pH Titration Curves

The shape of the curve is governed by the auto-ionization of water ($K_w = [H^+][OH^-] = 1.0 \times 10^{-14}$) and the dissociation constants of the reactants ($K_a$ or $K_b$).

In the Buffer Region of a weak acid titration, the solution contains significant amounts of both the weak acid and its conjugate base, resisting large changes in pH as described by the Henderson-Hasselbalch equation: $pH = pK_a + \log\frac{[A^-]}{[HA]}$.

At the Half-Equivalence Point, exactly half of the analyte has been neutralized, meaning $[HA] = [A^-]$, which simplifies the equation to $pH = pK_a$.

The pH at the equivalence point is determined by the properties of the salt formed; for example, the conjugate base of a weak acid will undergo hydrolysis, making the equivalence point basic ($pH > 7$).

Step-by-Step Curve Analysis

• Initial pH: Calculate the pH based solely on the initial concentration of the analyte (strong or weak acid/base).
• Pre-Equivalence: For weak species, use the buffer equation; for strong species, calculate the remaining moles of analyte divided by the total volume.
• Equivalence Point: Identify the volume where $n_{acid} = n_{base}$. Calculate the pH based on the hydrolysis of the resulting salt.
• Post-Equivalence: Calculate the pH based on the concentration of excess titrant added to the solution.

Indicator Selection

• Choose an indicator whose transition range (pKin ± 1) encompasses the pH of the equivalence point to ensure the end point accurately reflects the equivalence point.

• Equivalence Point vs. End Point: The equivalence point is a stoichiometric fact, while the end point is an experimental observation dependent on the indicator's properties.

• Monoprotic vs. Polyprotic: Monoprotic acids show one 'step' or equivalence point, while polyprotic acids (like $H_2SO_4$ or $H_3PO_4$) show multiple steps corresponding to the loss of each proton.

• The 'Neutral' Myth: A common mistake is assuming the equivalence point is always at pH 7. This is only true for strong acid-strong base titrations; salt hydrolysis shifts the pH for weak species.

• Ignoring Dilution: Students often forget that adding titrant increases the total volume of the solution, which affects the molarity of all species present.

• Indicator Mismatch: Using an indicator like methyl orange (range 3.1-4.4) for a weak acid-strong base titration will result in a premature end point because the equivalence point occurs in the basic range.