- The reaction rate depends on the frequency of successful collisions between \(Ca(OH)_2\) and \(CO_2\).
- Lowering the temperature or pressure decreases collision frequency, and using larger pieces of the solid reduces available surface area, all of which slow the reaction.
- Reducing the container volume increases the concentration of the \(CO_2\) gas, which significantly increases the frequency of collisions with the solid surface.
- The correct way to speed up the reaction is to reduce the volume of the container, so the final answer is \(\boxed{d}\).
Explanation
- Problem Analysis and Collision Theory
The reaction given is the formation of calcium carbonate from calcium hydroxide and carbon dioxide:
\[Ca(OH)_2(s) + CO_2(g) \rightarrow CaCO_3(s) + H_2O(l)\]
This is a heterogeneous reaction occurring between a solid surface (\(Ca(OH)_2\)) and a gas (\(CO_2\)). According to collision theory, the reaction rate is proportional to the frequency of effective collisions between the reactant particles. To speed up the reaction, we need to increase the frequency of these collisions.
- Evaluating the Options
We evaluate each option based on its effect on collision frequency:
- (a) Lowering the temperature: Decreasing temperature reduces the average kinetic energy of the molecules, leading to slower movement and less frequent, less energetic collisions. This slows down the reaction.
- (b) Lowering the pressure: Reducing the pressure decreases the concentration of the \(CO_2\) gas in the container. With fewer gas particles per unit volume, the collision frequency with the solid \(Ca(OH)_2\) surface decreases, slowing the reaction.
- (c) Using larger pieces of \(Ca(OH)_2\): Larger pieces have a smaller total surface area relative to their volume. Since the reaction occurs at the surface, decreasing the available surface area reduces the number of sites where gas molecules can collide with the solid, slowing the reaction.
- (d) Reducing the volume of the container: By reducing the volume occupied by the gas while keeping the amount of gas constant, the concentration (number of molecules per unit volume) of \(CO_2\) increases. This increased concentration leads to a higher probability and frequency of collisions with the \(Ca(OH)_2\) surface, thereby increasing the reaction rate.
- Conclusion
Based on the analysis, reducing the volume of the container is the most effective way among the choices to increase the frequency of collisions between the gaseous \(CO_2\) and the solid \(Ca(OH)_2\). Thus, option (d) is the correct choice. The final answer is \(\boxed{d}\).
Examples
In chemical industry, controlling reaction rates is vital for production efficiency. For instance, in carbon capture systems where \(CO_2\) is removed from flue gas by reacting it with solid bases like calcium hydroxide, reactors are often designed to maximize contact time and surface interaction. By controlling the pressure and volume of the reaction chamber, engineers can optimize the collision frequency to capture more \(CO_2\) per second, making the industrial process much faster and more cost-effective. Understanding these kinetic principles allows for better design of such systems.