Then, by varying r C and r ∆pKa , it becomes possible to map the properties of all mixtures of four weak acids with the same average pK a . Figure presents the study of the first critical point for these systems by plotting (a) the value of ∆pK c a as a function of r C and r ∆pKa , (b) the dependency of the number of roots of β for ∆pK a > ∆pK c a and (c) the corresponding number of roots of β". The domain plotted was restricted to an "interesting" area, as for larger values of r C and/or r ∆pKa , the behaviour becomes monotonous. Indeed, we observe the existence of a domain on the border of which ∆pK c a values undergo an inflexion, and this border corresponds to a zone of transition of the number of roots from 5 to 3 for ∆pK a immediately above ∆pK c a . The maximum of that area is observed at r c = 1.37 and r ∆pKa = 0.293 and it disappears for r C > 3.12.