Chemical measurements

Whenever a measurement is made in chemistry, there is always some uncertainty in the result obtained. There are many causes of uncertainty in chemical measurements. For example it may be difficult to judge:

  • whether a thermometer is showing a temperature of 24.0°C, 24.5°C or 25.0°C
  • exactly when a chemical reaction has finished

There are two ways of estimating uncertainty:

  • by considering the resolution of measuring instruments
  • from the range of a set of repeat measurements

Estimating uncertainty from measuring instruments

The resolution of a measuring instrument is the smallest change in a quantity that gives a change in the reading that can be seen. A thermometer with a mark at every 1.0°C has a resolution of 1.0°C. It has a higher resolution than a thermometer with a mark at every 2.0°C.

The uncertainty of a measuring instrument is estimated as plus or minus (±) half the smallest scale division. For a thermometer with a mark at every 1.0°C, the uncertainty is ± 0.5°C. This means that if a student reads a value from this thermometer as 24.0°C, they could give the result as 24.0°C ± 0.5°C.

For a digital measuring instrument, the uncertainty is half the last digit shown on its display. For a timer reading to 0.1 s, the uncertainty is ± 0.05 s.

Estimating uncertainty from sets of repeat measurements

For a set of repeat measurements, the uncertainty is ± half the range. This means that the value can be given as the mean value ± half the range.

Worked example

Question

The table shows five measurements for the volume of acid required in a neutralisation reaction.

Calculate the mean volume and estimate the uncertainty.

Test number12345
Volume24.024.523.525.023.0

mean = \frac{24.0+24.5+23.5+25.0+23.0}{5}

= 24.0 cm3

range = (biggest value - smallest value)

= 25.0 - 23.0

= 2.0 cm3

uncertainty = ± half the range

= \frac{2.0}{2} cm3

= ± 1.0 cm3

So the volume is 24.0 cm3 ± 1.0 cm3.

Showing uncertainty on a graph

Uncertainty can also be shown on a graph. All the repeat readings for each value of the independent variable are plotted. Vertical lines joining these values represent the uncertainty.

A graph showing the repeat readings for each value of the independent variable. The short vertical lines represent uncertaintyA graph showing the repeat readings for each value of the independent variable. The short vertical lines represent uncertainty.