13.3 - Processing Data & Precision

What a calculation question looks like

Practical exam calculations usually involve finding a titre, a temperature change, a percentage, or a rate.

A typical question

The initial temperature of a mixture was 24.0 °C and the highest temperature reached was 46.5 °C. Calculate the temperature increase. Give your answer to the same number of decimal places as the temperatures given. [1]

Marks are awarded in stages:

1. Selecting the correct data and carrying out the calculation.
2. Rounding the answer to the requested precision: 46.5 - 24.0 = 22.5 °C.

Staged marking principles

• Units - Where an answer requires a unit, omitting it can lose a mark even if the calculated value is correct.
• Error carried forward (ecf) - If an earlier value is wrong but used correctly in later steps, subsequent marks can still be awarded - provided you show your working.

A typical question

A student measured the temperature of a mixture of magnesium ribbon and dilute sulfuric acid before and after the reaction. The initial temperature was 24.0 °C and the highest temperature reached was 46.5 °C. Calculate the temperature increase. Give your answer to the same number of decimal places as the temperatures given. [1]

Titre differences and the best titration result

A titration reading is a subtraction: the volume added is the final burette reading minus the initial reading.

Formula for volume added

Example - a burette reads 18.8 cm³ at the end and 4.2 cm³ at the start:

18.8 - 4.2 = 14.6 cm³

Choosing concordant results

• When calculating the mean titre, use only concordant results - titres that agree closely with each other (usually within 0.10 cm³).
• Exclude the initial rough titre or any anomalous readings.

Example - Three titres of 24.6 cm³, 23.8 cm³, and 24.0 cm³:

• 24.6 cm³ is a rough titre and is set aside.
• The mean of the concordant titres (23.8 cm³ and 24.0 cm³) is:

$$\text{Mean titre}=\frac{23.8+24.0}{2}=23.9{\text{cm}}^3$$

Temperature changes, percentages, and rates

• Rate units - The unit comes from the two quantities divided (e.g. length in cm divided by time in s gives cm/s).
• Percentages - Always divide the part by the whole it's a percentage of, not the other way round.

Precision - Decimal places, not significant figures

Practical papers assess recorded readings and calculated answers by decimal places rather than significant figures.

Rounding rules

• Match the data - Give the answer to the same number of decimal places as the raw data provided (e.g. 17.9 - 8.0 = 9.9, not 9.90 or 10).
• Do not round intermediate values - Carry full values through intermediate steps and round only the final answer.
• Maintain consistency - Paired or repeated answers must have the same number of decimal places.
• Include units - Where an answer requires a unit (such as °C or cm/s), omitting it can lose a mark.

Common exam questions

Question 1

A burette reads 27.3 cm³ at the end of a titration and 7.5 cm³ at the start. Calculate the volume added.

27.3 - 7.5 = 19.8 cm³.

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Question 2

Three titres are obtained: 25.1 cm³, 19.9 cm³, and 20.0 cm³. Which should be used to calculate a mean, and why?

The 19.9 cm³ and 20.0 cm³ results, because they are concordant, agreeing closely with each other; the 25.1 cm³ result is a rough titre well away from the other two and should be set aside rather than averaged in.

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Question 3

A student records an initial temperature of 22.0 °C and a highest temperature of 41.0 °C. Calculate the temperature increase, giving your answer to the appropriate precision.

41.0 - 22.0 = 19.0 °C, given to one decimal place to match the readings it came from.

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Question 4

A sample of brass with a mass of 2.00 g is reacted with acid, leaving 1.30 g of unreacted copper. Calculate the percentage of the brass, by mass, that was copper.

$\frac{1.30}{2.00}\times 100=65\%$ - the mass of copper (the part) divided by the mass of brass (the whole), not the other way round.

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Question 5

A 5 cm length of magnesium ribbon takes 20 s to disappear in an acid. Calculate the rate of reaction, giving a unit.

$\frac{5}{20}=0.25$ cm/s - the length reacted divided by the time taken, with the unit coming from the two quantities divided.

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Question 6

Why does an examiner mark a rounding mistake separately from the calculation itself?

Because the two things are checked in separate stages: whether the arithmetic is done correctly, and whether the answer is then given to the precision - in decimal places - that the question or the data requires. A correct calculation can still lose the rounding mark if it is left unrounded or rounded to the wrong number of decimal places.