During an acid-base titration, pH changes as the titrant is added. Plotting pH against the volume of acid or base added produces a titration curve. The shape of this curve depends entirely on the strengths of the acid and base being titrated, and it determines which indicator is suitable to detect the end point.
The point in a titration where the moles of acid and base are stoichiometrically equal. It represents the midpoint of the vertical steep section of the pH curve.
The point in a titration where an indicator changes colour. For a successful titration, the end point must closely match the equivalence point.
The range of pH values over which an indicator changes colour. For a suitable indicator, this range must fall entirely within the vertical steep section of the titration curve.
🔑 Key Principle
An indicator is a weak acid that has a different colour from its conjugate base. In an acid-base titration, we choose an indicator whose transition pH range fits completely within the vertical portion of the pH curve. This ensures that the addition of a single drop of titrant near the equivalence point will cause a large, sudden pH change, triggering a complete and sharp colour change.
The Four Main Titration Curves
We classify titration curves by the strength of the acid and base. Below are the key characteristics of the curves when adding a strong base (alkali) to an acid:
- Strong Acid - Strong Base (e.g. HCl + NaOH): Starts very low (pH ~1). Remains flat, then rises extremely steeply between pH 3 and 11 near the equivalence point. Equivalence point is exactly at pH 7.
- Weak Acid - Strong Base (e.g. CH3COOH + NaOH): Starts slightly higher (pH ~3). Rises slightly at first, then flattens out (the buffer region) before rising steeply between pH 7 and 11. Equivalence point is above 7 (typically pH 8 to 9) because the conjugate base hydrolyses water to form OH- ions.
- Strong Acid - Weak Base (e.g. HCl + NH3): Starts very low (pH ~1). Rises steeply between pH 3 and 7. Equivalence point is below 7 (typically pH 5 to 6) because the conjugate acid hydrolyses water to form H+ ions.
- Weak Acid - Weak Base (e.g. CH3COOH + NH3): Starts around pH 3. Rises gradually throughout the titration without any steep vertical section. There is no suitable indicator for this titration.
Common Indicators and Selection
The table below lists the two key indicators specified in the AQA syllabus, their colour transitions, and pH ranges:
| Indicator | pH Range | Colour in Acid | Colour in Alkali | Suitable Titrations |
|---|---|---|---|---|
| Methyl Orange | 3.1 to 4.4 | Red | Yellow | Strong Acid - Strong Base, Strong Acid - Weak Base |
| Phenolphthalein | 8.3 to 10.0 | Colourless | Pink | Strong Acid - Strong Base, Weak Acid - Strong Base |
The Buffer Region and Half-Equivalence Point
During the titration of a weak acid with a strong base (as shown in the red curve above), there is a flat region before the equivalence point known as the buffer region. Here, the solution contains a mixture of unreacted weak acid and the salt formed by neutralisation. This forms an active buffer system that resists changes in pH.
🔑 Key Principle: The Half-Equivalence Point
At exactly half-equivalence (when half the volume of alkali required for neutralisation has been added), exactly half of the weak acid HA has been converted into the conjugate base A-.
Therefore, \( [\text{HA}] = [\text{A}^-] \).
Substituting this into the Ka expression:
\( \text{K}_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]} \quad \text{simplifies to} \quad \text{K}_a = [\text{H}^+] \)
Taking the negative logarithm of both sides: \( \text{pH} = \text{pK}_a \).
This relationship is a very common exam calculation. If you are given a graph showing the titration of a weak acid, you can determine its pKa by finding the equivalence point volume (e.g. 30 cm3), dividing it by 2 to get the half-equivalence volume (15 cm3), and reading the pH from the graph at this volume. The pH value at this point is equal to the pKa, and you can calculate Ka using \( \text{K}_a = 10^{-\text{pH}} \).
Step 1: Identify the type of titration:
HCl is a strong acid and NH3 is a weak base. This is a strong acid - weak base titration.
Step 2: Determine the steep vertical pH range:
For a strong acid - weak base titration, the steep vertical section of the pH curve lies in the acidic range, typically between pH 3 and 7.
Step 3: Evaluate suitability of each indicator:
- Methyl orange: The pH transition range is 3.1 to 4.4. This range falls entirely within the steep vertical section (pH 3 to 7). Therefore, methyl orange is suitable and will show a sharp colour change.
- Phenolphthalein: The pH transition range is 8.3 to 10.0. This range lies in the alkaline region, which is past the vertical equivalence point on this curve. Therefore, phenolphthalein is not suitable and would change colour gradually before the equivalence point is reached.
Step 1: Identify the half-equivalence point:
The equivalence point volume is 24.0 cm3. The volume at half-equivalence is: \[ \frac{24.0}{2} = 12.0\text{ cm}^3 \]
Step 2: Relate pH to pKa:
At the half-equivalence point, \( [\text{acid}] = [\text{salt}] \), meaning: \[ \text{pK}_a = \text{pH} = 4.76 \]
Step 3: Convert pKa to Ka:
\[ \text{K}_a = 10^{-\text{pK}_a} = 10^{-4.76} = 1.74 \times 10^{-5}\text{ mol dm}^{-3} \]
The Ka of the weak acid is \( 1.74 \times 10^{-5}\text{ mol dm}^{-3} \).
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