Accuracy in Measurements

Accuracy in Measurements
The measurements we make have a certain degree of uncertainty.
During chemical experiments, it is important to reduce errors in measurements.
Systematic errors
 The instruments you use may not be calibrated accurately so the measurements show
a regular (or systematic) error.
 Experimenter bias eg. parallax error.
Random (accidental) errors
 Normally, repeated measurements do not yield exactly the same results. These small differences
are the result of unknown factors, so cannot be controlled. They are called random or accidental errors.
 Making many measurements will help to ensure the reliability of your data.
Limits of reading
 Each measuring instrument’s accuracy is affected by the ‘limit of reading’ of its scale.
 For example, a thermometer may have 1 °C graduations. This is its limit of reading.
 The error is half the limit of reading (that is, ±0.5 °C).
 To reduce this error, you could use a thermometer with smaller graduations.
Experimental accuracy
 The accuracy of a result is how close a measurement is to the accepted value.
 The absolute error or percentage error is a measure of the degree of accuracy of the measurement.
 Example: If a student measures the heat of combustion of ethanol and obtains a value of 1310 kJ/mol
instead of the accepted value of 1367 kJ/mol, the:
(a) absolute error = 1367 – 1310 = 57 kJ
(b) percentage error = 57/1367 x 100/1 = 4%.
 It is important that the result of an experiment is reproducible each time you or other chemists repeat
the experiment. Precision is a measure of the reproducibility of the measurement.
 The results of all the repeated experiments should be consistent and clustered around the mean (with
small standard deviations).
 If the uncertainty is small, the measurements are very precise.
Consider the following experimental measurements of the enthalpy of combustion of methane using two
different pieces of equipment. The average deviations from the mean in the experimental measurements
and the accepted values from the literature are shown.
Apparatus 1: ΔH(methane) = –920 ± 20 kJ/mol
Apparatus 2: ΔH(methane) = –880 ± 80 kJ/mol
Accepted value: ΔH(methane) = –890 kJ/mol
Measurement of the heat of combustion of methane in apparatus 1 was more precise than that in apparatus
2; the average deviation from the mean was lower because successive measurements were more closely
However, the accuracy of measurements in apparatus 2 was greater as the percentage error in apparatus 2
(1%) was lower than in apparatus 1 (3%). This means that apparatus 2 produced more accurate results.