Which of the following modifications will increase the rate of the reaction the most? — Kinetics Chemistry Question

### STEPS:

1. Identify the phases of the reacting species:
The chemical reaction in this experiment occurs between solid calcium carbonate ($\text{CaCO}_3(s)$) in the eggshells and aqueous hydronium ions ($\text{H}^+(aq)$) supplied by the hydrochloric acid ($\text{HCl}(aq)$).

2. Recognize the kinetic constraint of a heterogeneous reaction:
Because this is a heterogeneous reaction involving a solid and an aqueous solution, the reaction can only occur at the boundary interface where the solid surface meets the liquid. The rate of the reaction is directly proportional to the frequency of successful collisions between the $\text{H}^+(aq)$ ions and the solid $\text{CaCO}_3(s)$ particles.

3. Analyze the impact of powdering the solid reactant:
Grinding the eggshells into a fine powder physically breaks the larger solid pieces into a massive number of tiny particles. This physical modification dramatically increases the total surface area of the solid reactant exposed to the solution while keeping the overall mass constant.

4. Connect surface area to collision frequency and rate:
With a significantly greater surface area, a far higher number of $\text{CaCO}_3$ molecules are in direct contact with the $\text{H}^+(aq)$ ions at any given instant. This increases the frequency of successful molecular collisions per unit of time, which increases the overall rate of the reaction the most, confirming Option D as the correct choice.

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### WHY_OTHERS_WRONG:

• Option A is incorrect: Acetic acid ($\text{CH}_3\text{COOH}$) is a weak acid that only partially ionizes in water, whereas hydrochloric acid ($\text{HCl}$) is a strong acid that ionizes completely. At equal concentrations ($2.0\text{ M}$), the weak acid has a much lower concentration of free $\text{H}^+$ ions, which would significantly *decrease* the collision frequency and *lower* the reaction rate.
• Option B is incorrect: Cooling a reaction lowers the average kinetic energy of the particles. This reduces both the frequency of collisions and the fraction of collisions that have enough energy to overcome the activation energy barrier, which *decreases* the rate of the reaction.
• Option C is incorrect: Reducing the volume of the reaction vessel increases the concentration/pressure of gaseous species, but it has no effect on the concentration of ions in an aqueous solution or the surface area of a solid reactant. Therefore, it will not increase the rate of this heterogeneous reaction.