IB Chemistry home > Syllabus 2016 > Stoichiometry > Errors and inaccuracies in experimentation

It is physically impossible to measure to 100% accuracy. Chemistry, as an experimental science, by its very nature involves errors and inaccuracies in the course of experimental work. The important issue here is that the inaccuracies are minimised and errors recognised as part of the results and conclusions process.

Experimentation and measurement

Chemistry is an experimental science. All of the laws, rules and principles of chemistry have been elaborated by experiment and observation over many years.

This process is known as the experimental method and involves the following stages:


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Experimental science in schools

In principle, there are few actual measuring devices in common use in the laboratory of a normal school. Direct measurements may usually be made of the following quantities:

A more specialised laboratory also may have devices for measuring:


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Apparatus and instrumentation

The common laboratory apparatus used to take direct measurements:

Concept
Instrument
units
abbreviation
     
Temperature Thermometer degrees Celsius
ºC
Mass Electronic balance grams / kilograms
g / kg
Time Stopwatch seconds
s
Length Ruler / Micrometer metres
m
Liquid volume Measuring cylinder / pipette / burette centimetres cubed / litres
cm3 / dm3
Gas volume Gas syringe centimetres cubed / litres
cm3 / dm3

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Inaccuracy

Any experiment has inherent inaccuracies that must be considered when analysing results. These inaccuracies, or errors, derive from three general sources.

  1. Instrumental tolerance
  2. Experimental design
  3. Human limitations

The reliability of any experimental data must take these factors into consideration. In many cases it is possible to estimate the degree of accuracy quantitatively by consideration of the percentage error in the measurements at each stage of a procedure.


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Instrument tolerance

The instrumental tolerance is the degree of accuracy of a specific instrument, or piece of apparatus, being used to take a measurement. The instrument or apparatus may have the tolerance written on it, or a judgement must be made regarding the accuracy of any measurement.

For example, a thermometer may have an inherent inaccuracy of ± 0.25 ºC. This means that its accuracy lies within this range. However, it is also possible that the ability of a person to read the thermometer lies outside of this range, eg ± 0.5 ºC. The greater error margin should be used in this case.

When deciding the error of a piece of apparatus, it is aso important to take into account the number of times that a reading must be taken.

For example, a burette must be read twice to record a liquid volume - once at the start and once at the end. This means that any inaccuracy in the reading is doubled to get the inaccuracy in the volume measured. If it is only possible to measure the liquid level to an accuracy of within ± 0.05 cm3 then the final inaccuracy in a liquid volume must be ± 0.1 cm3.

Instrument
Tolerance
comment
 
(typical values)
 
Thermometer
± 0.25 ºC
depends on the scale size.
Electronic balance (2dp)
± 0.005 g
probably the most accurate instrument in most laboratories
Stopwatch
± 0.2 s
may depend on other factors apart from reaction time, such as judgement of end point etc.
Ruler / Micrometer
± 0.05 cm
micrometers are obviously more accurate.
Measuring cylinder (100 cm3)
± 1 cm3
as the measuring cylinder gets smaller so the absolute tolerance improves.
Pipette (25 cm3)
± 0.04 cm3
pipettes have grades of accuracy and the value is usually written on the side.
Burette
± 0.05 cm3
the inaccuracy must be doubled to take into account the two readings taken.
Gas syringe (100 cm3)
± 1 cm3
collection of gases is also possible over water using an inverted burette.

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Error recording

The inaccuracy of any reading must be recorded in the results tables.

A typical table of results for a titration would look like this

Experiment

initial burette reading
/cm3 (± 0.05)

final burette reading /cm3 (± 0.05)
titre /cm3 (± 0.1)
1
0.00
21.75
21.75
2
0.00
21.70
21.70
3
0.00
21.70
21.70

It is clear from this table that the measurements were taken in cm3 and that the final titre considered the inaccuracy of the two readings.


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Percentage error calculation

In any procedure there are often many different kinds of measurements taken.

The simplest way to deal with errors and inaccuracy in a quantitative manner is to convert all of the estimated errors into percentage errors and to sum them for each stage of the procedure.

Using the above titration table as an example. If experiments 2 and 3 were taken to represent the average titre, then the final value would be 21.70 cm3 ( ± 0.1 ). To convert this inaccuracy into percentage error, the absolute error (± 0.1) must be divided by the value (21.70 cm3 ) and the whole multiplied by 100.

absolute error = ± 0.1

percentage error = ± 0.1/21.70 x 100 = ± 0.46%


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Multi-stage procedures

Most experiments involve more than one operation. These are called multi-stage procedures. In order to assess the error of the final results of an experiment, the inaccuracies at each stage of the procedure must be taken into account. To do this the individual measurement errors are normally converted into percentage errors.

These can be summed to give a final percentage error that, in turn, is re-converted into an absolute error, or inaccuracy, in the final answer.

Example experimental procedure

If a student prepares a standard solution and then uses this solution to find the molarity of an unknown he would follow the general procedure:

Weigh out a mass (say 5.20g) of a standard solute

Transfer to a 250 cm3 (graduated) volumetric flask and make up to the mark with distilled water.

Using a pipette, transfer a 25 cm3 aliquot of the unknown solution to a conical flask and titrate against the standard solution.

Calculated average titre = 21.75 cm3 (± 0.1)

Error analysis

Tolerance of electronic balance = ± 0.005 g

percentage error in mass = 0.005/5.20 x 100 = 0.096%

Tolerance of volumetric flask = ± 0.23 cm3

percentage error in volumetric flask solution = 0.23/250 x 100 = 0.092%

Tolerance of pipette = ± 0.04 cm3

percentage error in pipette = 0.04/25 x 100 = 0.160%

Tolerance of burette = ± 0.1 cm3

Percentage error in burette = 0.1/21.7 x 100 = 0.461%

Total percentage error in titration 0.096 + 0.092 + 0.160 + 0.461 = 0.809%

It is this final error percentage that must be used to calculate the absolute error in the unknown solution concentration.


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