Acid–base titrations Knowledge-Based Study

Study notes

1. Overview of Titration

   An acid–base titration is a quantitative analytical technique used to determine the unknown concentration of an acid or a base by reacting it with a standard solution of known concentration.

   Key Definitions

   • Titrant: The solution of known concentration, typically delivered incrementally from a buret.
   • Analyte: The solution of unknown concentration, placed in an Erlenmeyer flask beneath the buret.
   • Equivalence Point: The theoretical point in the titration where chemically equivalent quantities of acid and base have reacted according to the reaction stoichiometry:

   For a monoprotic acid and base:

   $$n_{\text{H}^+} = n_{\text{OH}^-}$$

   • End Point: The experimental point at which an observable physical change occurs, usually a color change signaled by an acid–base indicator. In an ideal titration, the end point coincides closely with the equivalence point.

   Titration Curve Characteristics

   When a strong acid such as $\text{HCl}$ is titrated with a strong base such as $\text{NaOH}$, four distinct stages characterize the titration curve:

   1. Initial Point: Before any base is added, the pH is determined entirely by the complete dissociation of the strong acid: $$\text{pH} = -\log[\text{H}^+]$$
   2. Before Equivalence: Added $\text{OH}^-$ neutralizes some $\text{H}^+$. The pH rises slowly because excess hydronium remains in solution.
   3. Equivalence Point: Exactly equal moles of $\text{H}^+$ and $\text{OH}^-$ have combined to form water. The resulting ions (e.g., $\text{Na}^+$ and $\text{Cl}^-$) are spectator ions that do not hydrolyze. Therefore, at 25 °C: $$\text{pH} = 7.00$$
   4. After Equivalence: Excess $\text{OH}^-$ ions dictate the pH. The concentration of unreacted hydroxide is calculated from the remaining excess divided by the total solution volume.

   The curve features a very steep, near-vertical inflection between pH 4 and 10 surrounding the equivalence point.

   The Buffer Region and Conjugate Base Hydrolysis

   Titrating a weak acid ($\text{HA}$) with a strong base produces a distinct curve with key structural differences from a strong acid curve:

   1. The Buffer Region

   As strong base is gradually added, weak acid is converted into its conjugate base ($\text{A}^-$):

   $$\text{HA}(aq) + \text{OH}^-(aq) \rightarrow \text{A}^-(aq) + \text{H}_2\text{O}(l)$$

   The coexistence of appreciable amounts of both unreacted $\text{HA}$ and generated $\text{A}^-$ creates a buffer solution, resisting rapid changes in pH.

   2. The Half-Equivalence Point

   At exactly half the volume required to reach equivalence, half of the initial $\text{HA}$ has been converted to $\text{A}^-$:

   $$[\text{HA}] = [\text{A}^-]$$

   According to the Henderson–Hasselbalch equation:

   $$\text{pH} = \text{p}K_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) = \text{p}K_a$$

   Thus, at the half-equivalence point, the measured pH equals the $\text{p}K_a$ of the weak acid.

   3. The Equivalence Point

   At the equivalence point, all $\text{HA}$ has been converted to $\text{A}^-$. The conjugate base undergoes hydrolysis in water:

   $$\text{A}^-(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{HA}(aq) + \text{OH}^-(aq)$$

   Because hydroxide ions are produced, the equivalence point pH is always greater than 7.00 at 25 °C.

   Weak Base–Strong Acid Titrations

   When titrating a weak base (such as $\text{NH}_3$) with a strong acid (such as $\text{HCl}$):

   • At the half-equivalence point, $[\text{B}] = [\text{BH}^+]$, giving $\text{pOH} = \text{p}K_b$ (or $\text{pH} = 14 - \text{p}K_b$ at 25 °C).
   • At the equivalence point, the conjugate acid $\text{BH}^+$ hydrolyzes to produce $\text{H}_3\text{O}^+$: $$\text{BH}^+(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{B}(aq) + \text{H}_3\text{O}^+(aq)$$ Consequently, the equivalence point pH is always less than 7.00 at 25 °C.

   Criteria for Indicator Selection

   Acid–base indicators are themselves weak organic acids or bases whose protonated and deprotonated forms display different colors. To ensure minimal titration error:

   1. The transition interval of the indicator ($\text{pH} = \text{p}K_{\text{In}} \pm 1$) must lie on the steep vertical inflection portion of the titration curve.
   2. For strong acid–strong base titrations, either methyl red or phenolphthalein is suitable due to the wide vertical range.
   3. For weak acid–strong base titrations, an indicator changing color in the basic range (such as phenolphthalein, transition range 8.2–10.0) is necessary.
   4. For weak base–strong acid titrations, an indicator changing color in the acidic range (such as methyl red, transition range 4.4–6.2) must be used.