Choosing an Indicator for a Weak-Acid Titration
A teacher gives students 25.00 mL of an unknown weak monoprotic acid and 0.100 M NaOH. A pH titration curve shows the half-equivalence point at pH 4.80 and the equivalence point at 24.60 mL and pH 8.90. One student uses phenolphthalein (color change pH 8.2-10.0) and records an endpoint at 24.20 mL. Another uses methyl orange (pH 3.1-4.4) and records an endpoint at 23.90 mL. A third student argues that methyl orange is better because its color change is sharper and occurs closer to the start of the steep rise. The teacher has one class period to decide which indicator to approve, how to calculate Ka and the acid concentration, and how to address the third student's claim.
1. Select the appropriate indicator and justify the choice using the titration curve, including the pH at equivalence and the buffer region.
Read the worked answer
Phenolphthalein is the appropriate indicator. Its transition range, about pH 8.2-10.0, brackets the equivalence pH of 8.90, so the color change occurs on the steep part of the curve near the true equivalence volume. Methyl orange changes at pH 3.1-4.4, which lies in the buffer region where the weak acid and its conjugate base coexist. At that point the curve is relatively flat, so a small addition of NaOH produces a color change before equivalence. The half-equivalence pH of 4.80 confirms that the acid has a pKa near 4.8 and that the solution is buffered in the methyl orange range. The teacher should not choose an indicator solely because its color change looks sharp; the indicator's transition range must match the equivalence pH. Phenolphthalein's earlier endpoint at 24.20 mL is a small negative error, whereas methyl orange's endpoint at 23.90 mL is systematically before equivalence.
2. Calculate the acid concentration and Ka from the data, showing units and assumptions.
Read the worked answer
At equivalence, moles of NaOH equal moles of acid for a monoprotic acid. Moles NaOH = (0.100 mol/L)(0.02460 L) = 2.460 × 10^-3 mol. The acid concentration is 2.460 × 10^-3 mol / 0.02500 L = 0.0984 M. At half-equivalence, [HA] ≈ [A−], so pH = pKa. Therefore pKa = 4.80 and Ka = 10^-4.80 = 1.58 × 10^-5. The calculation assumes the acid is monoprotic, the reaction goes to completion, activities are approximated by concentrations, and the temperature is constant. The endpoint volumes from the students should not be used for the calculation because both are slightly off; the equivalence volume from the curve, 24.60 mL, is the appropriate value. The teacher should have students show the mole ratio explicitly and check that the units cancel.
3. Evaluate the third student's claim and explain why the phenolphthalein endpoint is 0.40 mL early. What correction or instructional point follows?
Read the worked answer
The third student's claim confuses a sharp color change with a valid endpoint. Methyl orange changes in the buffer region, well before the equivalence point, so its sharpness is misleading. Phenolphthalein is correct because its range includes the equivalence pH. The 0.40 mL early endpoint is a visual judgment error: the first faint pink may be detected before the stoichiometric point, or the student may have added NaOH too quickly near the endpoint. The teacher should instruct students to add NaOH dropwise near pH 8 and to stop at the first pale pink that persists for 30 seconds. A pH meter or a conductometric check could confirm the equivalence volume. The instructional point is that indicator choice depends on the equivalence pH, while endpoint accuracy depends on technique and on recognizing the correct color transition.