The Indicator Mismatch
A student titrates 25.0 mL of 0.100 mol L−1 ethanoic acid (Ka = 1.8 × 10^−5) with 0.100 mol L−1 NaOH. Using methyl orange (colour change pH 3.1–4.4), the student stops at the first orange tint and records 24.8 mL. A supervisor says the result is 'close enough' because 24.8 mL is near the expected 25.0 mL. The student asks whether phenolphthalein (pH 8.2–10.0) would be better and whether 24.8 mL is acceptable for a quantitative result.
1. Calculate the pH at the equivalence point and decide which indicator is appropriate.
Read the worked answer
Moles of acid = 0.0250 L × 0.100 M = 0.00250 mol. At equivalence, 0.00250 mol NaOH has been added, giving 25.0 mL; total volume = 50.0 mL. The acetate concentration is 0.00250/0.0500 = 0.0500 M.
Kb = Kw/Ka = 1.0 × 10^−14 / 1.8 × 10^−5 = 5.6 × 10^−10.
[OH−] = √(Kb × C) = √(5.6 × 10^−10 × 0.0500) = √(2.8 × 10^−11) = 5.3 × 10^−6 M.
pOH = 5.28, so pH = 8.72.
Phenolphthalein changes in the pH 8.2–10.0 range, which brackets 8.72, so it is appropriate. Methyl orange changes at pH 3.1–4.4, far before equivalence; it signals the buffer region, not the equivalence point.
2. Evaluate the supervisor's 'close enough' claim. Is 24.8 mL acceptable? Support your answer with a calculation or a clear argument.
Read the worked answer
No. The 24.8 mL endpoint is early because methyl orange changes in the buffer region, not at equivalence. At 24.8 mL, 0.00248 mol NaOH has been added, leaving 0.000020 mol acid in about 49.8 mL, so [H+] is roughly 4 × 10^−4 M and pH ≈ 3.4-well inside the methyl orange range but about 5 pH units away from the true equivalence pH.
The volume error is 0.2 mL out of 25.0 mL, or −0.8%, which may look small, but it is a systematic indicator error, not random scatter. For quantitative analysis, the endpoint must match the equivalence pH. The student should repeat with phenolphthalein and use concordant titres.
3. How would absorbed CO2 affect this titration, and what precaution should be taken?
Read the worked answer
CO2 from air dissolves to form carbonic acid, which can consume hydroxide and alter the pH at the endpoint. If the NaOH solution absorbs CO2, its effective concentration falls, so more titrant is needed and the calculated acid concentration is too high. If the acid sample absorbs CO2, the titration is less straightforward because carbonic acid contributes extra acidic protons.
Precaution: use freshly boiled, cooled, CO2-free deionised water; keep the NaOH reservoir protected with a CO2-absorbing guard tube; stopper the flask and titrate promptly; run a blank. The indicator choice should still be phenolphthalein for the ethanoic acid/NaOH system, because the equivalence pH is 8.72.