When Does the Fizzing Really Stop?
In a school laboratory in Bamenda, a student adds 1.00 g of washed marble chips (assume pure calcium carbonate, M = 100 g mol⁻¹) to 25.0 cm³ of 1.00 mol dm⁻³ hydrochloric acid at 25 °C. The gas produced is collected in a 250 cm³ gas syringe. After 90 s the syringe reads 180 cm³; after a further 90 s it reads 200 cm³. The student concludes that the reaction has finished because 'the acid must be used up'. The teacher points out that the mixture still fumes and gives a pH of about 2. A classmate suggests repeating the experiment with the same mass of powdered marble and 0.50 mol dm⁻³ acid to see whether concentration affects the rate. The teacher asks the class to decide whether the student's conclusion is valid and how to design a fair comparison.
1. Show by calculation whether the acid is in excess, and calculate the maximum volume of carbon dioxide that could be collected at room temperature and pressure (molar volume = 24.0 dm³ mol⁻¹).
Read the worked answer
Moles of calcium carbonate:
n(CaCO₃) = 1.00 g ÷ 100 g mol⁻¹ = 0.0100 mol
Moles of hydrochloric acid:
n(HCl) = 0.0250 dm³ × 1.00 mol dm⁻³ = 0.0250 mol
Equation:
CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + CO₂(g) + H₂O(l)
0.0100 mol CaCO₃ needs 0.0200 mol HCl. Only 0.0250 mol HCl is present, so the acid is in excess by 0.0050 mol; calcium carbonate is the limiting reactant.
Maximum carbon dioxide:
n(CO₂) = n(CaCO₃) = 0.0100 mol
V(CO₂) = 0.0100 mol × 24.0 dm³ mol⁻¹ = 0.240 dm³ = 240 cm³
After 180 s only 200 cm³ has been collected, about 83% of the maximum. The reaction has not finished; it is simply slowing down.
2. Explain, using collision theory, why the rate decreases between the two 90 s intervals even though some acid remains. State whether the student's conclusion is valid.
Read the worked answer
The rate depends on the frequency of effective collisions between H⁺ ions and the calcium carbonate surface. As the reaction proceeds, the marble chips are used up and become smaller, so their surface area decreases. Fewer collisions occur per second, so the rate falls. The concentration of H⁺ also falls as acid is consumed, which further reduces the collision frequency.
The student's conclusion is not valid. The syringe reading is still increasing (180 cm³ to 200 cm³), and the pH of about 2 corresponds to [H⁺] ≈ 1 × 10⁻² mol dm⁻³, so acid is still present. The reaction has slowed down, not stopped. A further clue is that the mixture still fumes, showing that gas is still being produced.
3. The classmate's proposed comparison changes two variables: particle size and acid concentration. Explain why this is not a fair test and describe a better pair of experiments to test the effect of concentration.
Read the worked answer
A fair test changes only one independent variable. The classmate changes both particle size (chips to powder) and concentration (1.00 to 0.50 mol dm⁻³), so any difference in rate could be caused by either change; the result cannot be attributed to concentration alone.
A better comparison would use the same mass and the same particle size of marble chips in both experiments, the same volume of acid and the same temperature. One experiment would use 1.00 mol dm⁻³ HCl and the other 0.50 mol dm⁻³ HCl. The rate could be measured by the volume of gas collected in the first 30 s, or by the time taken to collect a fixed volume such as 50 cm³. This changes only the concentration.