Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Question
![A chemical reaction is represented as follows:
\[ A(aq) \rightarrow B(aq) + C(aq) \]
A plot of \(\ln[A]\) versus time gives a straight line with a negative slope. What is the order of the reaction?
**Explanation:**
In chemical kinetics, if a plot of the natural logarithm of the concentration of a reactant (\(\ln[A]\)) versus time yields a straight line with a negative slope, this indicates that the reaction is first-order with respect to the reactant \(A\). The linear relationship suggests that the rate of reaction depends exponentially on the concentration of \(A\).
**Key Concepts:**
- **First-Order Reaction:** The rate is directly proportional to the concentration of one reactant. For a first-order reaction, the integrated rate law is \(\ln[A] = -kt + \ln[A_0]\), where \(k\) is the rate constant and \([A_0]\) is the initial concentration.
- **Graphical Representation:** The straight line on the plot demonstrates a linear relationship as predicted by the first-order kinetics, with the slope being equal to \(-k\).
Understanding these concepts assists in predicting reaction behaviors and calculating reaction rates.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe983b18-ee33-44db-82aa-7c6bfcc1e549%2F67778b54-a751-4f15-93fb-f26da0a3f5b8%2Foxvnlo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A chemical reaction is represented as follows:
\[ A(aq) \rightarrow B(aq) + C(aq) \]
A plot of \(\ln[A]\) versus time gives a straight line with a negative slope. What is the order of the reaction?
**Explanation:**
In chemical kinetics, if a plot of the natural logarithm of the concentration of a reactant (\(\ln[A]\)) versus time yields a straight line with a negative slope, this indicates that the reaction is first-order with respect to the reactant \(A\). The linear relationship suggests that the rate of reaction depends exponentially on the concentration of \(A\).
**Key Concepts:**
- **First-Order Reaction:** The rate is directly proportional to the concentration of one reactant. For a first-order reaction, the integrated rate law is \(\ln[A] = -kt + \ln[A_0]\), where \(k\) is the rate constant and \([A_0]\) is the initial concentration.
- **Graphical Representation:** The straight line on the plot demonstrates a linear relationship as predicted by the first-order kinetics, with the slope being equal to \(-k\).
Understanding these concepts assists in predicting reaction behaviors and calculating reaction rates.
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