Problem 93 - Chemistry The Science in Context

Question

If the reaction \(A \rightarrow B\) is first order in \(A\) and first order overall, does it occur in just one step?

Step-by-Step Solution

Answer

#Answer# Yes, the reaction \(A \rightarrow B\) is a single-step reaction, as it is first order in \(A\) and first order overall with no intermediate species involved.

Step 1: Identify the given reaction order

The reaction \(A \rightarrow B\) is given as first order in \(A\) and first order overall. This means that the rate of the reaction depends solely on the concentration of \(A\).

Step 2: Analyze the reaction

The reaction is a simple conversion of a reactant \(A\) into a product \(B\). There are no intermediate steps or species involved in the reaction. Therefore, the rate law for this reaction can be written as: \[Rate = k [A]\]

Step 3: Determine if the reaction occurs in one step

Since the reaction's rate law is dependent only on the concentration of \(A\), and there are no intermediate species, we can conclude that the reaction occurs in one step. This is because there is a direct relationship between the reactant \(A\) and the product \(B\).

Key Concepts

Reaction Order

Understanding the concept of reaction order is vital in chemical kinetics. Reaction order refers to the power to which the concentration of a reactant is raised in the rate law equation. This reflects how changes in concentration impact the rate of the reaction. For example, if the reaction is first order with respect to a particular reactant, it means that the rate of reaction changes linearly with changes in the concentration of that reactant. In a first order reaction like the conversion of A to B, doubling the concentration of A doubles the rate of reaction as well.
This concept helps chemists predict how a reaction's rate will change with varying concentrations, which is essential for controlling reaction speeds in industrial processes and understanding reaction mechanisms.

Rate Law

The rate law of a chemical reaction is an equation that links the rate of reaction to the concentration of the reactants. For a simple reaction such as the conversion of A to B, the rate law is expressed as \(Rate = k [A]\). Here, \(k\) is the rate constant, a proportional factor that remains constant at a given temperature.

• The rate law provides part of the picture needed to understand how quickly a reaction proceeds under specific conditions.
• It offers clarity on which reactants influence the rate, helping to deduce the mechanism of the reaction.

The simplicity of the rate law in first order reactions suggests that the process occurs in a single step, without intermediate stages, creating a direct transformation from A to B.

First Order Reaction

A first order reaction involves reactants in which the reaction rate is directly proportional to the concentration of only one reactant. This is typified by the reaction \(A \rightarrow B\), where the rate equation \(Rate = k [A]\) indicates a dependence solely on the concentration of A.
The characteristic behavior of first order reactions is evident from their reaction kinetics:

• The half-life of a first order reaction is constant, meaning it does not change with the concentration of reactants.
• The rate of reaction decreases over time as the concentration of A decreases, following an exponential decay pattern.

These features are pivotal in predicting how the reaction progresses over time, making first order reactions a fundamental concept in chemical kinetic studies. Understanding such reactions helps in fields such as pharmacology, where drug dosages relate directly to how first order processes eliminate substances from the body.