Titration of a weak acid with a strong base is a fundamental analytical chemistry technique used to determine the concentration of an acid that does not fully dissociate in water. Worth adding: unlike the reaction between a strong acid and a strong base, this process produces a solution that is basic at the equivalence point, creating a distinct titration curve with a buffer region and a steep pH jump that requires careful indicator selection. Understanding the stoichiometry, equilibrium shifts, and pH calculations at every stage is essential for students and professionals performing quantitative analysis in laboratories.
Understanding the Chemical Reaction
When a weak acid (represented as HA) reacts with a strong base like sodium hydroxide (NaOH), the hydroxide ions ($\text{OH}^-$) act as a powerful proton acceptor. The net ionic equation for the reaction is:
$ \text{HA}{(aq)} + \text{OH}^-{(aq)} \rightarrow \text{A}^-_{(aq)} + \text{H}2\text{O}{(l)} $
Because the strong base dissociates completely, the reaction goes essentially to completion. The conjugate base ($\text{A}^-$) formed during the titration is a weak base that hydrolyzes in water, producing hydroxide ions and making the solution basic at the equivalence point. This hydrolysis reaction is the key reason why the pH at equivalence is greater than 7:
$ \text{A}^-{(aq)} + \text{H}2\text{O}{(l)} \rightleftharpoons \text{HA}{(aq)} + \text{OH}^-_{(aq)} $
Common examples of weak acids used in this type of titration include acetic acid ($\text{CH}_3\text{COOH}$), formic acid ($\text{HCOOH}$), and hypochlorous acid ($\text{HClO}$). The strength of the weak acid is quantified by its acid dissociation constant ($K_a$), which directly influences the shape of the titration curve and the pH at the half-equivalence point.
The Titration Curve: Four Distinct Regions
The titration curve—a plot of pH versus volume of titrant added—is the visual roadmap of the reaction. It is divided into four critical regions, each governed by different chemical principles.
1. Initial Point (Before Titrant Addition)
Before any strong base is added, the solution contains only the weak acid. The pH is determined solely by the acid's dissociation equilibrium:
$ \text{HA} \rightleftharpoons \text{H}^+ + \text{A}^- $
Using an ICE table (Initial, Change, Equilibrium) and the $K_a$ expression, the hydrogen ion concentration can be approximated by $[\text{H}^+] \approx \sqrt{K_a \times C_a}$, provided the percent ionization is less than 5%. The pH is calculated as $-\log[\text{H}^+]$. This starting pH is higher than that of a strong acid of the same concentration because the weak acid only partially ionizes.
2. Buffer Region (Before Equivalence Point)
As the strong base is added, it neutralizes a portion of the weak acid, converting it into its conjugate base. The solution now contains significant amounts of both the weak acid (HA) and its conjugate base ($\text{A}^-$). This mixture acts as a buffer solution, resisting drastic pH changes.
The pH in this region is elegantly calculated using the Henderson-Hasselbalch equation:
$ \text{pH} = \text{p}K_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) $
Because the volume is the same for both species, the ratio of concentrations equals the ratio of moles. This region is characterized by a gradual, almost linear increase in pH Still holds up..
3. Half-Equivalence Point
This is a singular, critically important point where exactly half of the weak acid has been neutralized. At this volume:
- Moles of HA remaining = Moles of $\text{A}^-$ formed.
- The ratio $[\text{A}^-]/[\text{HA}] = 1$.
- $\log(1) = 0$.
Which means, $\text{pH} = \text{p}K_a$.
This provides an experimental method to determine the $K_a$ of an unknown weak acid simply by reading the pH at the half-equivalence volume on the titration curve. It is also the point of maximum buffer capacity That alone is useful..
4. Equivalence Point
The equivalence point occurs when the moles of added strong base exactly equal the initial moles of weak acid. All HA has been converted to $\text{A}^-$. The solution now contains only the conjugate base (and the spectator cation, e.g., $\text{Na}^+$) Took long enough..
Because $\text{A}^-$ is a weak base, the pH is greater than 7. To calculate the exact pH, one must solve the base hydrolysis equilibrium using the base dissociation constant $K_b$, where $K_b = K_w / K_a$ Worth knowing..
$ K_b = \frac{[\text{OH}^-]^2}{C_{\text{salt}} - [\text{OH}^-]} \approx \frac{[\text{OH}^-]^2}{C_{\text{salt}}} $
Here, $C_{\text{salt}}$ is the concentration of the conjugate base at equivalence, accounting for the total volume change (initial acid volume + titrant volume). Once $[\text{OH}^-]$ is found, $\text{pOH} = -\log[\text{OH}^-]$ and $\text{pH} = 14 - \text{pOH}$ But it adds up..
5. Post-Equivalence Point (Excess Strong Base)
Beyond the equivalence point, the weak acid has been completely consumed. The pH is dictated entirely by the concentration of the excess strong base ($\text{OH}^-$) added. The contribution of the conjugate base hydrolysis becomes negligible compared to the excess hydroxide ions. The pH calculation simplifies to:
$ [\text{OH}^-] = \frac{\text{moles excess OH}^-}{\text{total volume}} $ $ \text{pH} = 14 + \log[\text{OH}^-] $
The curve in this region merges asymptotically with the curve of a strong acid-strong base titration.
Selecting the Correct Indicator
Choosing an appropriate visual indicator is arguably the most practical aspect of this titration. Because the equivalence point is basic (typically pH 8–10 depending on the acid strength and concentration), the indicator must change color within the steep vertical portion of the curve surrounding the equivalence point.
- Phenolphthalein (transition range pH 8.2 – 10.0) is the standard choice for most weak acid–strong base titrations. Its colorless-to-pink transition falls perfectly within the basic equivalence point region.
- Bromothymol blue (pH 6.0 – 7.6) is generally unsuitable. Its transition range ends before the equivalence point is reached, leading to a significant titration error (under-titration).
- Methyl red (pH 4.4 – 6.2) changes color far too early, in the buffer region, resulting in a massive error.
Using a pH meter or a Gran plot analysis eliminates indicator error entirely, providing the most accurate determination of the equivalence volume.
Step-by-Step Calculation Example
Consider the titration of 25.100 M Acetic Acid ($\text{CH}_3\text{COOH}$, $K_a = 1.In practice, 00 mL of 0. Also, 8 \times 10^{-5}$) with 0. 100 M NaOH Simple, but easy to overlook..
1. Initial pH: $ [\text{H}^+] = \sqrt{(1.8 \times 10^{-5})(0
