A student investigates the reaction between small pieces of zinc metal and excess dilute sulfuric acid: Zn(s) + H2SO4(aq) → ZnSO4(aq) + H2(g) The flask is placed on a balance, and the loss in mass (due to escaping hydrogen gas) is recorded at regular time intervals. (a) Explain,…

Answer: ((a)) A more concentrated acid has more H2SO4 particles in the same volume, so there is a greater frequency of collisions between acid particles and the zinc surface per second, increasing the initial rate. ((b)) Raising the temperature increases the average kinetic energy of the particles, broadening and shifting the Maxwell-Boltzmann distribution to higher energies. Because the distribution has a long high-energy tail, even a modest rise in temperature causes a disproportionately large… ((c)) As temperature rises, the peak of the curve moves to a higher energy and becomes lower and broader (the curve flattens and stretches out), while the total area under the curve stays the same, since the total number of particles has not changed. The activation energy, EA, is a fi…. Part (a): Effect of concentration Increasing the concentration of sulfuric acid, with the same volume of solution, means there are more H2SO4 particles present in that same volume. This increases the frequency with which acid particles col…

AS Chemistry 9701: Collision Theory and the Boltzmann Distribution

A student investigates the reaction between small pieces of zinc metal and excess dilute sulfuric acid: $\text{Zn(s)} + \text{H}_2\text{SO}_4\text{(aq)} \rightarrow \text{ZnSO}_4\text{(aq)} + \text{H}_2\text{(g)}$ The flask is placed on a balance, and the loss in mass (due to escaping hydrogen gas) is recorded at regular time intervals.

(a) Explain, in terms of collision theory, why using a more concentrated solution of sulfuric acid (with the same volume of acid and the same mass of zinc) increases the initial rate of reaction. [2]

(b) The student repeats the experiment using the original concentration of acid, but at a temperature $20\text{ °C}$ higher than before. Using ideas about the Maxwell–Boltzmann distribution of molecular energies, explain why this temperature increase produces a much larger increase in rate than doubling the acid concentration would. [4]

(c) Describe how the shape of the Maxwell–Boltzmann distribution curve for the acid particles changes when the temperature is raised, and explain how this change relates to the activation energy, $E_A$ , of the reaction. [3]

Part (a): Effect of concentration

Increasing the concentration of sulfuric acid, with the same volume of solution, means there are more $\text{H}_2\text{SO}_4$ particles present in that same volume. This increases the frequency with which acid particles collide with the surface of the zinc per second. Since a fixed proportion of these collisions still has energy $\ge E_A$ (concentration does not affect the energy distribution), a higher collision frequency means more successful collisions per second, so the initial rate of reaction increases.

Part (b): Effect of temperature vs. concentration

Raising the temperature increases the average kinetic energy of the particles. This has two effects, but one is far more significant than the other:

It slightly increases the frequency of collisions (particles move faster).
It shifts and broadens the Maxwell–Boltzmann energy distribution towards higher energies.

Because the distribution has a long “tail” at high energy, a small increase in the average energy causes a disproportionately large increase in the number of particles with energy $\ge E_A$ . The fraction of particles able to react on collision rises sharply.

By contrast, doubling the acid concentration doubles the collision frequency only; it does not change the fraction of collisions that are energetically successful, since the energy distribution of the particles is unaffected by concentration.

$\text{rate} \propto (\text{collision frequency}) \times (\text{fraction of collisions with } E \ge E_A)$

A temperature rise increases both factors (very slightly for frequency, but hugely for the energy fraction), whereas a concentration increase affects only the frequency term, so, for a typical $20\text{ °C}$ rise, the temperature effect on rate is much larger than doubling the concentration.

Part (c): Change in the Maxwell–Boltzmann distribution

At the higher temperature:

The peak of the curve shifts to a higher energy value.
The peak becomes lower, and the curve becomes broader/flatter (spread over a wider range of energies).
The total area under the curve is unchanged, because the total number of particles has not changed. Only how that fixed number of particles is distributed across the energy range changes.

The activation energy, $E_A$ , is a single fixed point on the energy axis (it does not move when temperature changes). Because the curve at the higher temperature is shifted and broadened towards higher energies, the area under the curve to the right of this fixed $E_A$ value, representing the number/fraction of particles with enough energy to react, is now considerably larger than at the lower temperature.

Final answers

(a) More acid particles per unit volume $\Rightarrow$ more frequent collisions with zinc $\Rightarrow$ faster initial rate.
(b) A temperature rise greatly increases the fraction of particles with $E \ge E_A$ (via the shape of the Boltzmann distribution), while a concentration increase only increases collision frequency, so the temperature effect dominates.
(c) The curve flattens, broadens and shifts to higher energy (same total area); the area beyond the fixed $E_A$ value increases, showing more particles can now react.