1) Error Analysis
Apparatus Errors (uncertainty)
Every time you make a measurement with a piece of apparatus, there is a small margin of error (i.e. uncertainty) in that
measurement due to the apparatus itself.
For example, no balance can measure an exact mass but a very expensive and high resolution balance may be able to
measure a mass to the nearest 0.0001 g, while a cheaper, lower resolution balance may only measure it to the nearest
0.1 g.
Errors such as this are known as apparatus error (uncertainties) and cannot be avoided, although they can be reduced
3
by using the highest resolution equipment available. For example, when measuring out 25 cm of a solution, a pipette is
much offers higher resolution than a measuring cylinder.
When you do quantitative experiments (those that require you to measure a quantity), you will have to calculate the total
apparatus error from the sum of the apparatus error for each piece of equipment you use to make a measurement.
Apparatus error for each piece of equipment = 100 x margin of error
quantity measured
3
For example, imagine a pupil doing an experiment where she measured out 1.245 g of a base, make it up to 250 cm of
3
solution in a volumetric flask, pipetted 25 cm of that solution into a conical flask, and then found that it reacted with
3
23.30 cm of acid in a titration using a burette.
Balance (± 0.001 g) 100 x (0.001/1.245) = 0.08%
3
Pipette (± 0.1 cm ) 100 x (0.1/25) = 0.40%
3
Volumetric flask (± 0.1 cm ) 100 x (0.1/250) = 0.04%
3
Burette (± 0.15 cm ) 100 x (0.15/23.30) = 0.64%
Total apparatus error = 1.16%
This means that the result of the experiment should be within 1.16% of the correct value.
When experiments are designed, we aim to ensure that the total apparatus error is minimised by working on a suitable
3
scale and with suitable apparatus. A very small titre for example (e.g. 5 cm ) leads to a very large apparatus error for
the burette (3%).
Experimental Errors
When you do an experiment you will make some small errors due to your technique being less than perfect. You can
calculate your experimental error as shown:
Experimental error = 100 x (real answer – experiment answer)
real answer
If experimental error is smaller than apparatus error, then you have an accurate result. However, if experimental error is
larger than apparatus error, then the result is inaccurate.
For example, imagine in the experiment above that the acid concentration was being measured and was found to be
-3 -3
0.0995 mol dm compared to the real value of 0.101 mol dm .
Experimental error = 100 x (0.101 – 0.0995) = 1.49%
0.101
The experimental error (1.49%) is greater than the apparatus error (1.16%) meaning that the results are inaccurate.
© www.CHEMSHEETS.co.uk 12-Jul-12 Chemsheets AS 062 1
, 2) Titrations
Preparation of stock solutions
1) Find the mass of a clean, dry weighing bottle (high precision balance). All masses should be recorded in a table.
2) Measure out the approximate mass of sample (low precision balance). Always take the bottle off the balance when
adding sample (to avoid spilling sample on the balance which can both damage the balance and makes the
weighing inaccurate).
3) Find the mass of the sample on the high precision balance.
3
4) Wash the contents of the weighing bottle into a 250 cm volumetric flask using de-ionised water and a clean funnel.
5) Add more de-ionised water and shake well to dissolve.
3
6) Make up to 250 cm (shake well before and after reaching the mark – make up to mark using a clean teat pipette.
Titrations
1) Wash burette with water and then the solution to be used.
2) Fill the burette, ensuring the bottom part is filled. Make sure you take the funnel out of the burette before doing a
titration.
3) Clean pipette first with water (blow out all water with the filler and dry the outside with a cloth) and then with the
solution that it going to be measured in it.
3
4) Transfer 25 cm with pipette into a clean conical flask (drain by gravity and touch the tip under the surface at the
end).
5) Add a few drops of indicator to the conical flask.
6) The first titration is rough (unless judged to be accurate) – note the start and end burette readings.
7) Repeat titrations, going dropwise near the end point – washing and swirling (a white tile may help, as may another
flask with original colour).
3
8) Repeat until you have concordant results (two within 0.10 cm )
3 3
9) Record results to the nearest 0.05 cm , e.g. 24.80 cm , etc., in a table similar to the one below.
rough accurate 1 accurate 2 accurate 3
3
initial reading (cm ) 0.10 24.35 0.00 23.90
final reading (cm3) 24.35 48.40 23.85 28.00
3
titre (cm ) 24.25 24.05 23.85 24.10
used in mean
10) Indicate which results are used in the mean (only use concordant results within the mean).
Cleaning glassware
Weighing bottle Wash and put in oven to dry (lids should go in the drying rack area).
Volumetric flask Wash and return to cupboard (with stopper in flask).
Burette Wash and return to drawer.
Pipette Wash and return to drawer.
Other glassware Wash and put back in trays.
Other apparatus Return to where it came from.
© www.CHEMSHEETS.co.uk 12-Jul-12 Chemsheets AS 062 2
Apparatus Errors (uncertainty)
Every time you make a measurement with a piece of apparatus, there is a small margin of error (i.e. uncertainty) in that
measurement due to the apparatus itself.
For example, no balance can measure an exact mass but a very expensive and high resolution balance may be able to
measure a mass to the nearest 0.0001 g, while a cheaper, lower resolution balance may only measure it to the nearest
0.1 g.
Errors such as this are known as apparatus error (uncertainties) and cannot be avoided, although they can be reduced
3
by using the highest resolution equipment available. For example, when measuring out 25 cm of a solution, a pipette is
much offers higher resolution than a measuring cylinder.
When you do quantitative experiments (those that require you to measure a quantity), you will have to calculate the total
apparatus error from the sum of the apparatus error for each piece of equipment you use to make a measurement.
Apparatus error for each piece of equipment = 100 x margin of error
quantity measured
3
For example, imagine a pupil doing an experiment where she measured out 1.245 g of a base, make it up to 250 cm of
3
solution in a volumetric flask, pipetted 25 cm of that solution into a conical flask, and then found that it reacted with
3
23.30 cm of acid in a titration using a burette.
Balance (± 0.001 g) 100 x (0.001/1.245) = 0.08%
3
Pipette (± 0.1 cm ) 100 x (0.1/25) = 0.40%
3
Volumetric flask (± 0.1 cm ) 100 x (0.1/250) = 0.04%
3
Burette (± 0.15 cm ) 100 x (0.15/23.30) = 0.64%
Total apparatus error = 1.16%
This means that the result of the experiment should be within 1.16% of the correct value.
When experiments are designed, we aim to ensure that the total apparatus error is minimised by working on a suitable
3
scale and with suitable apparatus. A very small titre for example (e.g. 5 cm ) leads to a very large apparatus error for
the burette (3%).
Experimental Errors
When you do an experiment you will make some small errors due to your technique being less than perfect. You can
calculate your experimental error as shown:
Experimental error = 100 x (real answer – experiment answer)
real answer
If experimental error is smaller than apparatus error, then you have an accurate result. However, if experimental error is
larger than apparatus error, then the result is inaccurate.
For example, imagine in the experiment above that the acid concentration was being measured and was found to be
-3 -3
0.0995 mol dm compared to the real value of 0.101 mol dm .
Experimental error = 100 x (0.101 – 0.0995) = 1.49%
0.101
The experimental error (1.49%) is greater than the apparatus error (1.16%) meaning that the results are inaccurate.
© www.CHEMSHEETS.co.uk 12-Jul-12 Chemsheets AS 062 1
, 2) Titrations
Preparation of stock solutions
1) Find the mass of a clean, dry weighing bottle (high precision balance). All masses should be recorded in a table.
2) Measure out the approximate mass of sample (low precision balance). Always take the bottle off the balance when
adding sample (to avoid spilling sample on the balance which can both damage the balance and makes the
weighing inaccurate).
3) Find the mass of the sample on the high precision balance.
3
4) Wash the contents of the weighing bottle into a 250 cm volumetric flask using de-ionised water and a clean funnel.
5) Add more de-ionised water and shake well to dissolve.
3
6) Make up to 250 cm (shake well before and after reaching the mark – make up to mark using a clean teat pipette.
Titrations
1) Wash burette with water and then the solution to be used.
2) Fill the burette, ensuring the bottom part is filled. Make sure you take the funnel out of the burette before doing a
titration.
3) Clean pipette first with water (blow out all water with the filler and dry the outside with a cloth) and then with the
solution that it going to be measured in it.
3
4) Transfer 25 cm with pipette into a clean conical flask (drain by gravity and touch the tip under the surface at the
end).
5) Add a few drops of indicator to the conical flask.
6) The first titration is rough (unless judged to be accurate) – note the start and end burette readings.
7) Repeat titrations, going dropwise near the end point – washing and swirling (a white tile may help, as may another
flask with original colour).
3
8) Repeat until you have concordant results (two within 0.10 cm )
3 3
9) Record results to the nearest 0.05 cm , e.g. 24.80 cm , etc., in a table similar to the one below.
rough accurate 1 accurate 2 accurate 3
3
initial reading (cm ) 0.10 24.35 0.00 23.90
final reading (cm3) 24.35 48.40 23.85 28.00
3
titre (cm ) 24.25 24.05 23.85 24.10
used in mean
10) Indicate which results are used in the mean (only use concordant results within the mean).
Cleaning glassware
Weighing bottle Wash and put in oven to dry (lids should go in the drying rack area).
Volumetric flask Wash and return to cupboard (with stopper in flask).
Burette Wash and return to drawer.
Pipette Wash and return to drawer.
Other glassware Wash and put back in trays.
Other apparatus Return to where it came from.
© www.CHEMSHEETS.co.uk 12-Jul-12 Chemsheets AS 062 2
