Interpreting a Rate Experiment with Conflicting Data
Students react magnesium ribbon with 1.0 M hydrochloric acid and measure gas volume every 10 s. Run 1 uses 2.0 cm of ribbon and 50 mL of acid at 25 °C. Run 2 uses 4.0 cm of ribbon and 50 mL of acid at 25 °C. Run 3 uses 2.0 cm of ribbon and 50 mL of acid at 40 °C. The initial rate in Run 2 is roughly double that of Run 1, but the final gas volume is also double. Run 3 reaches the same final volume as Run 1 but much faster. One student claims 'doubling the magnesium doubled the rate, so the reaction is first order with respect to magnesium'. Another student says the rate should depend on acid concentration, not magnesium, because magnesium is a solid.
1. Evaluate the first student's claim that the reaction is first order with respect to magnesium.
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The claim is not supported. In Run 2 both the mass of magnesium and the total gas produced double, so the initial rate doubles simply because twice as much reaction occurs - the graph is scaled, not necessarily steeper in a meaningful kinetic sense. To test order with respect to a solid, you compare the rate at the same extent of reaction (for example, the slope at a fixed small volume of gas, or the time to produce a fixed volume such as 10 mL). If the time to reach 10 mL is halved when the surface area is doubled, that indicates the rate depends on the available surface area, not a simple concentration order.
Furthermore, magnesium is a solid, so its 'concentration' is effectively constant and is not treated as a variable in the rate law. The correct interpretation is that increasing the amount (and hence surface area) of magnesium increases the rate by exposing more surface, but this does not establish a first-order dependence. The student has confused total yield with rate.
2. Explain why Run 3 reaches the same final volume faster, and identify what limits the final volume in each run.
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Run 3 is at 40 °C rather than 25 °C. Higher temperature increases the fraction of collisions with energy above the activation energy and increases collision frequency, so the rate rises and the curve is steeper. The final volume is unchanged because it depends on the amount of limiting reactant, not on temperature.
Final volume is limited by the reactant present in the smaller stoichiometric amount. Mg + 2HCl → MgCl₂ + H₂. Moles of HCl = 1.0 × 0.050 = 0.050 mol. Moles of Mg in 2.0 cm of ribbon: if the ribbon is about 0.010 g/cm, mass ≈ 0.020 g, moles ≈ 0.020 / 24.3 ≈ 8.2 × 10⁻⁴ mol. Mg is limiting, so H₂ ≈ 8.2 × 10⁻⁴ mol, volume ≈ 0.020 L at room conditions. In Run 2, doubling Mg doubles the gas, consistent with Mg still being limiting. The judgement is that temperature changes rate but not yield, while the amount of limiting reactant changes yield.
3. The second student says rate should depend on acid concentration, not magnesium. Assess this view.
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The second student is partly right and partly wrong. Acid concentration does affect rate because HCl is a reactant in solution; increasing [H⁺] increases collision frequency with the metal surface. However, it is incorrect to say rate cannot depend on the magnesium. For a heterogeneous reaction, the rate depends on the surface area of the solid, since reaction occurs at the surface. A larger mass of ribbon of the same dimensions has more surface area and therefore a higher rate at the same acid concentration.
A proper rate law for this system would include [HCl] (often first order in H⁺) and a surface-area term for Mg. The solid's 'concentration' is constant, so it does not appear as a concentration variable, but its exposed area does influence rate. The correct judgement is that both factors matter: acid concentration and magnesium surface area. Neither student's exclusive claim is fully correct, and the experiment as designed does not isolate either variable cleanly.