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Chapter 13: Problem 79

How does the magnitude of a reaction's activation energy influence the rate of a reaction?

Short Answer

Expert verified
Answer: The magnitude of a reaction's activation energy is directly related to the rate of the reaction. A higher activation energy results in a slower reaction rate, while a lower activation energy leads to a faster reaction rate. This is because a higher activation energy requires more energy for the reaction to occur, leading to fewer reactant molecules possessing enough energy to overcome the energy barrier and react. In contrast, a lower activation energy allows a greater number of reactant molecules to have the necessary energy to react, resulting in a faster reaction rate.

Step by step solution

01

Understand the concept of activation energy

Activation energy is the minimum amount of energy required for a chemical reaction to occur. In other words, it is the energy barrier that must be overcome for reactants to be transformed into products. When the reactants have enough energy to surpass this barrier, the reaction will proceed.
02

Discuss the relationship between activation energy and reaction rate

The rate of a reaction is determined by the number of successful collisions between reactant molecules that have sufficient energy to overcome the activation energy barrier. Given that a higher activation energy requires more energy for the reaction to proceed, fewer reactant molecules will possess enough energy to surpass this barrier, resulting in a slower reaction rate. Conversely, a lower activation energy means that a greater number of reactant molecules will have enough energy to react, leading to a faster reaction rate.
03

Understand the role of temperature in reaction rate

Temperature plays a crucial role in determining the reaction rate, as it affects the kinetic energy of the molecules in the reacting substances. With an increase in temperature, the kinetic energy of the reactant molecules also increases, making it more likely that they will possess enough energy to overcome the activation energy barrier and react. As a result, the reaction rate generally increases with increasing temperature.
04

Explain the concept of catalysts and their effect on activation energy

Catalysts are substances that can increase the reaction rate without being consumed by the reaction. They work by providing an alternative reaction pathway with a lower activation energy, allowing more reactant molecules to possess sufficient energy to react, thus increasing the rate of the reaction. The catalyst itself remains unchanged after the reaction and can be reused in another reaction.
05

Provide examples of reactions with different activation energies and rates

To illustrate the relationship between activation energy and reaction rate, consider the following examples: 1. The reaction between hydrogen and oxygen to form water has a high activation energy, so it takes place very slowly at room temperature. However, in the presence of a catalyst like platinum, the activation energy is lowered, enabling the reaction to proceed more rapidly. 2. Decomposition of hydrogen peroxide into water and oxygen has a relatively low activation energy, allowing the reaction to occur spontaneously at room temperature. Adding a catalyst, like manganese dioxide, further lowers the activation energy and increases the reaction rate significantly. These examples demonstrate that the magnitude of a reaction's activation energy has a direct influence on the rate of the reaction: a higher activation energy leads to a slower reaction rate, while a lower activation energy results in a faster reaction rate.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Reaction Rate
In chemistry, the rate of a reaction refers to how quickly reactants are transformed into products. This speed鈥攐r rate鈥攄epends on several factors, with one of the most crucial being activation energy. Activation energy is like a hurdle that reactants need to jump over in order to turn into products. If very few reactants have enough energy to jump this hurdle, the reaction will proceed slowly. If more reactants can jump over, the reaction speeds up.

The key is in the collisions between molecules:
  • Molecules need to collide with enough energy to overcome the activation energy.
  • Only the successful collisions lead to a reaction.
This is why reactions can be slow if the activation energy is high because fewer molecules have the needed energy.
Temperature Influence
Temperature greatly impacts the reaction rate because it influences the kinetic energy of molecules. Imagine the molecules as little racers that move faster when it's "hot." As temperature rises, these racers pick up speed.

Here's how temperature does its magic:
  • Higher temperature increases the kinetic energy of molecules.
  • With more energy, more molecules can overcome the activation energy barrier.
  • This leads to more successful collisions, which increases the reaction rate.
In simple terms, heat makes molecules collide more often and with more force. Thus, reactions are faster at higher temperatures because more molecules have enough energy to leap over the activation energy barrier and react.
Catalysts
Sometimes reactions need a little help to go faster, and that's where catalysts come in. Catalysts are special substances that can speed up reactions without being used up themselves. It's like having a guide who shows reactants an easier path.

Here's what catalysts do:
  • They provide an alternative pathway with a lower activation energy.
  • This allows more reactant molecules to have enough energy to react.
  • Catalysts are not consumed in the reaction, so they can be used repeatedly.
By lowering the activation energy, catalysts make it easier for reactions to occur. They are like shortcuts that help more molecules jump over the energy barrier, leading to a faster reaction rate.
Kinetic Energy
Kinetic energy is the energy of motion. For molecules, it's how fast they're moving. This energy plays a crucial role in getting reactions going. The idea is that moving molecules can collide with one another with enough energy to cause change.

Here's how kinetic energy fits in the reaction story:
  • As kinetic energy increases, molecules move faster.
  • Faster movement leads to more and harder collisions.
  • This increases the chances of reactants overcoming activation energy and reacting.
So, kinetic energy of molecules is essential because it determines how much energy they bring to a collision. To put it simply, more kinetic energy means a higher possibility of effective collisions, leading to a higher reaction rate.

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Most popular questions from this chapter

During the decomposition of dinitrogen pentoxide, $$2 \mathrm{N}_{2} \mathrm{O}_{5}(g) \rightarrow 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$$ how is the rate of consumption of \(\mathrm{N}_{2} \mathrm{O}_{5}\) related to the rate of formation of \(\mathrm{NO}_{2}\) and \(\mathrm{O}_{2} ?\)

Two first-order decomposition reactions of the form \(A \rightarrow B+C\) have the same rate constant at a given temperature. Do the reactants in the two reactions have the same half-lives at this temperature?

Sulfur dioxide emissions in power-plant stack gases may react with carbon monoxide as follows: $$\mathrm{SO}_{2}(g)+3 \mathrm{CO}(g) \rightarrow 2 \mathrm{CO}_{2}(g)+\cos (g)$$ Write an equation relating each of the following pairs of rates: a. The rate of formation of \(\mathrm{CO}_{2}\) to the rate of consumption of CO b. The rate of formation of COS to the rate of consumption of \(\mathrm{SO}_{2}\) c. The rate of consumption of \(\mathrm{CO}\) to the rate of consumption of \(\mathrm{SO}_{2}\)

Tropospheric Ozone Tropospheric (lower atmosphere) ozone is rapidly consumed in many reactions, including $$\mathrm{O}_{3}(g)+\mathrm{NO}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$$ Use the following data to calculate the instantaneous rate of the reaction at \(t=0.000 \mathrm{s}\) and \(t=0.052 \mathrm{s}\) $$\begin{array}{cc}\text { Time (s) } & {[\mathrm{NO}](\mathrm{M})} \\\0.000 & 2.0 \times 10^{-8} \\\\\hline 0.011 & 1.8 \times 10^{-8} \\\\\hline 0.027 & 1.6 \times 10^{-8} \\\\\hline 0.052 & 1.4 \times 10^{-8} \\\\\hline 0.102 & 1.2 \times 10^{-8} \\\\\hline\end{array}$$

The order of a reaction is independent of temperature, but the value of the rate constant varies with temperature. Why?
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