Errors in Chemistry ExperimentsRohana Sirimanna

Reading errors (Data Collection)

• When reading off a scale the error is half the last decimal place you can use or the value given to you for this piece of equipment.

• Electronic Balance• If it reads to 0.001 g the error / uncertainty is ± 0.001 g

Pipettehttp://www.labsglassware.com

Pipette

BuretteWe have checked with our glassware suppliers and have decided the error will be ± 0.05 mL

Volumetric Flasks250.0 mL ± 0.15 mL 100.0 mL ± 0.1 mL

Other Equipment

• Thermometer:• Glass ± 0.25 oC Digital ± 0.1 oC• Measuring Cylinders:

– 100 mL ± 1 mL, – 10 mL ± 0.2 mL, – 25 mL ± 0.5 mL

Combining errors (Data Analysis)

• When data is added or subtracted the errors need to be added.

• Eg. 22.45 ± 0.01g - 20.32 ± 0.01 g

= 2.13 ± 0.02 g

When averaging data we will use the half range rule for the errors.

• This means subtracting the lowest reading from the highest reading and then dividing this answer by two.

• (If this number is smaller than the reading error, use the reading error.)

Average titration results

Average these titration results:24.3 ± 0.1 mL, 24.1 ± 0.1 mL, 24.5 ± 0.1 mL• The average of 24.3, 24.1 and 24.5 is 24.3• The range will be 24.5 – 24.1 = 0.4.

Divide this by 2 to get 0.2• Therefore the average titre is 24.3 ± 0.2 mL

Using data in formulae (Data Analysis)

• Most commonly this is done using

n = m/Mr

c = n/V • Δ H = msΔT or mole ratios.

The errors from above first need to be converted into percentage errors.

2.13 ± 0.01 g the percentage error is calculated by: 0.01 x 100 = 0.47% 2.13

The percentage errors for each piece of data used in the arithmetic are added.

Then the percentage error is converted back into a “real” error.

The errors from above first need to be converted into percentage errors.

• An answer for a concentration of 0.26 mol dm-3 ± 2.3% should be converted by:2.3% of 0.26 is .023 x 0.26 = 0.00598• This should be written as:

0.26 ± 0.01 mol dm-3

Significant figures

• In IB you have to be aware of using the correct number of significant figures in your calculations or you will lose marks.

Significant figures

• Examples

• 3.65 has 3 significant figures.• 52.9 has 3 significant figures.• 374.85 has 5 significant figures.• 0.5822 has 4 significant figures.

Zeroes• We need to be careful about zeroes

because sometimes they are counted and sometimes not.

• This will be apparent in the following examples:

1.If the zeroes precede the first non-zero digit they are NOT significant.

Eg 0.04 has 1 significant figure.0.00025 has 2 significant figures.

Zeroes2. If the zeroes are between non-zero digits they

ARE significant.

Eg 0.304 has 3 significant figures. 807 has 3 significant figures. 0.04092 has 4 significant figures.

Zeroes3. If the zeroes follow the non-zero digits we can't

be sure if there is no decimal point. If there is a decimal point we count the zeroes.

Eg 0.50 has 2 significant figures. 250.00 has 5 significant figures 21.60 has 4 significant figures. 35000 may have 2, 3, 4 or 5 significant

figures depending on the accuracy of the data. Using scientific notation helps here.

Using scientific notation helps here.

If it is 3.50 x 104 there are 3 significant figures.

If it is 3.5 x 104 there are 2 significant figures.

If it is 3.500 x 104 there are 4 significant figures.

If it is 3.5000 x 104 there are 5 significant figures.

Writing the Final Answer• The final answer must not have more

significant figures than the data with the least number of significant figures.

• In this modern age of calculators you are able to store many decimal places as the calculation is done.

• You must do this and then convert your answer to the appropriate number of significant figures at the end.

Worked examples• Pure washing soda crystals have the formula

Na2CO3 . 10H2O.• A student was given some old crystals which

were white and flaky and was asked to find out their formula. [It will not have 10 water molecules any more]

• This is the procedure the student used:1. “A crucible and lid were weighed. Some crystals

were placed in the crucible and weighed with the lid. 2. The crucible was heated, gently at first, and then more

strongly, with the lid being left slightly ajar. 3. The crucible, lid and residue were allowed to cool and

were then re-weighed.4. The heating, cooling and weighing were then repeated.

Calculation• The results were: (mass in g ± 0.01g)

Mass of crucible + lid 19.41Mass of crucible + lid + crystals

24.76Mass of crucible + lid + crystals after 1st heating 22.06Mass of crucible + lid + crystals after 2nd heating

22.06

Calculation

2Titration between 25.0 mL of 0.450 mol dm-3

NaOH and H2SO4 gave the following titres:

• Therefore the concentration of the sulfuric acid is 0.235 ± 0.003 mol dm-3

• Answer has 3 s. f. because the data with the lowest number of significant figures was the pipette and the NaOH concentration which both had 3. The burette volumes also had 3.

• The error should only affect the last decimal place hence it is

± 0.003 mol dm-3 and not ± 0.003008 mol dm-3.

• Notice how SMALL this error is and therefore how accurate your school laboratory equipment is.

• Remember this when you do your EVALUATION.