where P 1 , P 2 and P 3 are defined as in the previous section. ). Additionally, one can note that the multiplicity of the root evolves also with r. For large r values, as ∆pK a increases, there actually exists a domain with a single root, then with 3 roots and finally with 5 roots. In contrast, for low values of r, the transition goes straight from a single to a 5 roots situation. The value of r found to be the transition between these two types of behaviour is r ≈ 1.56. Another value of interest turns out to be the one for which the intermediate branches come to touch the pH = 7 solution, observed at r = 1.5. Indeed, figure .c shows the evolution of the buffer index for solutions of various values of r and ∆pK a = ∆pK c a . The value of r = 1.5 appears as the transition to a very flat behaviour, when mixtures parametrized with lower values of r present a non flat behaviour even if with a single maximum iii .