A 25.0\text{ cm}^3 portion of a 6.30\text{ g dm}^{-3} solution of an impure hydrated dipro… — JAMB UTME

A $25.0\text{ cm}^3$ portion of a $6.30\text{ g dm}^{-3}$ solution of an impure hydrated diprotic weak acid, $\text{H}_2\text{X}\cdot 2\text{H}_2\text{O}$ , requires $20.0\text{ cm}^3$ of $0.10\text{ mol dm}^{-3}$ sodium hydroxide ( $\text{NaOH}$ ) solution for complete neutralization. What is the percentage purity of the acid sample, and which indicator is most suitable for this titration?
[Molar mass of $\text{H}_2\text{X}\cdot 2\text{H}_2\text{O} = 126\text{ g mol}^{-1}$ ]

$80.0\%$ , using phenolphthaleinAnswer
B
$160.0\%$ , using phenolphthalein
C
$80.0\%$ , using methyl orange
D
$40.0\%$ , using phenolphthalein

Answer

80.0%, using phenolphthalein

The neutralization reaction requires two moles of sodium hydroxide for every mole of diprotic acid. Using

\frac{C_A V_A}{C_B V_B} = \frac{1}{2}

, the concentration of pure acid is

0.040\text{ mol dm}^{-3}

. Multiplying by the molar mass (

126\text{ g mol}^{-1}

) gives

5.04\text{ g dm}^{-3}

of pure acid. Dividing by the sample mass concentration (

6.30\text{ g dm}^{-3}

) and multiplying by

100\%

yields

80.0\%

. Because the titration involves a weak acid and a strong base, the solution at the end point is alkaline, which requires phenolphthalein as the indicator.

Step-by-Step Solution

Write the balanced chemical equation to determine the mole ratio.

\text{H}_2\text{X}\cdot 2\text{H}_2\text{O} + 2\text{NaOH} \rightarrow \text{Na}_2\text{X} + 4\text{H}_2\text{O}

, giving mole ratio

\frac{n_A}{n_B} = \frac{1}{2}

Diprotic acid yields two hydrogen ions per molecule, requiring two moles of sodium hydroxide for neutralization.

Calculate the molar concentration of the pure acid in solution using the titration formula.

\frac{C_A \times 25.0}{0.10 \times 20.0} = \frac{1}{2} \implies C_A = \frac{0.10 \times 20.0}{25.0 \times 2} = 0.040\text{ mol dm}^{-3}

Relating acid and base concentrations via volumes and stoichiometric coefficients.

Convert the molar concentration of pure acid to mass concentration.

\text{Mass concentration} = 0.040\text{ mol dm}^{-3} \times 126\text{ g mol}^{-1} = 5.04\text{ g dm}^{-3}.

Mass concentration equals molar concentration multiplied by molar mass.

Calculate the percentage purity of the acid sample.

\text{Percentage purity} = \left(\frac{5.04\text{ g dm}^{-3}}{6.30\text{ g dm}^{-3}}\right) \times 100\% = 80.0\%.

Percentage purity is the ratio of pure mass concentration to total sample mass concentration.

Select the correct indicator for the titration.

Phenolphthalein is selected.

Titrating a weak acid against a strong base produces a basic salt solution at equivalence (pH > 7), making phenolphthalein (pH range 8.3–10.0) the suitable indicator.

Key Concept

Volumetric Stoichiometry and Indicator Selection in Acid-Base Titrations

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