Training Analytical Chemistry Lab — Titrations, Spectrophotometry & Chromatography Acid-Base Titration — Titration Curves & Potentiometric Endpoint Detection
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Acid-Base Titration — Titration Curves & Potentiometric Endpoint Detection

60 min Analytical Chemistry Lab — Titrations, Spectrophotometry & Chromatography

Acid-Base Titration — Titration Curves & Potentiometric Endpoint Detection

A potentiometric acid-base titration monitors electrode potential (or pH) as titrant is added to the analyte. The resulting sigmoidal titration curve contains the equivalence point (stoichiometric endpoint), a buffer plateau governed by the Henderson–Hasselbalch equation, and regions where the strong acid or strong base dominates. Mathematical modelling of these curves underpins pH-meter calibration, pKa determination, and quantitative analysis of pharmaceutical formulations.

1. Strong Acid–Strong Base Titration

Titrating $V_a$ mL of strong acid ($C_a$ mol/L) with strong base ($C_b$ mol/L). At any added volume $V_b$:

$$[H^+] = \frac{C_a V_a - C_b V_b}{V_a + V_b} \quad (V_b < V_{eq})$$

At equivalence ($V_{eq} = C_a V_a / C_b$): $\text{pH} = 7.00$ (25°C). Beyond equivalence: $[OH^-] = (C_b V_b - C_a V_a)/(V_a + V_b)$. The pH jump at equivalence spans from $\sim 3$ to $\sim 11$ and is visible on the derivative plot $d\text{pH}/dV_b$ as a sharp maximum.

2. Weak Acid–Strong Base Titration

Titrating weak acid $HA$ ($K_a = 10^{-pK_a}$) with strong base $NaOH$. The reaction produces conjugate base $A^-$. Four regions:

  1. Before any base: $[H^+] = \sqrt{K_a C_a}$ (weak acid dissociation).
  2. Buffer region (partial neutralisation, $0 < f < 1$): $\text{pH} = pK_a + \log\frac{f}{1-f}$ where $f = V_b C_b / (V_a C_a)$ is the fraction neutralised. Half-equivalence ($f=0.5$): $\text{pH} = pK_a$.
  3. Equivalence point: only $A^-$ present, $[OH^-] = \sqrt{K_b C}$, $\text{pH} = 7 + \frac{1}{2}(pK_a - pK_w + \log C)$; equivalence pH $> 7$ for weak acid.
  4. Beyond equivalence: excess $NaOH$ dominates, $\text{pH} = 14 + \log\frac{C_b(V_b-V_{eq})}{V_a+V_b}$.

Buffer capacity $\beta$ (resistance to pH change): $\beta = -dC_{base}/d\text{pH} = 2.303 \cdot C \cdot K_a[H^+]/(K_a+[H^+])^2$. Maximum at $\text{pH} = pK_a$: $\beta_{max} = 2.303 \cdot C/4 = 0.576 C$.

3. Indicator Selection

An indicator $HIn$ changes colour over approximately $pK_{In} \pm 1$ pH units. The indicator should change colour at the equivalence point pH: for strong acid–strong base at pH 7 (phenolphthalein pH 8.2–10 or methyl red pH 4.4–6.2 both work due to the large pH jump); for weak acid–strong base at pH $> 7$ (phenolphthalein preferred).

4. Polyprotic Acid Titrations

A diprotic acid $H_2A$ ($pK_{a1}$, $pK_{a2}$) shows two equivalence points. If $pK_{a2} - pK_{a1} > 3$, the equivalence points are well-resolved. First equivalence: $\text{pH} \approx (pK_{a1}+pK_{a2})/2$ (amphiprotic species $HA^-$). Phosphoric acid ($pK_{a1}=2.15$, $pK_{a2}=7.20$, $pK_{a3}=12.35$) in physiological buffering: the $H_2PO_4^-$/$HPO_4^{2-}$ pair buffers at pH 7.2 — crucial for intracellular pH.

Worked Example — Weak Acid Titration at Half-Equivalence

50.0 mL of 0.100 M acetic acid ($pK_a = 4.76$) titrated with 0.100 M NaOH. At 25.0 mL added (half-equivalence): $\text{pH} = pK_a = 4.76$. Buffer capacity: $\beta = 0.576 \times 0.050 = 0.0288$ mol/L/pH unit (total volume = 75 mL, concentration of buffer pair $\approx C_{mix} = (0.100\times 50)/(75+25) \approx 0.050$ M). ✓

Virtual Acid-Base Titration
Equivalence volume =?mL
pH at equivalence =?
K_w check =1.0e-14

Practice Problems

1. Compute the pH at 0, 25, 49.9, 50.0, 50.1, and 100 mL for the titration of 50.0 mL of 0.100 M formic acid ($pK_a = 3.75$) with 0.100 M NaOH. Sketch the titration curve and indicate the buffer region.
2. Derive the expression for buffer capacity $\beta = -dC_{base}/d\text{pH}$ from the Henderson-Hasselbalch equation. Show that $\beta_{max} = 0.576C$ occurs at $\text{pH} = pK_a$. What is $\beta$ at $\text{pH} = pK_a \pm 1$?
3. A pharmaceutical QC lab titrates a sample containing $\sim$ 25 mmol of a monoprotic drug ($pK_a = 6.8$, MW = 250 g/mol) dissolved in 100 mL water. Design the titration: choose titrant concentration and volume, indicator, and the required buret precision to achieve $\pm 0.1\%$ accuracy in the drug assay.
Beer-Lambert Law & UV-Vis Spectrophotometry