IB Docs (2) Team MC test: Uncertainties & errors
Multiple choice test on 11.1 Uncertainties & errors
Use the following 'quiz' to test your knowledge and understanding of this sub-topic. You will need access to a periodic table (Section 6 of the IB data booklet).
If you get an answer wrong, read through the explanation carefully to learn from your mistakes.
Which statement best defines qualitative data?
Measurements do not have to be made to obtain qualitative data. It includes all observations such as colour change, evolution of gas and heat etc.
Which is not an SI unit for the given quantity?
The SI unit of mass is the kilogram, kg.
Which errors/uncertainties may be associated with the use of a mercury thermometer to measure the temperature of a solution?
Random errors are associated with all measurements. If the thermometer has been wrongly calibrated then it can also produce a systematic error.
Which will give the greatest degree of uncertainty when used to measure 50.0 cm3 of 0.100 mol dm−3 hydrochloric acid solution?
Because of the wide surface area of the contents, using a beaker is a much less accurate way to measure volume than the other three pieces of apparatus.
Three sets of five measurements of the same time were made. All the readings are in seconds. A different recording instrument was used for each of the three sets. The accurate value of the time is 15.0 s.
| I | II | III |
| 14.5 | 15.3 | 15.1 |
| 14.5 | 14.9 | 14.9 |
| 14.4 | 14.5 | 14.9 |
| 14.4 | 15.6 | 15.1 |
| 14.5 | 14.7 | 15.0 |
Which results can be described as precise and accurate?
I is the most precise but the least accurate. II and III are both accurate, as the average value in both cases is15.0 s, but only III is precise and accurate.
A student determined the molar mass of calcium carbonate by reacting a known mass of solid calcium carbonate with a known quantity of excess hydrochloric acid. Once all the calcium carbonate had reacted the excess hydrochloric acid was titrated with standard sodium hydroxide solution. The value obtained for the molar mass of calcium carbonate was 97.2 g mol-1.
What was the percentage error in this experiment?
M(CaCO3) = 40.08 + 12.01 + (3 x 16.00) ≈ 100 g mol−1. Percentage error = 100 x (100 - 97.2) ÷ 100 = 2.8%
A burette, pipette, volumetric flask and balance were used in an experiment to determine the percentage of iron in a tablet. The relative uncertainty associated with each of the four pieces of apparatus was calculated to be 0.4%, 0.4%, 0.3% and 0.1% respectively. The percentage of iron in the tablet was found to be 39.8%. Which is the correct way to present this result.
The total uncertainty = sum of the individual uncertainties = (0.4 + 0.4 + 0.3 + 0.1) = 1.2%. 1.2% of 39.8 = 0.48% = 0.5% to one decimal place. Note that a more sophisticated way of calculating the total uncertainty is that it equals the square root of the sum of the squares of the relative uncertainties, i.e. ((0.42 + 0.42 + 0.32 + 0.12)1/2 = 0.65%. 0.65% of 39.8 = 0.26 = 0.3% so the answer could be given as 39.8 ± 0.3%. This method is described in the Oxford IB text book but is not required by the IB.
22.50 cm3 of 0.1 mol dm−3 hydrochloric acid was required to neutralize 20.00 cm3 of a solution of sodium hydroxide. What was the concentration of the sodium hydroxide solution?
The number of significant figures in a result is based on the figures given in the data. Since the concentration of the acid is only given to one significant figure the concentration of the sodium hydroxide solution can only be quoted to one significant figure.
The mass of a sample of magnesium was obtained by first weighing an empty crucible then weighing it with the magnesium inside. After completely combusting the magnesium in oxygen the contents of the crucible were reweighed.
Mass of empty crucible = 16.455 g
Mass of crucible + magnesium = 17.670 g
Mass of crucible + magnesium oxide = 18.480 g
Which row lists the masses correctly?
| Row | Mass of magnesium / g | Mass of oxygen combined with magnesium / g |
| 1 | 1.215 | 0.81 |
| 2 | 1.2150 | 0.810 |
| 3 | 1.215 | 0.810 |
| 4 | 1.22 | 0.81 |
When subtracting masses it is the total number of decimal places that are important.
Despite repeated trials, an experiment to determine the concentration of a solution of sulfuric acid by titrating with a standard solution of potassium hydroxide consistently produced a result that was 10% less than the known value. Which factor might explain this discrepancy?
If it had been assumed that the sulfuric acid was monoprotic the result would have been consistently higher by 100%. The volume from the burette would still be quite accurate if the top of the meniscus was taken for the initial and final readings as the difference would cancel out the error and it would not be as great as 10%. It does not matter if there is distilled water in the conical flask as the amount of acid added to the flask will be unchanged. If the strength of the standard solution is wrong it will be a systematic error which will produce the discrepancy in the result.
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