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A1.8 · Analyse evidence, solve quantitative problems, and evaluate error

Learn to analyse evidence, solve quantitative problems, and evaluate error through clear examples and targeted practice.

Ontario Grade 12 Chemistry

Scientific Investigation Skills and Career Exploration

A practical approach to interpreting measurements and judging conclusions

A chemistry result is only as useful as the evidence and reasoning behind it. A change in colour, a measured mass, or a calculated concentration can support a conclusion, but each needs careful interpretation. This lesson develops a repeatable approach: examine the evidence, choose a suitable calculation, and consider how measurement limits affect the result. The methods apply to many chemistry investigations without assuming that one particular experiment has been performed.

What you will learn

Separate observations, measurements, and conclusions when analysing chemistry evidence.
Choose and use a suitable equation to solve a quantitative problem.
Report units and significant digits consistently.
Identify sources of error and explain how they may affect a result.

1. From observation to evidence-based conclusion

An observation is a recorded description of what is seen or measured. For example, a solution becoming cloudy is a qualitative observation because it describes a quality rather than a number. A measured temperature change is quantitative because it includes a number and a unit. Evidence is the set of observations or measurements used to support a conclusion.

Before interpreting results, check what was measured, how it was measured, and whether the comparison is fair. In a fair comparison, the factor being studied changes while other relevant conditions are kept as similar as possible. Also check whether the measurements are repeated, whether units are stated, and whether any result is unusual compared with the others.

A conclusion should match the strength of the evidence. Measurements that show a consistent difference may support a claim that two conditions produce different results. They do not automatically prove why the difference occurred. State what the data show, then distinguish that statement from a possible explanation.

At the particle level, chemical changes involve particles rearranging or interacting. Measurements such as temperature, mass, or volume are observable effects of the system, not direct pictures of individual particles. Use a particle explanation only when it is consistent with the evidence and the chemistry being studied.

Describe the measurement before explaining it.
Check units, repeated results, and the conditions of comparison.
Do not claim more than the evidence supports.

2. Set up quantitative problems clearly

A quantitative problem uses measured or supplied numbers to find an unknown quantity. Begin by listing the known values with their units and identifying the quantity requested. Then choose an equation that connects those quantities. Rearrange it if needed before substituting values. This makes it easier to check whether the calculation answers the question.

For example, concentration in grams per litre is mass of dissolved substance divided by solution volume. The volume must be in litres when using this unit. If it is given in millilitres, convert it first:

1000\ \mathrm{mL}=1\ \mathrm{L}

. Units act like labels that help reveal an incorrect conversion or an unsuitable equation.

Substitute values with units, carry units through the calculation, and check whether they simplify to the requested unit. A result that is numerically plausible but has the wrong unit is not a complete answer. Include a short statement that interprets the result in the context of the question.

Significant digits communicate the precision of a reported measurement. In multiplication and division, the answer is generally reported with the same number of significant digits as the measured value with the fewest significant digits. Keep extra digits during intermediate calculations, then round the final result. Do not report more precision than the measurements support.

c=\frac{m}{V}

List known values, units, and the unknown before calculating.
Convert units before substitution when the equation requires it.
Keep guard digits during working and round the final answer appropriately.

3. Understand and evaluate error

In chemistry, error means a difference between a measured or calculated result and a reference value, or a limitation that affects a measurement. It does not necessarily mean that someone made a careless mistake. Instruments have limits, and procedures can introduce consistent or changing effects.

A systematic error shifts measurements in a similar direction each time. For instance, a balance that is not zeroed may make every measured mass too high or too low. Repeating the measurement alone may not remove this effect. A random error causes measurements to vary unpredictably, such as small differences in reading a meniscus. Repeated measurements can help reveal this variation.

When a reference value is supplied, percent error describes the size of the difference relative to that reference. Use the absolute difference so that percent error is not negative. The reference value must be appropriate for the comparison, and both values must use the same unit. Percent error does not by itself identify the cause of a difference.

When evaluating a result, identify a plausible source of error and explain its likely effect. For example, if some liquid remains in a transfer container, less material reaches the final solution. This may affect a calculated concentration, but the direction and size depend on which quantity was measured and how the calculation was set up. Avoid claiming a specific cause without evidence.

\%\text{ error}=\frac{|\text{measured}-\text{reference}|}{\text{reference}}\times100\%

Systematic error tends to shift results; random error tends to create scatter.
Percent error compares a result with a stated reference value.
A useful evaluation links a possible error to its effect on the measured or calculated quantity.

4. A dependable reasoning routine

Use the same sequence whether a question asks for a calculation or an interpretation. First, identify the evidence and the claim being considered. Second, decide which quantities and relationships matter. Third, calculate with units and suitable rounding. Finally, compare the result with the evidence or reference and state a careful conclusion.

A useful check is to ask whether the answer has the right unit and a reasonable size. For a percent error, the result should be non-negative because the numerator uses an absolute difference. If the measured and reference values are identical, the percent error is zero. These checks can catch arithmetic or setup errors before the result is reported.

Evidence evaluation is not separate from calculation. A correct calculation can still support a weak conclusion if measurements are unreliable, the comparison is unfair, or the chosen reference is unsuitable. Likewise, a small percent error does not prove that every part of an investigation was accurate. Explain what the number indicates and what it cannot establish.

Interpret the final number rather than reporting it alone.
Check both the arithmetic and the quality of the evidence.
Keep conclusions within the limits of the measurements.

Worked example

Calculate concentration and compare with a reference

A sample is prepared by dissolving 2.46 g of a substance to make 0.200 L of solution. A reference concentration is 12.0 g/L. Calculate the sample concentration and its percent error relative to the reference.

Identify the quantities
The dissolved mass is $2.46\ \mathrm{g}$ and the solution volume is $0.200\ \mathrm{L}$ . The requested concentration is in grams per litre, so the volume is already in the required unit.
Calculate the concentration
Divide the mass by the solution volume. The units divide to give grams per litre. Both measured values have three significant digits, so report the concentration to three significant digits.
$c=\frac{2.46\ \mathrm{g}}{0.200\ \mathrm{L}}=12.3\ \mathrm{g/L}$
Find the percent error
Compare the sample concentration with the supplied reference. The absolute difference is $0.3\ \mathrm{g/L}$ . Dividing by the reference and multiplying by 100% gives a percent error of 2.5% to two significant digits.
$\%\text{ error}=\frac{|12.3-12.0|\ \mathrm{g/L}}{12.0\ \mathrm{g/L}}\times100\%=2.5\%$
Interpret the result
The calculated sample concentration is slightly higher than the reference, with a percent error of 2.5%. This comparison describes the size of the difference; it does not identify its cause. More information about the measuring equipment and procedure would be needed to evaluate possible sources of error.

Answer: The sample concentration is 12.3 g/L, and its percent error relative to the reference is 2.5%.

Check: The concentration unit is g/L, and the percent error is positive because the difference is taken as an absolute value.

Common mistakes and how to avoid them

Treating a possible explanation as if it were directly measured.

Correction: Separate the observation from the explanation, and make clear which statements are supported by the data.

Using millilitres in an equation that requires litres without converting.

Correction: Check the required unit before substitution and convert the volume first.

Reporting too many digits because a calculator displays them.

Correction: Round the final answer to match the precision supported by the measurements.

Calling every difference from a reference a careless mistake.

Correction: Use error to describe a difference or measurement limitation, then assess plausible causes using evidence.

Lesson summary

Analyse evidence by checking what was measured, the units, and the fairness of the comparison.
Solve quantitative problems by identifying knowns and unknowns, choosing a suitable equation, and tracking units.
Use significant digits to avoid implying more measurement precision than is available.
Evaluate error by comparing with an appropriate reference and linking possible measurement limits to their effects.

Check your understanding

Question 1

A sample has a measured concentration of 9.6 g/L. The reference value is 10.0 g/L. What is the percent error?

4.0%
0.4%
104%
-4.0%

Show answer and explanation

4.0%

The absolute difference is 0.4 g/L. Dividing by 10.0 g/L and multiplying by 100% gives 4.0%. Percent error is not negative.

Question 2

A balance reads 0.02 g when nothing is on it, and the reading is not corrected. What type of error is most likely?

Systematic error
Random error only
No error, because the reading is small
A percent error that cannot be evaluated

Show answer and explanation

Systematic error

An uncorrected zero reading can shift measurements in a consistent direction, which is characteristic of systematic error.

Question 3

Two reported measurements are 15.2 g and 15.3 g. Which statement is best supported by this information alone?

The measurements are close in value, but the cause of their difference is not established.
The second measurement is definitely more accurate.
The substance changed chemically between measurements.
The measurements prove there is no error.

Show answer and explanation

The measurements are close in value, but the cause of their difference is not established.

The values differ by 0.1 g, but no reference value or procedure details are given to establish accuracy or explain the difference.

Key terms

Evidence: Observations or measurements used to assess a claim.
Quantitative: Expressed using numbers and units.
Systematic error: An effect that tends to shift measurements in a consistent direction.
Random error: Unpredictable variation among measurements.
Significant digits: Digits that communicate the precision supported by a measurement.
Percent error: The absolute difference between a measured result and a reference, expressed as a percentage of the reference.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 12 Chemistry (SCH4U), expectation A1.8. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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