Analysis of data and sources
A headline says that a new fuel is "carbon neutral", and a campaign group says a lake is "dangerously high" in phosphate. Both sound convincing. Before you believe either, you need to ask: what data is this based on, who collected it, and does it actually support the claim? In Leaving Cert Chemistry you are expected to handle data and judge sources like a scientist, in the Chemistry in Practice Investigation and in the written exam. By the end of this page you will be able to answer the "carbon neutral" question for yourself.
Describing and processing data
Start with what the numbers show, then calculate. Use the data to support every statement you make.
Describing a trend means saying what changes, by how much and over what period. "CO₂ rises" is weak. "CO₂ rises from 339 ppm in 1980 to 414 ppm in 2020" is a proper description.
| Quantity | How to find it |
|---|---|
| Mean | sum of values ÷ number of values |
| Range | largest value − smallest value |
| Change | final value − initial value |
| Average change per year | change ÷ number of years |
| Percentage change | $\dfrac{\text{change}}{\text{original value}} \times 100$ |
| Percentage difference from a stated value | $\dfrac{\text{measured} - \text{stated}}{\text{stated}} \times 100$ |
Rates and ratios
When data is a time taken (for example, time for a reaction to finish), the rate is proportional to $1/t$. A shorter time means a faster rate. A ratio of rates compares two conditions: $\dfrac{1/t_2}{1/t_1} = \dfrac{t_1}{t_2}$.
The table shows atmospheric $\mathrm{CO_2}$ concentration measured at an observatory. | Year | $\mathrm{CO_2}$ (ppm) | |---|---| | 1980 | 339 | | 2000 | 369 | | 2020 |…
The table shows atmospheric $\mathrm{CO_2}$ concentration measured at an observatory.
| Year | $\mathrm{CO_2}$ (ppm) |
|---|---|
| 1980 | 339 |
| 2000 | 369 |
| 2020 | 414 |
- a) Describe the trend shown.
- b) Calculate the increase between 1980 and 2020.
- c) Calculate the average increase per year over this period.
Nitrate concentrations ($\text{mg}\,\text{L}^{-1}$) were measured in a river downstream of a farm: Mon 18, Tue 22, Wed 35, Thu 31, Fri 20. Heavy rain fell on Tuesday…
Nitrate concentrations ($\text{mg}\,\text{L}^{-1}$) were measured in a river downstream of a farm: Mon 18, Tue 22, Wed 35, Thu 31, Fri 20. Heavy rain fell on Tuesday night.
- a) Calculate the mean nitrate concentration.
- b) Identify the peak value and suggest, using the rainfall information, an explanation.
- c) The EU limit for drinking water is $50\,\text{mg}\,\text{L}^{-1}$ nitrate. Comment on the results.
- d) Suggest one improvement to the sampling design.
Reliability, validity and experimental error
These words have precise meanings. Use them carefully.
A set of results can be reliable but not accurate. For example, a burette that was never rinsed properly might give titres that all agree but are all too high. This is a systematic error. A random error makes repeats scatter around the true value. Repeating and averaging reduces random error but does not remove systematic error.
To improve confidence in a result you can: repeat and take the mean (concordant titres within 0.1 cm³), use more precise apparatus, calibrate instruments, increase the sample size, take samples at several sites and times, and control the variables.
A student measures the pH of a stream at the same point on five days: 6.8, 7.0, 6.9, 7.1, 6.8. a) Calculate the mean pH. b) State the range of the data. c) State what is…
A student measures the pH of a stream at the same point on five days: 6.8, 7.0, 6.9, 7.1, 6.8.
- a) Calculate the mean pH.
- b) State the range of the data.
- c) State what is meant by a reliable set of results.
A graph of a titration of a monoprotic acid with sodium hydroxide gives an equivalence point at $24.6\,\text{cm}^3$ of $0.100\,\text{M}$ NaOH for a $25.0\,\text{cm}^3$…
A graph of a titration of a monoprotic acid with sodium hydroxide gives an equivalence point at $24.6\,\text{cm}^3$ of $0.100\,\text{M}$ NaOH for a $25.0\,\text{cm}^3$ acid sample.
- a) Calculate the concentration of the acid.
- b) The manufacturer states the concentration is $0.105\,\text{M}$. Calculate the percentage difference from the stated value.
- c) Suggest two possible sources of experimental error.
- d) State what you would do to improve confidence in the result.
Evaluating sources and claims
Not every source deserves the same trust. Ask these questions about any source.
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Who wrote it, and what are their qualifications?
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Has it been peer reviewed? Other scientists have checked the method and conclusions before publication.
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Where does the data come from? How large is the sample, how was it collected, and is it recent?
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Who paid for it, and who gains? A company selling a product or a campaign group may have a reason to present data one way.
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Can the results be checked or repeated by others?
A peer-reviewed journal article is usually more reliable than a company blog. However, even a good source can be wrong. Compare several independent sources and check they agree.
Correlation and causation
Two things can rise together without one causing the other.
To test for a cause you need a control group (same conditions, but without the factor being tested), a large enough sample, and the other variables controlled. Ideally the study is repeated by others.
Two sources give information on the safety of a food additive. Source A is a peer-reviewed journal article. Source B is a blog post by a company selling an alternative…
Two sources give information on the safety of a food additive. Source A is a peer-reviewed journal article. Source B is a blog post by a company selling an alternative product.
- a) State which source is more reliable.
- b) Give two reasons for your answer.
- c) Explain what is meant by bias.
A news headline states: "Chemical X in tap water causes illness." The report gives that among 20 people who drank water with X, 3 became ill, and no control group was…
A news headline states: "Chemical X in tap water causes illness." The report gives that among 20 people who drank water with X, 3 became ill, and no control group was studied.
- a) Calculate the percentage who became ill.
- b) Explain why the lack of a control group prevents a conclusion about cause.
- c) Suggest how a better study could be designed.
- d) Distinguish between correlation and causation.
Evaluating claims in context
Hard questions combine everything above: process the data, then judge how strong the evidence is. A good structure for an "evaluate" answer is:
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Calculate what the data actually shows.
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Judge the method: sample size, number of sites and repeats, time period, controls.
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Check for bias in who produced the report.
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Say what extra data would settle the question.
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Give a balanced conclusion, supported by evidence.
Testing a rule of thumb against data
A claim such as "the rate doubles for every 10 °C rise" can be tested. Calculate $1/t$ at each temperature, then the ratio of successive rates. If the ratios are close to 2 the claim is a fair approximation. Then explain it: higher temperature means particles have greater kinetic energy, so a larger fraction of collisions have energy at least the activation energy, and collisions are more frequent. The fraction with enough energy does not rise by exactly the same factor at every temperature, so "doubling" is only approximate.
Life-cycle thinking: is it really "carbon neutral"?
Now return to the headline. A fuel made from waste cooking oil is said to be "carbon neutral" because the CO₂ released was absorbed by plants. To judge this you must list the assumptions and check the whole life cycle: growing, collecting and transporting the oil, production (electricity from a grid that is 40% fossil-fuelled gives CO₂), combustion, and disposal of by-products. The CO₂ from combustion may be offset by the plants that made the oil, but the CO₂ from the electricity and transport is not. So the fuel can have lower net emissions than a fossil fuel, but "carbon neutral" overstates it. A life-cycle assessment needs data on the energy and emissions at every stage, an agreed system boundary, and independent verification.
Back to the start: the "carbon neutral" claim is not justified as stated. The combustion CO₂ may be recycled by plants, but production uses electricity that is 40% fossil-fuelled, and transport and processing add emissions. A fair statement is "lower carbon", pending a full life-cycle assessment.
Two reports estimate the effect of a new wastewater plant on a lake. Report 1 (by the council) states average phosphate fell from $80$ to…
Two reports estimate the effect of a new wastewater plant on a lake. Report 1 (by the council) states average phosphate fell from $80$ to $55\,\mu\text{g}\,\text{L}^{-1}$ using monthly samples over 3 years at four sites. Report 2 (by a campaign group) states that phosphate "remains dangerously high" using one sample taken after a storm at one site.
- a) Calculate the percentage reduction in Report 1.
- b) Evaluate the validity and reliability of each report.
- c) Identify possible bias in each.
- d) Describe the further data you would need to conclude whether the plant is effective.
A student claims that "the rate of reaction doubles for every $10\,^{\circ}\text{C}$ rise". The student's data for the time to complete a reaction are: | Temperature…
A student claims that "the rate of reaction doubles for every $10\,^{\circ}\text{C}$ rise". The student's data for the time to complete a reaction are:
| Temperature (°C) | 20 | 30 | 40 | 50 |
|---|---|---|---|---|
| Time (s) | 160 | 82 | 38 | 21 |
- a) Calculate the relative rate ($1/t$, in $\text{s}^{-1}$) at each temperature.
- b) Calculate the ratio of rates for each $10\,^{\circ}\text{C}$ step.
- c) Evaluate the student's claim, using the data.
- d) Explain, using collision theory, why rate increases with temperature, and why the claim is only an approximate rule.
An article claims that a new "green" fuel is carbon neutral. It provides: the fuel is made from waste cooking oil; production consumes electricity from a grid that is…
An article claims that a new "green" fuel is carbon neutral. It provides: the fuel is made from waste cooking oil; production consumes electricity from a grid that is 40% fossil-fuelled; and combustion releases $2.4\,\text{kg}$ of $\mathrm{CO_2}$ per litre, of which the article says all is "recycled" by the oil-producing plants.
- a) Identify the assumptions behind the claim of carbon neutrality.
- b) Explain why the electricity used in production affects the claim.
- c) Suggest what additional data would allow a life-cycle assessment.
- d) Write a balanced conclusion on whether the claim is justified on the evidence given.
Summary
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Describe data with numbers: trend, change, mean, range, average change per year, percentage change (divide by the original value) and rates ($1/t$).
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Reliable means repeats agree; valid means a fair test measuring what it claims; accurate means close to the true value. Repeating reduces random error, not systematic error.
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Judge a source by author, peer review, sample size, method, funding and possible bias.
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Correlation does not prove causation: you need a control group, a large sample and controlled variables.
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For "evaluate" questions: calculate, judge the method, check for bias, say what extra data is needed, then give a balanced conclusion.
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Claims such as "carbon neutral" need a life-cycle assessment, with the assumptions made explicit.