Titrating an Unknown Acid with a Contaminated NaOH Solution
A student prepares a standard solution of sodium hydroxide by dissolving 4.00 g of NaOH pellets in distilled water to make 1.00 L. The label on the pellets notes they have absorbed water and are only 92% pure NaOH by mass (the rest is inert). The student titrates 25.0 mL of a monoprotic acid HX of unknown concentration with this NaOH solution. Phenolphthalein is used as indicator. The student records that 22.4 mL of the NaOH solution is needed to reach the endpoint. During a second trial, the student accidentally overshoots the endpoint by adding 1.5 mL extra NaOH solution. The molar mass of NaOH is 40.0 g/mol.
1. Calculate the true concentration of the NaOH solution and then determine the concentration of the acid HX. Show how the purity affects the result.
Read the worked answer
Step 1 - Actual mass of pure NaOH: 4.00 g × 0.92 = 3.68 g pure NaOH.
Step 2 - Moles of NaOH: n = 3.68 g ÷ 40.0 g/mol = 0.0920 mol.
Step 3 - Concentration: C(NaOH) = 0.0920 mol ÷ 1.00 L = 0.0920 mol/L.
Step 4 - Titration stoichiometry (1:1 for monoprotic acid vs NaOH): n(HX) = C(NaOH) × V(NaOH) = 0.0920 mol/L × 0.0224 L = 2.06 × 10⁻³ mol.
Step 5 - Acid concentration: C(HX) = 2.06 × 10⁻³ mol ÷ 0.0250 L = 0.0824 mol/L.
Purity effect: If the student ignored the 92% purity and used 4.00 g directly, C(NaOH) would be 0.100 mol/L, giving C(HX) = 0.0896 mol/L - an error of about 8.7% too high. The impurity inflates the apparent concentration, so the acid concentration is overestimated.
2. Explain why the second trial (with 1.5 mL overshoot) gives a systematically high value, and propose two concrete procedural improvements to reduce this error.
Read the worked answer
Why overshoot inflates the result: The endpoint is taken as the point where the indicator just turns pink. Adding 1.5 mL extra means the recorded volume is 22.4 + 1.5 = 23.9 mL instead of 22.4 mL. Since n(HX) is computed from V(NaOH), the calculated moles of acid increase by a factor 23.9/22.4 ≈ 1.067, a ~6.7% overestimate. The extra NaOH does not correspond to any additional acid, so the volume read is larger than the equivalence volume.
Improvements:
- Use a more precise indicator or a pH meter. Phenolphthalein changes colour over a pH range; a pH meter allows plotting the titration curve and locating the equivalence point as the steepest part of the curve, independent of indicator judgement.
- Perform a rough trial first, then add dropwise near the endpoint. A preliminary coarse titration locates the approximate endpoint; subsequent trials can be run quickly to within 1–2 mL and then finished dropwise (or half-dropwise with swirling), sharply reducing overshoot.
A third acceptable improvement: use a burette with finer graduations and read the bottom of the meniscus at eye level to reduce reading error.