Titration Decision: Which Indicator and Is the Result Trustworthy?
A student titrates 25.00 mL of an unknown weak monoprotic acid, HA, against 0.100 mol/L NaOH. Phenolphthalein (colour change pH 8.2–10.0) is used. Three concordant titres average 22.40 mL. The student then calculates the acid concentration and also the Ka, using the pH at the half-equivalence point, which was measured as 4.85. A second student repeats the titration using methyl orange (colour change pH 3.1–4.4) and obtains 22.35 mL, then claims the acid must be strong because "the indicator changed at the start."
1. Calculate the concentration of HA and its Ka from the data. State any assumptions.
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Concentration. At the equivalence point, moles of NaOH = moles of HA (1:1 for a monoprotic acid and NaOH). n(NaOH) = cV = 0.100 × 0.02240 = 2.240 × 10⁻³ mol. So n(HA) = 2.240 × 10⁻³ mol in 25.00 mL. c(HA) = 2.240 × 10⁻³ / 0.02500 = 0.0896 mol/L.
Ka from the half-equivalence point. At half-equivalence, [HA] ≈ [A⁻], so Ka = [H⁺] when the approximation holds. pH = 4.85 gives [H⁺] = 10⁻⁴·⁸⁵ = 1.41 × 10⁻⁵ mol/L. Hence Ka ≈ 1.4 × 10⁻⁵.
Assumptions. (1) The acid is monoprotic. (2) Activity coefficients are ignored. (3) At half-equivalence the dilution is small enough that [HA] ≈ [A⁻]; strictly, the half-equivalence volume is 11.20 mL and the total volume is 36.20 mL, so both concentrations are diluted equally and the ratio is preserved. (4) The pH meter was calibrated and the temperature is constant, since Ka depends on temperature. Note that Ka ≈ 1.4 × 10⁻⁵ is consistent with a weak acid such as acetic acid, which supports the weak-acid classification.
2. Assess the second student's claim and explain why phenolphthalein is the better choice for this titration.
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The claim is wrong. The second student's titre (22.35 mL) agrees closely with the first (22.40 mL), confirming the stoichiometry and concentration. The methyl orange changed colour early because its transition range (pH 3.1–4.4) is reached well before the equivalence point of a weak acid–strong base titration. Early colour change does not mean the acid is strong; it means the indicator is inappropriate.
Why phenolphthalein is correct. For a weak acid titrated with a strong base, the salt formed (NaA) hydrolyses to give a basic solution at equivalence. The equivalence pH is above 7, typically 8–9 for a weak acid of this Ka. Phenolphthalein's range (8.2–10.0) brackets the steep part of the titration curve near equivalence, so the endpoint closely matches the equivalence point. Methyl orange changes in the buffer region, where pH rises slowly, giving a premature and less sharp endpoint.
Conclusion. The phenolphthalein result is trustworthy; the methyl orange result should be rejected as an endpoint, even though numerically similar, because the sharpness and location of the change are inappropriate. The correct indicator is chosen by matching its transition range to the equivalence pH, which depends on the strength of the acid and base.