Author:
Morales Juan C.,Arango Carlos A.
Abstract
AbstractA closed-form analytical expression for $${[\hbox {H}_{3}\hbox {O}^{+}]}$$
[
H
3
O
+
]
has been obtained for aqueous solutions of diprotic acids and its soluble salts. This formula allows to calculate the pH of aqueous solutions of diprotic acids, their buffer solutions, and the titrations of these two by a strong base, from the values of p$$K_1$$
K
1
, p$$K_2$$
K
2
, and the effective concentrations of the acid and the base, $$\bar{C}_\textrm{a}$$
C
¯
a
and $$\bar{C}_\textrm{b}$$
C
¯
b
respectively. It is shown that a strong base titration of an acid, or its buffer solutions, is always a linear path in the $$\bar{C}_\textrm{a}$$
C
¯
a
–$$\bar{C}_\textrm{b}$$
C
¯
b
plane, which allows a simple analysis of the pH stability of buffer solutions. The mathematical analysis of the equilibrium equations of the dissolution of a diprotic acid in water and the physical constraints allowed to obtain two approximate equations for the diprotic acids. One of the approximations is useful for acids with $$\textrm{p}K_2-\textrm{p}K_1\le \log _{10}4$$
p
K
2
-
p
K
1
≤
log
10
4
, the other for acids with $$\textrm{p}K_2-\textrm{p}K_1\le -\log _{10}4$$
p
K
2
-
p
K
1
≤
-
log
10
4
.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Chemistry
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