Problem 57 - Chemistry The Central Science In Si Units

Question

Indicate whether each statement is true or false. (a) If you compare two reactions with similar collision factors, the one with the larger activation energy will be faster. (b) A reaction that has a small rate constant must have a small frequency factor. (c) Increasing the reaction temperature increases the fraction of successful collisions between reactants.

Step-by-Step Solution

Answer

(a) False, (b) False, (c) True.

Step 1: Analyzing Part (a)

In part (a), we're comparing two reactions with similar collision factors. The activation energy ( E_a ) is a barrier that must be overcome for a reaction to proceed. According to the Arrhenius equation, a reaction with a larger activation energy compared to another will generally be slower because it requires more energy for reactants to successfully collide and form products. Thus, the statement is false.

Step 2: Analyzing Part (b)

In part (b), the statement deals with the rate constant ( k ot the frequency factor ( A ), in the Arrhenius equation k = A e^{-E_a/RT} . The rate constant can be small due to a high activation energy ( E_a ), which is a common reason, or a small frequency factor ( A ). Therefore, a small rate constant does not necessarily imply a small frequency factor. Thus, the statement is false.

Step 3: Analyzing Part (c)

For part (c), increasing the reaction temperature usually increases the kinetic energy of the molecules, leading to more frequent and energetic collisions. This increase in temperature raises the fraction of collisions that have enough energy to overcome the activation energy barrier, thereby increasing the fraction of successful collisions. Thus, the statement is true.

Key Concepts

Activation Energy

Activation energy is the minimum energy required for a chemical reaction to occur. This concept is crucial in understanding why some reactions proceed faster than others. Picture a hill where the reactants need enough kinetic energy to reach the top before sliding down to form products. The height of this hill is the activation energy. The larger the activation energy, the harder it is for the reactants to overcome this barrier, often resulting in a slower reaction.

In a chemical formula, activation energy is denoted as \( E_a \). When comparing two reactions, even if they have the same initial collision factors, the one with the higher activation energy will typically be slower. This is because more energy is needed to start the reaction.

• Higher activation energy corresponds to more energy needed to start the reaction.
• A larger \( E_a \) generally means a slower reaction rate.

This explains why catalysts are often used in reactions. Catalysts work by providing an alternative path with a lower activation energy, allowing the reaction to proceed more quickly without being consumed in the process.

Arrhenius Equation

The Arrhenius Equation is a mathematical representation that demonstrates the effect of temperature on the rate constant \( k \) of a reaction. It is expressed as:\[ k = A e^{-E_a/RT} \]Where:

• \( k \) is the rate constant, which indicates how fast a reaction occurs.
• \( A \) is the frequency factor, representing the number of times reactants collide with the correct orientation.
• \( E_a \) is the activation energy.
• \( R \) is the universal gas constant.
• \( T \) is the temperature in Kelvin.

The equation shows that a higher activation energy \( E_a \) reduces the rate constant \( k \), assuming other factors remain constant, because it hinders the formation of products. The factor \( e^{-E_a/RT} \) represents the fraction of molecules having energy greater than \( E_a \).

Similarly, higher temperatures lead to a larger rate constant, indicating a faster reaction, because the reactants have more energy to overcome the activation energy barrier.

Collision Theory

Collision theory provides insights into how molecules interact during a chemical reaction. For a reaction to happen, the reacting particles must collide with each other with enough energy and the proper orientation. This energy threshold that needs to be surpassed is what we call activation energy. The theory helps us predict how certain factors, like temperature, affect reaction rates.

Several factors affect the efficacy of collision:

• Energy: Only collisions with sufficient energy, which is greater than or equal to activation energy, result in a reaction.
• Orientation: The molecules must be aligned properly during collision to form new bonds.

Temperature plays a crucial role as it essentially increases the kinetic energy of molecules, making them move faster and collide more often with adequate energy. Thus, increasing temperature improves both the frequency and success rate of these collisions, leading to a quicker reaction.

This understanding aligns with the observation that raising the temperature increases the fraction of successful collisions, hence boosting reaction rates.