letters Hydrolysis of Salts To the Editor
I would like to make a couple of comments about papers (1, 2) that use and discuss my simplified approach (3) for the hydrolysis of a salt from both monoprotic acid and base: 1. Malinowski ( I ) describes the same computer method I used to calculate exact pH values. He stresses a very important practical point, which I recognize I did not even mention in my paper, and that is the use of my farmula as a f ~ sapproximation t for the iterative pmeedure. 2. Cardinali et al. (2) make a very careful and valuable mathematical analysis, hut in my opinion, it has little chemical feeling. Areasonable concentration range for the analysis should he lo4 < c < 10" and not 0 < e < =a. I would summarize my own "chemicalfeeling contribution" with the aid of the accompanyingfigure:My approximate
lo4 < c < lo-', we have to point out that no explicit indication was given in his article a s regards the range where his approximate formula (eq 10) yields almost exact results. However, the important points in our analysis remain the statements that: 1. a solution of a salt of the kind under discussion has a [HI]
value that must lie within the range between Kwm and ( K , . K. I K ~ )and ~ ,not between K, and Kb, the actual value depending on the analytical concentratioif; 2 a not.negligible portion of the corren range cannot ror can only grossly hr repmducrd by Agu~rrr-Ode'sformula, unKt, >> K,I2 are satisless b f h conditions K, >> KmL1and licd As for the '%hemica1feeling contribution" provided by the figure in Aguirre-Ode's letter, it would confirm graphically the numerical results in Table 2 of our article, but there is a n important point to be made. For any given salt concentration, the upper and lower curves in the figure, which should mark the beeinnine of sienificant errors. though being symmetrical &h respect todiagonal D, are not svmmetrical to the other diagonal D' (crossing - D a t DK* = 7, $ C b = 7 and not shown in the figure), contrary to what the shape of the curves seems to suggest. Actually, beyond D', where K.. Kt,
