Problem 70 - Chemistry Matter and Change

Question

Suppose that a chemical reaction takes place in a two-step mechanism. Step 1 (fast) \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}\) Step \(2(\text { slow }) \mathrm{C}+\mathrm{D} \rightarrow \mathrm{E}\) Which step in the reaction mechanism is the ratedetermining step? Explain.

Step-by-Step Solution

Answer

The rate-determining step of the given reaction mechanism is step 2 (\(C + D \rightarrow E\)), as it is the slowest step and controls the overall rate at which the reaction proceeds.

Step 1: Identifying the given steps and their speeds

We know that the reaction takes place in two steps: 1. Step 1 (fast): A + B → C 2. Step 2 (slow): C + D → E

Step 2: Identifying the rate-determining step

The rate-determining step (RDS) is the slowest step in a reaction mechanism. In our given reaction, step 1 is fast and step 2 is slow. Therefore, the slowest step is step 2.

Step 3: Conclusion

The rate-determining step of the given reaction mechanism is step 2, where C + D → E. This is because step 2 is the slowest step and it controls the overall rate at which the reaction proceeds.

Key Concepts

Chemical Reaction Mechanism

To understand a chemical process thoroughly, it is crucial to delve into the chemical reaction mechanism. This involves a step-by-step sequence of elementary reactions by which a chemical change occurs. Think of it as the detailed pathway from reactants to products, including all the intermediate species and transition states involved.

When analyzing mechanisms, chemists break down the overall reaction into simpler, more fundamental steps. Each of these steps is characterized by a unique speed and specific reactants and products. By knowing the mechanism, scientists can predict the behavior of a reaction under various conditions, design better catalysts, and control reaction outcomes.

Referring back to the exercise, the reaction mechanism is two steps: a fast initial reaction between 'A' and 'B' to form 'C', followed by a slower second step where 'C' reacts with 'D' to yield the final product 'E'. Understanding this sequence allows for the identification of the rate-determining step, thereby characterizing the reaction kinetics.

Reaction Rates

Reaction rate is a measure of how fast a chemical reaction occurs. It is usually expressed in terms of the change in concentration of a reactant or product over time. Factors such as concentration, surface area, temperature, and catalysts can influence the rate. High concentration and temperature generally increase the reaction rate, whereas a catalyst provides an alternative pathway with a lower activation energy for the reaction to occur more rapidly.

In our exercise, we look at the rates of two steps to determine which one controls the overall rate of the reaction. Since step 2 is slow and step 1 is fast, the reaction's pace will be dictated by the slower event, much like how the speed of a caravan is determined by its slowest member. Understanding that the rate-determining step sets the tempo allows us to focus on modifying this particular step if we wanted to increase the overall reaction speed.

Reaction Step Speed

Each step within a chemical reaction mechanism proceeds at a different speed, defined as reaction step speed. Steps can range from very fast to very slow, depending on various factors including reactant collisions, energy profiles, and the presence of catalysts.

In some cases, one step is significantly slower than the others, becoming the bottleneck of the process - this is known as the rate-determining step (RDS). The RDS is especially important because it governs the reaction's overall rate, much like the narrowest point of a funnel dictates the flow rate of a liquid. In the exercise, the second step, despite being the latter, is slower and therefore is the RDS. This critical insight helps chemists focus their efforts when optimizing a reaction, whether by increasing reactant concentration or adding catalysts to specifically target and enhance the rate of the RDS.