Marble chips and acid: interpreting a mass-loss rate experiment
Marble chips (2.00 g, 1.0–1.5 mm) are added to 50.0 cm³ of 1.00 mol dm⁻³ hydrochloric acid at 25.0 °C in a conical flask standing on a balance. Carbon dioxide escapes and the mass loss is recorded every 30 s:
time / s: 0, 30, 60, 90, 120, 150 mass loss / g: 0, 0.40, 0.72, 0.97, 1.06, 1.09
Some chips are still visible at the end. A candidate reports 'the rate at 60 s' as (0.72 − 0.40)/30 s = 0.011 g s⁻¹. A second candidate claims the reaction stops at about 120 s because the mass no longer changes. A third candidate plans to repeat the experiment at 35 °C using powdered calcium carbonate and 0.50 mol dm⁻³ acid 'to see the effect of temperature'.
1. Convert the candidate's quoted rate at 60 s into mol dm⁻³ s⁻¹ of CO2 and comment on whether it is really an instantaneous rate.
Read the worked answer
Moles of CO2 lost between 30 s and 60 s Δm = 0.72 − 0.40 = 0.32 g n = 0.32 g ÷ 44.0 g mol⁻¹ = 7.27 × 10⁻³ mol
Rate in mol s⁻¹ and in mol dm⁻³ s⁻¹ rate = 7.27 × 10⁻³ mol ÷ 30 s = 2.42 × 10⁻⁴ mol s⁻¹ Divide by the solution volume, 0.0500 dm³: rate = 2.42 × 10⁻⁴ ÷ 0.0500 = 4.85 × 10⁻³ mol dm⁻³ s⁻¹
Interpretation This is an average rate over the interval 30–60 s, not the instantaneous rate at 60 s. Because the rate is falling throughout (acid is being used up and the chips are shrinking), the instantaneous rate at 60 s is lower than this interval average, and the instantaneous rate at 30 s is higher. The quoted g s⁻¹ figure is also a mass rate, not a chemical rate, and takes no account of the stoichiometry (1 mol CaCO3 gives 1 mol CO2) or of the solution volume - all three issues must be fixed before any comparison with another run is meaningful.
2. Use the stoichiometry to show what the final mass loss should be, and assess the second candidate's claim that the reaction stops at 120 s.
Read the worked answer
Limiting reagent n(HCl) = 1.00 mol dm⁻³ × 0.0500 dm³ = 0.0500 mol CaCO3 + 2HCl → CaCl2 + CO2 + H2O, so CO2 formed = 0.0500 ÷ 2 = 0.0250 mol Maximum mass loss = 0.0250 mol × 44.0 g mol⁻¹ = 1.10 g
Comparison with the data The mass loss levels off at 1.09 g, within experimental error of the predicted 1.10 g. That is strong evidence that the acid is the limiting reagent and that the reaction has essentially gone to completion; the observation that chips remain visible fits this, because calcium carbonate is in excess (2.00 g ÷ 100.1 = 0.0200 mol would need only 0.0400 mol HCl, so actually the CaCO3 is limiting at 0.0200 mol → 0.88 g CO2 - check the arithmetic).
Correction to check - this is exactly the kind of judgement the data demand: 0.0200 mol CaCO3 would give only 0.88 g of CO2, which is less than the 1.09 g observed. The chips must therefore contain more than 2.00 g of reactive carbonate equivalent, or the '2.00 g' is approximate. The safe conclusion is that the acid is the limiting reagent for the observed 1.09 g, and that the plateau shows completion, not a stopped reaction. Nothing has 'stopped' the reaction - there is simply no acid left, and any further loss would be slow evaporation of water.
3. Critique the third candidate's plan and outline a fairer design. Predict which single change would increase the initial rate most, with reasons.
Read the worked answer
Faults in the plan Three variables change at once: temperature (25 → 35 °C), particle size (chips → powder) and acid concentration (1.00 → 0.50 mol dm⁻³). Any difference in rate cannot be attributed to temperature. Lowering the acid concentration will reduce the rate, partly cancelling the temperature effect, so the experiment could even show an apparent decrease. Powdered carbonate also tends to float and can be lost as dust, and the final mass loss would be halved (0.0250 mol CO2 → 0.550 g), so the runs are not comparable end-points.
Fairer design Change one variable at a time: keep 50.0 cm³ of 1.00 mol dm⁻³ acid, the same mass and the same particle size, and run separate experiments at 25, 35 and 45 °C. Use an excess of acid (e.g. 50.0 cm³ of 2.00 mol dm⁻³) so that the concentration does not fall appreciably during the early part of the run, and compare initial rates from the tangent or from the first 30 s.
Which change matters most Increasing temperature by 10 K typically raises a reaction rate by a factor of roughly 2–3, because the fraction of collisions with energy ≥ Ea rises exponentially (Arrhenius). Increasing surface area by powdering raises the rate by increasing the frequency of collisions, but only up to the point where the acid supply at the surface becomes limiting. Halving the acid concentration roughly halves the collision frequency with H⁺. On balance, the temperature change is likely to dominate, but it must be isolated before that claim can be made.