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Processing Data in Chemistry (DP IB Chemistry): Revision Note

Richard Boole

Written by: Richard Boole

Reviewed by: Philippa Platt

Updated on

Processing Data in Chemistry

  • This is the "calculation" phase of your investigation.

  • Data processing involves applying mathematical calculations to your raw data to determine the final values you need to answer your research question

    • For example, calculating a concentration, a rate of reaction, or an enthalpy change.

  • The goal is to carry out relevant and accurate calculations, including the propagation of uncertainties, and to present the results clearly.

Principles of data processing

Carry out relevant and accurate data processing

  • Your processed data should be presented in a new, clearly labelled table.

    • It is good practice to show the raw data and processed data in separate tables.

  • Show your working clearly.

    • For every type of calculation you perform, you must show one full, worked example.

  • Calculating an average.

    • When you have repeat trials, you must calculate an average (mean) value to use in further calculations.

    • In titrations, you should only average concordant results (titres that are within ±0.10 cm3 of each other).

      • You must exclude the rough titre and any anomalous results from your average.

  • Propagating uncertainties

    • The uncertainties from your raw measurements must be carried through your calculations to find the uncertainty in your final, processed result. The rules for this depend on the calculation:

      • For addition or subtraction:

        • Add the absolute uncertainties.

        • Example: A titre is final reading - initial reading.

        • The uncertainty is (uncertainty of final reading) + (uncertainty of initial reading).

        • For a burette, this is 0.05 cm3 + 0.05 cm3 = 0.10 cm3.

      • For multiplication or division:

        • Add the percentage uncertainties.

        • Example: To calculate n = C × V, you would add the % uncertainty in C to the % uncertainty in V to get the % uncertainty in n.

  • Significant figures

    • Your final calculated answer should be given to a number of significant figures that reflects the precision of the raw data used.

      • The general rule is that your final answer should have the same number of significant figures as the least precise piece of data used in the calculation.

Worked Example

Research question:

  • "What is the concentration of ethanoic acid in commercially sold vinegar?"

Raw data table:

Trial

Initial burette reading / cm3 (±0.05)

Final burette reading / cm3 (±0.05)

Titre / cm3 (±0.10)

Rough

0.00

23.85

23.85

1

0.20

23.60

23.40

2

0.15

23.50

23.35

3

1.50

24.90

23.40

Processing the data:

  1. Calculate the average titre:

    • The concordant results are Trial 1 (23.40 cm3), Trial 2 (23.35 cm3) and Trial 3 (23.40 cm3).

    • The rough titre is excluded.

    • Average titre = fraction numerator open parentheses 23.40 space cm cubed plus space 23.35 space cm cubed plus space 23.40 space cm cubed close parentheses over denominator 3 end fraction= 23.38 cm3

  2. Calculate moles of NaOH used

    • n = C × V

    • n(NaOH) = 0.100 mol dm-3 × open parentheses fraction numerator 23.48 space cm cubed over denominator 1000 space dm cubed end fraction close parentheses = 0.002338 mol

  3. Determine moles of CH₃COOH

    • Using the 1:1 mole ratio from the equation
      CH3COOH + NaOH → CH3COONa + H2O)

    • n(CH3COOH) = n(NaOH) = 0.002338 mol

  4. Calculate concentration of diluted CH3COOH

    • C = n / V

    • The volume of the original vinegar sample was 25.00 cm3 (0.025 dm3)

    • C(CH3COOH) = fraction numerator 0.002338 space mol over denominator 0.025 space dm cubed end fraction= 0.09352 mol dm-3.

  5. Calculate concentration of original vinegar:

    • This accounts for the 10x dilution.

    • C(original) = 0.09352 × 10 = 0.9352 mol dm-3.

    • The concentration of NaOH was given to 3 s.f., so the final answer should also be to 3 s.f.

    • Final answer = 0.935 mol dm-3

Worked Example

Worked Example

Research question:

  • "What is the effect of temperature on the rate of reaction?"

Raw data for the 40.0°C condition:

  • Time (s): 31.5, 30.9, 31.2

Processing the data:

  1. Calculate the average time:

    • Average time = fraction numerator open parentheses 31.5 space plus 30.9 plus 31.2 close parentheses over denominator 3 end fraction= 31.2 s

  2. Calculate the rate of reaction

    • Rate = 1 / time

    • Rate =fraction numerator 1 over denominator 31.2 end fraction = 0.03205 s-1

    • Given the raw data has 3 s.f., the rate should be 0.0321 s-1.

  3. Propagate the uncertainty:

    • The uncertainty in the stopwatch reading was ±0.2 s.

    • Percentage uncertainty in time = (absolute uncertainty / measured value) × 100

      • % uncertainty = (fraction numerator 0.2 over denominator 31.2 end fraction) × 100 = 0.641%

    • For Rate = 1/t, the percentage uncertainty in the rate is the same as the percentage uncertainty in time.

      • So, % uncertainty in rate = 0.641%.

    • Absolute uncertainty in rate = (0.641 / 100) × 0.03205 = 0.000205 s-1.

    • The uncertainty should be given to one significant figure: 0.0002 s-1.

  • The final rate should be quoted to the same number of decimal places as the uncertainty.

    • Final processed result: Rate = 0.0321 ± 0.0002 s-1

Examiner Tips and Tricks

  • Show one full worked example.

    • Even if you use a spreadsheet, you must show the assessor how you got from your raw data to your processed data for one set of values.

    • This is essential for gaining full marks.

  • Watch your significant figures.

    • A common error is to write down the full calculator display.

    • Always round your final answer to the correct number of significant figures based on your raw data.

  • Don't forget units.

    • Every calculated value in your processed data table must have the correct units.

    • Creating new quantities like 'rate' means you will have to derive the units (e.g., s-1 or mol dm-3 s-1).

  • Propagate uncertainties.

    • For a high-scoring IA, you must show a sample calculation for propagating the uncertainty for your main processed result.

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    Author
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    Richard Boole

    Author: Richard Boole

    Expertise: Chemistry Content Creator

    Richard has taught Chemistry for over 15 years as well as working as a science tutor, examiner, content creator and author. He wasn’t the greatest at exams and only discovered how to revise in his final year at university. That knowledge made him want to help students learn how to revise, challenge them to think about what they actually know and hopefully succeed; so here he is, happily, at SME.

    Philippa Platt

    Reviewer: Philippa Platt

    Expertise: Chemistry Content Creator

    Philippa has worked as a GCSE and A level chemistry teacher and tutor for over thirteen years. She studied chemistry and sport science at Loughborough University graduating in 2007 having also completed her PGCE in science. Throughout her time as a teacher she was incharge of a boarding house for five years and coached many teams in a variety of sports. When not producing resources with the chemistry team, Philippa enjoys being active outside with her young family and is a very keen gardener