Example Calculation - 3

This worked example finds the overall percentage uncertainty in a titration result.Question: a 25.0 cm³ pipette (± 0.06 cm³) is used to transfer sodium hydroxide to a conical flask. The burette (± 0.05 cm³ per reading) reads 0.00 cm³ at the start and 23.40 cm³ at the end point. Calculate the total percentage uncertainty from the volume measurements.Step 1: uncertainty in the titre. The titre comes from two readings, so the uncertainties add:uncertainty = 0.05 + 0.05 = ± 0.10 cm³percentage uncertainty = (0.10 ÷ 23.40) × 100 = 0.43%Step 2: uncertainty in the pipette volume. The pipette is filled to one mark, so its tolerance is used once:percentage uncertainty = (0.06 ÷ 25.0) × 100 = 0.24%Step 3: combine. The concentration is calculated by multiplying and dividing these volumes, so the percentage uncertainties add:total = 0.43 + 0.24 = 0.67%Interpreting the result: the burette is the larger contributor. If the concentrations were changed so the titre was only about 12 cm³, its percentage uncertainty would roughly double to about 0.8%. That is why titrations are designed to give titres in the range of about 20 to 30 cm³.If the standard solution also has a stated uncertainty in its concentration, add that percentage to the total as well.