Question

What happens when the temperature of a reaction system is increased by \(10^{\circ} \mathrm{C}\) ? a. The effective number of collisions between the molecules possessing certain threshold energy increases atleast by \(100 \%\). b. The total number of collisions between reacting molecules increases atleast by \(100 \%\) c. The activation energy of the reaction is increased d. The total number of collisions between reacting molecules increases merely by \(1-2 \%\).

Short answer

Option a is correct: effective collisions increase by at least 100%.

Step-by-step solution

Understand the Concepts

To solve this problem, it is important to understand how temperature affects chemical reactions. When temperature increases, molecules move faster, leading to more frequent collisions between them.

Analyze each Option

Examine each option to see how it fits with the known effects of temperature changes: - Option a states that the effective number of collisions with the required energy increases by at least 100%. This is in line with the Arrhenius equation, where an increase of 10°C can roughly double the reaction rate. - Option b is incorrect because the overall number of collisions doesn't necessarily double with temperature increase; only the effective collisions do. - Option c is incorrect because the activation energy is a characteristic of a reaction and does not change with temperature. - Option d states a plausible effect, as the total number of collisions might indeed increase slightly because of increased molecular motion.

Identify the Correct Answer

Based on the analysis, the statistical increase in effective collisions (option a) is significant. The actual number of total collisions only slightly increases (option d). Therefore, the best choice is option a, as the significant increase in effective collisions supports this choice.

Conclusion

The correct answer is option a, which states that the effective number of collisions between the molecules possessing certain threshold energy increases by at least 100% when the temperature of a reaction system is increased by 10°C.

Key concepts

Collision Theory

Collision theory helps us understand how chemical reactions occur and why reaction rates vary under different conditions. It posits that molecules must collide to react; however, not every collision leads to a reaction. There are specific conditions required for successful reactions:

• The molecules must collide with the right orientation. Think of it like fitting a key into a lock – only the right position will work.
• The molecules must also have sufficient energy, called the activation energy, to break existing bonds and form new ones.

Temperature plays a crucial role by increasing the kinetic energy of molecules. As the kinetic energy rises, molecules move faster and collide more often. While the total number of collisions increases slightly, it's the effective collisions where the energy is enough that significantly increase with temperature. This aligns with collision theory, explaining why temperature can dramatically affect reaction rates.

Arrhenius Equation

The Arrhenius Equation is a mathematical formula that provides insights into how temperature affects reaction rates. It states:

\[ k = A e^{-\frac{E_a}{RT}} \]

• Here, \( k \) is the rate constant of the reaction.
• \( A \) is the frequency factor, related to the number of times molecules collide in the correct orientation.
• \( E_a \) represents the activation energy required for the reaction.
• \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

This equation shows that as temperature \( T \) increases, the exponential term becomes less negative, thus increasing the rate constant \( k \), and consequently, the reaction rate. It's important to note that a small increase in temperature can lead to a large increase in the reaction rate, a concept demonstrated by option a of the original exercise.

Activation Energy

Activation energy \( E_a \) is the minimum energy barrier that reacting molecules must overcome for a reaction to occur. This can be visualized as a hill that reactants need to climb before they can convert into products.

In chemical reactions:

• Low activation energy means that it's easier for reactions to occur, as less energy is needed to overcome the barrier.
• High activation energy results in slower reaction rates because more energy is needed to start the reaction.

Activation energy remains unchanged with temperature; it's intrinsic to the nature of the reaction itself. Therefore, despite the temperature change, the activation energy doesn't increase or decrease. This is why option c from the original exercise is incorrect.

Reaction Rate

The reaction rate indicates how quickly reactants convert into products in a chemical reaction. Several factors influence it, including temperature, concentration, and the presence of catalysts.

When the temperature increases:

• The kinetic energy of molecules increases, leading to more frequent collisions.
• There is a significant rise in the number of effective collisions, where molecules collide with sufficient energy and proper orientation to react.

This is why an increase of just \(10^{\circ} \mathrm{C}\) can significantly enhance the reaction rate by raising the number of successful molecule interactions. However, the overall number of collisions goes up only slightly, around 1-2%, which is captured by option d of the original exercise.