# Chemical measurements

Whenever a measurement is made in chemistry, there is always some 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 of measuring instruments
• from the 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 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 number Volume 1 2 3 4 5 24 24.5 23.5 25 23

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 uncertainty.