Problem 70 - Chemistry Matter and Change

Question

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

Step-by-Step Solution

Answer

Step 2 is the rate-determining step because it is the slowest step.

Step 1: Understand the Reaction Steps

The reaction is given in two steps. The first step is a fast reaction where \( A + B \rightarrow C \). The second step is a slow reaction where \( C + D \rightarrow E \).

Step 2: Identify the Rate-Determining Step

The rate-determining step in a reaction mechanism is the slowest step because it has the highest energy barrier to overcome. This step effectively controls the rate at which the entire reaction proceeds.

Step 3: Compare Step Speeds

Given the two steps, Step 1 is described as 'fast' and Step 2 as 'slow'. This clearly indicates that Step 2 takes more time or energy to proceed than Step 1.

Step 4: Conclude the Rate-Determining Step

Since Step 2 is the slow step, it is the rate-determining step of the reaction mechanism. In a multistep reaction, the overall reaction rate is governed by the slowest step. This is why Step 2 is considered the rate-determining step.

Key Concepts

Rate-Determining Step

In any multistep chemical reaction, the rate-determining step plays a crucial role. It acts like a bottleneck in an assembly line. Imagine you are building a car, and one part takes significantly longer to install than all the others. This slow step controls how quickly the entire car can be built. Similarly, in a chemical reaction, the rate-determining step is the slowest step. This is because it has the highest energy barrier, making it the most time-consuming part of the reaction.

• The rate-determining step controls the speed of the entire reaction.
• It has the highest activation energy compared to other steps.
• In our example, step 2 is the rate-determining step.

Understanding this concept is vital because it highlights which part of the reaction pathway requires the most energy and time, dictating the pace of the whole reaction.

Reaction Kinetics

Reaction kinetics is all about understanding how fast reactions occur. It studies the rates of chemical processes and helps chemists determine how different conditions affect the speed of a reaction. Reaction kinetics considers various factors:

• The concentration of reactants – Higher concentrations generally increase reaction rates.
• Temperature – Usually, increasing the temperature speeds up reactions.
• The presence of a catalyst – Catalysts can lower the activation energy, making the reaction faster.

In the case of multistep reactions, kinetics explains why the rate-determining step is pivotal. The slowest step sets the overall pace, making it the hub of kinetic studies in complex reactions.

Multistep Reaction

Not all chemical reactions occur in a single step. Sometimes, they involve a series of smaller steps, each with its own reactants and products. Such sequences are known as multistep reactions. These types of reactions can be likened to a relay race:

• Each runner (or step) has a defined path and goal.
• The baton (intermediates like substance C in our example) is passed from one to the next.
• The slowest runner (step) in the group sets the pace for the whole team, much like the rate-determining step.

Multistep reactions require a broader understanding since each step might involve different conditions, intermediates, and energy requirements.

Reaction Rate

The term reaction rate refers to how fast or slow a chemical reaction proceeds. It measures the change in concentration of reactants or products per unit time. Several factors influence reaction rates:

• The physical state of reactants – Gas reactions often proceed quicker than liquid or solid reactions.
• Surface area – More exposed surface typically results in faster reactions.
• Pressure – Particularly in gaseous reactions, where increased pressure can speed up the reaction rate.

The reaction rate concept is crucial in industries where production time is key, as well as in natural processes like metabolism. In our example, understanding why the second step slows down the overall reaction aids in calculating the practical time frame needed for the total reaction completion.