Marble Chips and Acid: When the Rate Curve Surprises
A student reacts 5.00 g of marble chips (calcium carbonate, CaCO3) with 50.0 cm³ of 0.200 mol/dm³ hydrochloric acid at 25 °C. She collects the carbon dioxide in a gas syringe and records the volume every 30 s. After 3.0 min, 118 cm³ of gas has been collected and the reaction has almost stopped. She repeats the experiment with 5.00 g of powdered marble under the same conditions and collects 118 cm³ in 40 s. She then repeats the first experiment at 40 °C and gets 118 cm³ in 1.5 min. She claims that “the powder and the higher temperature both increase the rate because they increase the concentration of the acid”. The acid is the limiting reactant. The syringe has a small leak, and the balance reads 5.00 g ± 0.05 g.
1. Write the balanced equation for the reaction. Calculate the maximum volume of CO2 that the acid can produce at 24.0 dm³/mol, and compare it with the 118 cm³ collected. Suggest one reason for the difference.
Read the worked answer
Balanced equation:
CaCO3(s) + 2HCl(aq) → CaCl2(aq) + H2O(l) + CO2(g)
Amount of HCl = 0.0500 dm³ × 0.200 mol/dm³ = 0.0100 mol.
From the equation, 2 mol HCl produces 1 mol CO2, so n(CO2) = 0.0100 / 2 = 0.00500 mol.
V(CO2) = 0.00500 × 24.0 = 0.120 dm³ = 120 cm³.
The 5.00 g of CaCO3 is 5.00 / 100.1 ≈ 0.0500 mol, which would need about 0.100 mol HCl. The acid is limiting, so the maximum volume is 120 cm³, not the much larger volume the marble could produce. The collected 118 cm³ is about 98% of the maximum. The small difference is consistent with the small leak, some CO2 dissolving in the water, and reading uncertainty on the syringe. It is not because the marble is limiting.
2. The student says powder and higher temperature increase rate “because they increase the concentration of the acid”. Evaluate this claim. Explain the real reasons and state what stays the same.
Read the worked answer
The claim is wrong for both changes. Powdering increases the surface area of the solid, so more CaCO3 particles are exposed to the acid. Collisions between acid particles and the solid occur more frequently, so the rate increases. The concentration of the acid is unchanged, and the amount of acid is unchanged.
Higher temperature increases the average kinetic energy of the acid particles. More particles have energy above the activation energy, and collisions are more frequent, so the rate increases. Again, the concentration of the acid is unchanged.
Both changes increase the rate, but the final volume of CO2 is the same, about 120 cm³, because the same amount of limiting acid is used. The 40 °C run reaching 118 cm³ in 1.5 min is faster, not larger. The student should say “surface area” and “temperature”, not “concentration”.
3. Describe how the student could test whether the reaction is exothermic, and explain why the 40 °C experiment alone does not prove it.
Read the worked answer
Use a thermometer or temperature probe in the reaction mixture, with a lid or cotton wool to reduce heat loss. Record the temperature of the acid before adding the marble and at intervals during the reaction. If the temperature rises above the starting temperature and then falls, the reaction is releasing heat, so it is exothermic.
The 40 °C experiment uses externally warmed acid or a water bath, so any temperature rise could come from the surroundings rather than from the reaction. To prove exothermicity, start both the acid and the marble at the same known room temperature, mix them without external heating, and compare with a control containing acid alone. The gas syringe should also be at room temperature, because warm gas expands and would make the reaction appear faster.