Problem 57 - Chemistry: The Central Science in SI Units, Global Edition

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: Statement (a) Analysis and Verification

Let's analyze the statement: If you compare two reactions with similar collision factors, the one with the larger activation energy will be faster. Activation energy is the energy barrier that must be overcome for a reaction to occur. The higher the activation energy, the slower the reaction rate as fewer molecules possess the necessary energy to overcome the barrier. Collision factors help determine the probability of successful collisions. Given that the collision factors are similar, the difference in reaction rates will depend only on the activation energy. Therefore, the statement is False.

Step 2: Statement (b) Analysis and Verification

Let's analyze the statement: A reaction that has a small rate constant must have a small frequency factor. The rate constant (k) is related to the frequency factor (A) and the activation energy (Ea) by the Arrhenius equation: \( k = Ae^{(-Ea/RT)} \) A small rate constant does not necessarily mean a small frequency factor, as it could also be due to a high activation energy or a low temperature. The statement does not mention either of these factors. Therefore, the statement is False.

Step 3: Statement (c) Analysis and Verification

Let's analyze the statement: Increasing the reaction temperature increases the fraction of successful collisions between reactants. Increasing the temperature provides more energy to the reactant molecules, which increases the number of molecules with enough energy to overcome the activation energy barrier. The higher the temperature, the greater the fraction of molecules possessing sufficient energy to react. Therefore, increasing the temperature increases the probability of successful collisions between reactants. Therefore, the statement is True.

Key Concepts

Activation Energy

Activation energy is like a hurdle that molecules need to jump over for a reaction to happen. It's the minimum energy required for reactants to transform into products. This means that the height of this energy barrier often dictates the speed of the reaction.

Think of it this way: imagine two reactions that both have similar propensities to collide. If one has a high activation energy while the other has a low one, the reaction with the higher activation energy will generally proceed more slowly. This is because fewer molecules will have the energy required to successfully surpass the barrier at any given time.

• A higher activation energy usually means a slower reaction rate.
• More energy required means fewer molecules can start the reaction instantly.
• Catalysts can lower activation energy, increasing reaction speed.

Thus, if you're comparing two similar reactions, the one with the larger activation energy barrier will typically be slower, not faster.

Reaction Temperature

Temperature plays a big role in chemical reactions. As you raise the temperature, you're essentially giving the molecules more energy. This increase in energy means molecules move faster and collide more frequently, which can lead to more successful reactions.

When you heat up a reaction, more molecules have enough energy to go past the activation energy hurdle. Higher temperatures mean a greater proportion of molecules have the energy needed to jumpstart the reaction.

• Higher temperatures lead to higher reaction rates.
• More energetic molecules can surpass activation energies easier.
• This often results in more successful collisions.

So, increasing the temperature generally increases the number of effective collisions, making it more probable for the reaction to occur.

Collision Theory

Collision theory helps us understand why and how reactions occur. It states that for molecules to react, they must collide with each other with the right energy and orientation. Just like playing billiards, if the balls don't hit each other in the right way, they'll just bounce off without doing anything exciting.

For a reaction, not just any collision will cut it. To form products, molecules need to collide with enough energy to overcome the activation energy and with the proper orientation to properly stay bound.

• Successful collisions depend on both energy and alignment.
• The more frequent the collisions, the higher the chance for a reaction.
• Factors like temperature and catalysts influence collision rates.

In summary, while collisions are necessary for reactions, only those with the right energy and direction lead to successful transformations.