that are stoichiometrically equivalent to the HW and HS, respectively; and R = (CH+ - COH-) (V + Vao)/Cb, where V, is the original volume of the acid solution and c b is the concentration of the titrant. Equation l a was considered to be of the form y = mx b, withy = V R - AV and x = - a H + ( u R - AV). After assuming an initial value of AV, a preliminary estimate of b (= V,) was obtained by linear regression to this equation. These values of AV and V, were used in Equation 1b to compute a value of 1/K at each experimental point, and were adjusted so as to minimize the sum of the squares of the deviations of the values of 1/K from their mean. Briggs and Stuehr correctly state that Equations 1 involve no explicit approximation, but they do contain a quantity R that cannot be evaluated without assigning some value to the single-ion molarity activity coefficient of hydrogen ion (and also to that of hydroxyl ion unless, as was true for all of their experimental data, COH-
