The use of approximation formulae in calculations of acid-base equilibria

In titrating a weak acid with a strong base, different calculation methods are applied at various stages. Initially, the pH of a weak acid like acetic acid is calculated using its dissociation constant (Ka) and an ICE table. Upon addition of a strong base such as sodium hydroxide, a buffer forms, and its pH is determined using the Henderson-Hasselbalch equation. As more base is added and the titration reaches the halfway point, the pH becomes equal to the pKa of the acid, indicating equal...

The ionization-constant expression for a solution of a weak acid can be written as:

Calculating pH for Titration Solutions: Weak Acid/Strong Base
For the titration of 25.00 mL of 0.100 M CH3CO2H with 0.100 M NaOH, the reaction can be represented as:

Calculating pH for Titration Solutions: Strong Acid/Strong Base
A titration is carried out for 25.00 mL of 0.100 M HCl (strong acid) with 0.100 M of a strong base NaOH. The pH at different volumes of added base solution can be calculated as follows:
(a) Titrant volume = 0 mL. The solution pH is due to the acid ionization of HCl. Because this is a strong acid, the ionization is complete and the hydronium ion molarity is 0.100 M. The pH of the solution is then:

Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
The first step is to identify all the chemical reactions involved, The...

The titration of a weak acid with a strong base results in the formation of water and the conjugate base of the acid. For instance, titrating acetic acid with sodium hydroxide leads to the formation of water and sodium acetate. A solution of acetic acid and sodium acetate constitutes a buffer whose relative concentration at different stages of the titration is indicated by the α values, which represent percentages of the weak acid and its conjugate base.
The α0 and α1 values represent the...