which does not depend on the concentration of the conjugated species as it could be factored out. By finding the roots of this polynomial in, say, the interval pH ∈ [0 : 14], one can determine the number of maxima and minima of the buffer index and the values of the corresponding roots. Figure .a represents the pH values for which β = 0 in the case where pK a = 4 as a function of ∆pK a = pK a2 -pK a1 i . The first obvious point is that a single root is always present, that for pH = pK a . A point at ∆pK c a = 1.1439 ii corresponds to the transition from the one to the three roots regime of the buffer index curve and matches the flattest buffer index that can be obtained at pH = 4 using two weak acids , in this case with pK a1 = 3.428 and pK a2 = 4.5720 (see figure .b). For ∆pK a < 1.1439 the single root in the derivative of β corresponds to a maximum, whereas it becomes a minimum surrounded by two maxima for ∆pK a > 1.1439.