Download MEASUREMENTS AND ERRORS and more Slides Chemistry in PDF only on Docsity!
MEASUREMENTS AND ERRORS
Accuracy A measure of the closeness of agreement between an individual result and the accepted value. An accurate result is in close agreement with the accepted value.
Error The difference between an individual measurement and the true value (or accepted reference value) of the quantity being measured.
Precision The closeness of agreement between independent measurements obtained under the same conditions. It depends only on the distribution of random errors (i.e. the spread of measurements) and does not relate to the true value.
Uncertainty An estimate attached to a measurement which characterises the range of values within which the true value is said to lie. It is written, for example, as 44.0 ± 0.4.
Reliability The opposite of uncertainty; high uncertainty = not very reliable measurement
Accuracy of measurements
Uncertainty is often taken to be half a division on either side of the smallest unit on the scale. However, the accuracy of measurements also depends on the quality of the apparatus used (e.g. Grade A or Grade B glassware.)
example If a 100 cm^3 measuring cylinder is graduated in 1 cm^3 divisions.
- Class A - maximum error of half a division (0.5 cm^3 )
- Class B - maximum error of a whole division (1 cm^3 )
Glassware
When glassware is manufactured there will always be a maximum error. This is usually marked on the glassware.
Temperature Volumetric equipment must not get warm because expansion of the glass will alter the volume; the temperature is marked on the apparatus.
In or out? Apparatus either...
holds an accurate measure (IN) or delivers an accurate volume (EX) volumetric flask burette measuring cylinder pipette
Measurements (^) F323 1
In 20°C 250cm^3
Ex 20°C Ex 20°C 25cm 3 25 cm^3
In 20°C 250 cm^3
Reading values
Digital • top pan balance or pH meter
- record all the digits shown
2-places 3-places
Non-digital • burette, measuring cylinder
- record all the figures that are known for certain
- read to half a division
- for a burette, record values to two decimal places ending in a 5 or a 0
Maximum errors
Burette • graduated in divisions every 0.1 cm^3
- maximum error is half a division i.e. ± 0.05 cm^3
- burettes are read twice, so the overall maximum error is 2 x 0.05 = ± 0.1 cm^3
Pipette • a 25 cm^3 pipette has a maximum error of 0.06 cm^3
- like all volumetric equipment it must be used properly
Balances a two-decimal place balance may a three-decimal place balance may have a maximum error of 0.005 g have a maximum error of 0.0005 g
The significance of the maximum error in a measurement depends upon how large a quantity is being measured. It is useful to quote this error as a percentage error.
(^2) F323 Measurements
2.45 cm^3
26.50 cm^3 3.00 cm^3
67.36 67.
67.32 67.33 67.357 67.
Q.1 Calculate the maximum error of a ...
- 50 cm^3 measuring cylinder cm^3 - 10 cm^3 measuring cylinder cm^3
Thermometers
Scale • maximum error depends on the scale and how many degrees per division
- maximum error when measuring a temperature change is one division
Temperature • the greater the temperature change, the lower the percentage error change
Significant figures When quoting a result, it should contain the same number of significant figures as the measurement that has the smallest number of significant figures.
Rounding off • if the last figure is between 5 and 9 inclusive round up
- if the last figure is between 0 and 4 inclusive round down
- should only be done at the end of a calculation
- should not be done after each step of a calculation (it causes rounding errors)
example 50.67 rounded to 3 sig figs is 50. 2 sig figs is 51 1 sig figs is 100
- for larger numbers, use standard form example 371 rounded to 2 sig figs is 3.7 x 10^2 3 sig figs is 3.71 x 10^2
(^4) F323 Measurements
Q.2 What is the reading on each thermometer?
A B
What is the maximum error involved? A B A B
Calculate the percentage error measuring a temperature change of 20°C using A B
Calculate the percentage error measuring a temperature change of 2°C using A B
°C
20
22
°C
20
21
Recording volumes during titrations
Burette measurements should be recorded to 2 decimal places with the last figure either 0 or 5.
During a titration, initial and final burette readings should be taken; the titre (actual volume delivered) is calculated by difference. Record titration results in a table as shown below.
Mean titres • repeat the titrations until there are two concordant titres (within 0.10 cm^3 )
- take an average of the concordant titres
- if this is not possible, use the two titres that have the closest agreement
example the two concordant titres are the 1st and 3rd (within 0.1 cm^3 of each other)
mean (average) titre value = 24.45 cm^3 + 24.35 cm^3 = 25.40 cm^3 2
overall maximum error = 2 x 0.05 = 0.10 cm^3 overall percentage error = 0.10 cm^3 x 100 = 0.39% 25.40 cm^3
There is a case for arguing that the accumulated errors indicate that one decimal place is more appropriate but this should not be used. The maximum error is the worst-case scenario and it is likely that the actual titre will in reality be more accurate than one decimal place.
If concordant titres within 0.05 cm^3 of one another are found there is a problem when calculating the mean titre. For example, a student may obtain three recorded titres of 24.45 cm^3 , 24.85 cm^3 and 24.40 cm^3.
mean titre value = 24.45 cm^3 + 24.40 cm^3 = 24.425 cm^3 2
This mean titre has a value that is more accurate than the burette can measure. The value of 24.425 cm^3 should more correctly be ‘rounded’ to 24.43 cm^3. It would seem very unfair not to credit a mean titre of 24.425 cm^3 in this case, especially as the results showed a better concordancy.
In assessed A level practical tasks, the mean of two titres of 25.25 cm^3 and 25.20 cm^3 will be allowed as 25.2 , 25.20 , 25.25 or 25.225 cm^3.
Measurements (^) F323 5
final volume / cm^3 initial volume / cm^3
tick if used to calculate mean
titre / cm^3
Approx 1 2 3
1.
26.
25.
**26.
24.** 3
**30.
24.**
**24.
24.** 3
