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The rate of decomposition of acetaldehyde, \(\mathrm{CH}_{3} \mathrm{CHO}(g)\), into \(\mathrm{CH}_{4}(g)\) and \(\mathrm{CO}(g)\) in the presence of \(\mathrm{I}_{2}(g)\) at \(800 \mathrm{~K}\) follows the rate law $$ \text { rate of reaction }=k\left[\mathrm{CH}_{3} \mathrm{CHO}\right]\left[\mathrm{I}_{2}\right] $$ The decomposition is believed to occur by the following two-step mechanism: (1) \(\mathrm{CH}_{3} \mathrm{CHO}(g)+\mathrm{I}_{2}(g) \rightarrow \mathrm{CH}_{3} \mathrm{I}(g)+\mathrm{HI}(g)+\mathrm{CO}(g)\) (2) \(\mathrm{CH}_{3} \mathrm{I}(g)+\mathrm{HI}(g) \rightarrow \mathrm{CH}_{4}(g)+\mathrm{I}_{2}(g)\) (a) What is the catalyst for the reaction? (b) Which step in the proposed mechanism is most likely the rate-limiting step?

Short Answer

Expert verified
(a) \( \mathrm{I}_{2} \) is the catalyst. (b) The first step is the rate-limiting step.

Step by step solution

01

Analysis of Catalyst

A catalyst is a substance that speeds up a reaction without being consumed in the process. It appears in the initial reactants and is regenerated in the final products. Here, iodine, \( \mathrm{I}_{2} \), appears as a reactant in the first step and is regenerated in the products of the second step. Therefore, \( \mathrm{I}_{2} \) acts as the catalyst.
02

Identify the Rate-Limiting Step

The rate law provided for the reaction is \( \text{rate} = k [\mathrm{CH}_{3}\mathrm{CHO}][\mathrm{I}_{2}] \). The rate law reflects the slowest step of the mechanism, which involves both \( \mathrm{CH}_{3}\mathrm{CHO} \) and \( \mathrm{I}_{2} \). In the given mechanism, the first step matches this rate law as it involves these species. Hence, the first step is likely the rate-limiting step.

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Key Concepts

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

Catalysis
Catalysis is an intriguing aspect of reaction kinetics, where a substance helps speed up a reaction but doesn't get consumed in the process. Imagine it as a facilitator or helper in a reaction. The magical part about catalysts is that they participate in the reaction initially but are regenerated after the reaction finishes.

In our acetaldehyde decomposition reaction, iodine \( \mathrm{I}_{2} \) is a perfect example of a catalyst. It kicks off the reaction by participating in the first step, but by the end of the second step, it's still there, unchanged and ready to go again! This means that it can continue to help more acetaldehyde molecules decompose over time without being depleted.

Catalysts are essential in many industrial processes, including the production of ammonia and the refining of petroleum. They work behind the scenes, making processes more efficient.
  • Speed up the reaction without getting consumed.
  • Appear both in the beginning and at the end of a reaction mechanism.
  • Must regenerate by the end of the reaction.
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Rate Law
The rate law is a powerful tool in reaction kinetics. It gives us the relationship between the concentration of reactants and the rate at which they react.

For our problem, the rate law is \( \text{rate} = k [\mathrm{CH}_{3}\mathrm{CHO}][\mathrm{I}_{2}] \). This tells us how the concentration of acetaldehyde \( \mathrm{CH}_{3}\mathrm{CHO} \) and iodine \( \mathrm{I}_{2} \) affect how fast the reaction proceeds.

Here's a breakdown of what this rate law implies:
  • The rate of reaction depends on the concentration of each reactant involved in the slowest, rate-limiting step of the reaction mechanism.
  • The rate constant \( k \) is crucial as it includes the reaction conditions and influences how quickly the reaction can go.
The rate law is specific to the mechanism of the reaction. It reflects the particular elementary steps involved. Understanding which step corresponds to the rate law can also help identify the rate-limiting step, which is often the slowest one.
Reaction Mechanism
A reaction mechanism is like a detailed step-by-step guide that describes how a reaction occurs at the molecular level. It reveals the sequence of elementary steps that lead from reactants to products.

In the decomposition of acetaldehyde, the reaction mechanism is:
  • Step 1: \( \mathrm{CH}_{3} \mathrm{CHO}(g) + \mathrm{I}_{2}(g) \rightarrow \mathrm{CH}_{3} \mathrm{I}(g) + \mathrm{HI}(g) + \mathrm{CO}(g) \)
  • Step 2: \( \mathrm{CH}_{3} \mathrm{I}(g) + \mathrm{HI}(g) \rightarrow \mathrm{CH}_{4}(g) + \mathrm{I}_{2}(g) \)
These reactions occur in sequence. The intermediate species, those that are produced in one step and consumed in another, are not found in the overall balanced equation for the reaction.

Identifying the rate-limiting step is crucial. This is typically the slowest step and determines the overall rate of the reaction. In our example, the first step is likely the rate-limiting step, based on the provided rate law which matches it. Understanding the mechanism provides insight into how the chemical transformation occurs and can help design better catalysts to improve reaction efficiency.

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