What lab questions test
Almost every year some FRQs are set in a lab: designing a procedure, processing data, analyzing error. The usual experiments are titration, gravimetric analysis, calorimetry, spectrophotometry, kinetics (measuring rates) and chromatography (each gets its own lesson in 4.4, the Lab Zone).
Five parts of an experimental design
- Purpose and the quantity to find: what is the final result, and which equation turns the measurements into it?
- What to measure, with what: mass (analytical balance), volume (buret, pipet, volumetric flask), temperature (thermometer), absorbance (spectrophotometer).
- Procedure: numbered steps, each specific about which equipment does what, such as “pipet 25.00 mL of the solution into a flask.”
- Controlled variables: change only the quantity being studied (the independent variable自变量), measure the quantity that responds (the dependent variable因变量), and keep everything else constant.
- Repetition: repeat measurements and average them to reduce random error.
Three steps for the direction of an error
- Which measurement changes? Too large or too small (for example, “unrinsed buret → volume used too large”).
- Where is it in the equation? In the numerator, the result moves the same way; in the denominator, the opposite way.
- Conclusion: too high, too low or no change. Write out the whole chain, not just the conclusion.
For a titration, [acid] = [base] × V(base) ÷ V(acid). V(base) is in the numerator, so if V(base) is too large, [acid] is too high.
Systematic and random error
- Systematic error系统误差 pushes every result the same way, such as an uncalibrated balance, an impure reagent or consistent heat loss. Repeating doesn’t remove it; the method or equipment has to change.
- Random error偶然误差 varies up and down, such as estimating the last digit of a reading. Averaging repeated measurements reduces it.
- Data close to one another are precise; an average close to the true value is accurate.
When asked for a source of error, vague answers like “human error” or “calculation error” earn nothing; name the specific action and its effect on a measurement.
Pick an experiment and decide whether each mistake makes the result too high, too low or unchanged:
25.00 mL of HCl of unknown concentration is titrated with NaOH of known concentration: [HCl] = [NaOH] × V(NaOH) ÷ 25.00 mL.
- The buret is rinsed with distilled water but not with the NaOH solution before filling
Water left in the buret dilutes the NaOH, so more volume is needed to reach the endpoint → V(NaOH) too large → [HCl] too high.
- 20 mL of distilled water is added to the flask before titrating
The moles of HCl don’t change, so neither does the NaOH needed → no change.
- The titration overshoots the endpoint, stopping only when the solution is deep pink
More NaOH is added than the reaction needs → V(NaOH) too large → [HCl] too high.
- The final buret reading is taken looking down at the meniscus
Buret markings increase downward, so reading from above gives a smaller value → V(NaOH) too small → [HCl] too low.
A chloride sample is dissolved, excess AgNO₃ is added to precipitate AgCl, and the AgCl is filtered, dried and weighed; the percent Cl in the sample is calculated from the mass of AgCl.
- The AgCl is weighed before it is completely dry
Water in the precipitate → mass too large → too much Cl calculated, so the result is too high.
- Some of the precipitate passes through the filter paper
Less AgCl is collected → mass too small → result too low.
- Not enough AgNO₃ is added, so not all the Cl⁻ precipitates
Less AgCl forms than it should → mass too small → result too low.
- The precipitate isn’t washed, and solid AgNO₃ is left on it after drying
The weighed mass includes AgNO₃ → mass too large → result too high.
HCl and NaOH solutions are mixed in a foam-cup calorimeter and the highest temperature is read; q = mcΔT is divided by the moles of water formed to give the size of the enthalpy of neutralization, |ΔH|.
- The calorimeter has no lid, so heat escapes to the air
Some of the heat doesn’t warm the solution → ΔT too small → q too small → |ΔH| too low.
- The highest temperature is read 0.5 °C too high
ΔT too large → q too large → |ΔH| too high.
- Twice the volume of each solution is used (same concentrations)
Both the heat released and the mass of solution double, so ΔT is unchanged, and so is ΔH per mole of water.
- The density of the solution is taken as 1.00 g/mL when it is really slightly higher
The mass used to calculate q is too small → q too small → |ΔH| too low.
A calibration curve (A = εbc) is made with a correctly zeroed spectrophotometer; then the absorbance of a sample solution is measured and its concentration read from the curve.
- When the sample is measured, there are fingerprints on the outside of the cuvette
Extra light is absorbed and scattered → measured absorbance too high → concentration too high.
- Before measuring the sample, the instrument isn’t zeroed with a blank, and the solvent absorbs slightly at this wavelength
The solvent’s absorbance is added to the sample’s → A too high → concentration too high.
- Too much water is added when diluting the sample, but the planned dilution factor is still used in the calculation
The solution measured is more dilute than intended → A too low → calculated concentration of the original sample too low.
- A different clean cuvette of the same type (same path length) is used
The path length b is the same and the cuvette is clean, so the absorbance is unchanged → no change.
Example 1: designing an experiment to find a molar mass
The lab has an unknown monoprotic solid acid, NaOH solution of known concentration, phenolphthalein, an analytical balance and standard glassware. Design an experiment to find the acid’s molar mass.
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The quantity and its equation. Molar mass = mass ÷ moles, and a monoprotic acid reacts 1 : 1 with NaOH, so:
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What to measure. The mass of acid (analytical balance) and the volume of NaOH used to reach the endpoint (buret).
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Procedure.
- Weigh about 0.2 g of the acid on the analytical balance, record the exact mass, transfer it to a flask, dissolve it in some distilled water and add 2–3 drops of phenolphthalein;
- rinse the buret with distilled water and then 2–3 times with small portions of the NaOH solution, fill it, and record the initial reading;
- titrate with swirling until a faint pink color lasts 30 seconds, and record the final reading.
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Calculation and repetition. V(NaOH) = final reading − initial reading; substitute to find M, then repeat twice more and average.
Example 2: a chain of reasoning for an error
In Example 1, a little of the weighed acid spills outside the flask during transfer (and the recorded mass isn’t changed). Is the measured molar mass too high or too low?
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Which measurement changes? The recorded mass m stays the same, but less acid ends up in the flask, so less NaOH is needed: V(NaOH) is too small.
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Where is it in the equation?
V(NaOH) is in the denominator.
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Conclusion. A smaller denominator with the same numerator makes M too high.
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The full answer. “Some acid spilled, so fewer moles of acid were in the flask and less NaOH volume was needed, making the calculated moles of acid too small; the recorded mass is unchanged, so M = m/n is too high.”
- Percent water in CuSO₄·5H₂O: heating stops before all the water is driven off
Too little water lost is measured → percent water too low.
- Gravimetric analysis: the precipitate is weighed before it’s fully dry (result: percent of the element)
Mass too large → result too high.
- Titration: the flask is rinsed with distilled water and not dried before use (result: acid concentration)
The moles of acid don’t change, so neither does the base needed.
- Calorimetry: poor stirring, so the highest temperature read is too low (result: |ΔH|)
ΔT too small → q too small → |ΔH| too low.
- Collecting H₂ over water, the vapor pressure of water isn’t subtracted (result: moles of H₂)
The total pressure is used as P(H₂), which is too large → n too high.
- Titration: an air bubble in the buret tip at the start disappears during the titration (result: acid concentration)
The reading includes the bubble’s volume → V(base) too large → concentration too high.
- Specific heat of a metal: some heat is lost while moving the hot metal into the water
The water gains less heat → calculated specific heat of the metal too low.
- A balance reads 0.02 g high every time, but the sample mass is found by subtracting two weighings
The offset cancels in the subtraction.
Common mistakes
Mistake 1: “For a source of error, ‘human error’ is enough.” The guidelines want a specific action (for example, “reading the buret from above at the endpoint”) and its effect on a measurement (“the reading is too small”), carried through to the result. Vague answers earn nothing.
Mistake 2: “Repeating the experiment removes all error.” Repetition only reduces random error. Systematic error pushes every trial the same way, so averaging can’t remove it; the method or calibration has to change.
Mistake 3: “Errors always make the result too low.” The direction depends on the equation: whether the affected quantity is in the numerator or denominator, and whether it’s too large or too small. Work through the equation every time.
Quick check
Which of these is a systematic error?
An error that pushes every reading the same way is systematic.
A set of results agree closely with each other, but their average is far from the true value. This shows:
Agreement means precision; being off the true value means inaccuracy, often from a systematic error.
In a titration, [acid] = [base] × V(base) ÷ V(acid). V(acid) is recorded as 25.00 mL, but the pipet actually delivered only 24.50 mL. How is the measured [acid] affected?
Less acid → less base needed → V(base) too small, while V(acid) is still taken as 25.00 mL → [acid] too low.
Why is a buret rinsed with the NaOH solution before it’s filled?
Leftover water dilutes the titrant, so more volume is needed.
When studying how temperature affects reaction rate, which must be kept constant?
Temperature is the independent variable and rate the dependent one; concentrations must be controlled.
Which is a sensible improvement to reduce heat loss in calorimetry?
Foam insulates, and a lid cuts heat loss from the surface.
AP-style practice
The concentration of a CuSO₄ solution is to be found by spectrophotometry. The lab has 0.100 M CuSO₄ standard solution, volumetric flasks, pipets, cuvettes and a spectrophotometer.
(a) Describe how to prepare a set of standard solutions of known concentration.
(b) Describe how to use them to make a calibration curve.
(c) Once the absorbance of the sample is measured, how is its concentration found?
(d) Before measuring the sample, a student doesn’t rinse the cuvette with the sample solution, so a little distilled water remains in it. Is the measured concentration too high or too low? Explain.
(e) Why is the absorbance measured at the wavelength where the solution absorbs most strongly?
Model answer and scoring
(a) Pipet different volumes (for example 2.00, 4.00, 6.00, 8.00 and 10.00 mL) of the 0.100 M standard into 50.00 mL volumetric flasks, dilute each to the mark with distilled water and mix, giving solutions of known concentration ([CuSO₄] = 0.100 × V ÷ 50.00).
(b) Set the wavelength and zero the instrument with distilled water (the blank); measure the absorbance of each standard; plot absorbance against concentration, which gives a straight line through about the origin (A = εbc).
(c) Measure the sample’s absorbance at the same wavelength and read its concentration from the calibration curve, or calculate it from the slope: c = A ÷ slope.
(d) Too low. The leftover water dilutes the sample in the cuvette → measured absorbance too small → concentration read from the curve too low.
(e) At the wavelength of strongest absorbance, a given change in concentration gives the largest change in absorbance, so the measurement is most sensitive and its relative error is smallest.
Scoring: (a) quantitative dilution with pipets and volumetric flasks; (b) zeroing, measuring absorbances and plotting absorbance vs concentration; (c) concentration from the curve or slope; (d) too low, with the chain of reasoning; (e) greatest sensitivity.
Summary
- Experimental design: purpose and equation → measurements and equipment → specific numbered steps → controlled variables → repetition.
- Direction of error in three steps: which measurement changes → where it sits in the equation → too high, too low or no change.
- Systematic error is removed by improving the method; random error is reduced by repetition. Name the specific action, never “human error.”
AP tip: Write error answers in three parts: “action → measurement too large (small) → result too high (low).” Even with the right conclusion, a missing middle link often costs the point.