Adding Uncertainties

Many measured quantities come from two readings subtracted from each other:• a titre = final burette reading − initial burette reading• a temperature change = final temperature − initial temperature• a mass by difference = mass of container with solid − mass of empty containerEach reading has its own uncertainty, and either could be too high or too low. In the worst case they work against each other, so the uncertainties are added, even though the readings are subtracted.uncertainty of a difference = uncertainty of reading 1 + uncertainty of reading 2Worked example 1: a burette is read to ± 0.05 cm³. The readings are 0.00 cm³ and 22.50 cm³.titre = 22.50 cm³, uncertainty = 0.05 + 0.05 = ± 0.10 cm³percentage uncertainty = (0.10 ÷ 22.50) × 100 = 0.44%Worked example 2: a thermometer is read to ± 0.5 °C. The temperature rises from 20.0 °C to 25.0 °C.temperature change = 5.0 °C, uncertainty = 0.5 + 0.5 = ± 1.0 °Cpercentage uncertainty = (1.0 ÷ 5.0) × 100 = 20%Notice how large the second value is. A small temperature change measured with an ordinary thermometer is often the biggest source of uncertainty in an enthalpy experiment.Note: a pipette or volumetric flask is filled to a single mark, so only its stated tolerance is used, not a doubled value.