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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![**Chemical Kinetics: Reaction Rate and Activation Energy**
1) **Rate Law Determination**
**Problem**: Write a basic form of the rate law for the following reaction.
\[ \text{ClO}_4^- + 8\text{Br}^- + 8\text{H}^+ \rightarrow \text{Cl}^- + 4\text{Br}_2 + 4\text{H}_2\text{O} \]
**Solution Approach**: The rate law is generally expressed as:
\[ \text{Rate} = k[\text{ClO}_4^-]^m[\text{Br}^-]^n[\text{H}^+]^p \]
where \( k \) is the rate constant, and \( m \), \( n \), and \( p \) are the orders of the reaction with respect to each species.
2) **Order of Reaction**
**Problem**: If doubling the concentration of perchlorate ion in the reaction above causes the rate of reaction to double, what is the order of reaction with respect to perchlorate ion?
**Solution Approach**: If doubling [ClO₄⁻] results in a doubling of the rate, then the reaction is first order with respect to perchlorate ion. Mathematically, this implies \( m = 1 \).
3) **Activation Energy Calculation**
**Problem**: A plot of ln(Rate) vs. \( 1/T \) for the above reaction gave a straight line with a slope of \(-5021\). What is the activation energy for this reaction?
**Solution Approach**: The relationship between the activation energy (Ea) and the slope of the Arrhenius plot is given by:
\[ \text{slope} = -\frac{E_a}{R} \]
where \( R \) is the gas constant (8.314 J/mol·K). Rearranging the equation for \( E_a \) gives:
\[ E_a = -\text{slope} \times R = -(-5021) \times 8.314 \]
Calculating \( E_a \) gives the activation energy for the reaction.
---
This exercise helps to understand the relationship between reaction rate, reaction order, and activation energy in chemical kinetics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40daf55f-9b36-4034-9111-c8b1fc526fc5%2Fb6aef8f5-e4b7-46a6-956a-b6d6116b0e38%2F8ll63kl.jpeg&w=3840&q=75)
Transcribed Image Text:**Chemical Kinetics: Reaction Rate and Activation Energy**
1) **Rate Law Determination**
**Problem**: Write a basic form of the rate law for the following reaction.
\[ \text{ClO}_4^- + 8\text{Br}^- + 8\text{H}^+ \rightarrow \text{Cl}^- + 4\text{Br}_2 + 4\text{H}_2\text{O} \]
**Solution Approach**: The rate law is generally expressed as:
\[ \text{Rate} = k[\text{ClO}_4^-]^m[\text{Br}^-]^n[\text{H}^+]^p \]
where \( k \) is the rate constant, and \( m \), \( n \), and \( p \) are the orders of the reaction with respect to each species.
2) **Order of Reaction**
**Problem**: If doubling the concentration of perchlorate ion in the reaction above causes the rate of reaction to double, what is the order of reaction with respect to perchlorate ion?
**Solution Approach**: If doubling [ClO₄⁻] results in a doubling of the rate, then the reaction is first order with respect to perchlorate ion. Mathematically, this implies \( m = 1 \).
3) **Activation Energy Calculation**
**Problem**: A plot of ln(Rate) vs. \( 1/T \) for the above reaction gave a straight line with a slope of \(-5021\). What is the activation energy for this reaction?
**Solution Approach**: The relationship between the activation energy (Ea) and the slope of the Arrhenius plot is given by:
\[ \text{slope} = -\frac{E_a}{R} \]
where \( R \) is the gas constant (8.314 J/mol·K). Rearranging the equation for \( E_a \) gives:
\[ E_a = -\text{slope} \times R = -(-5021) \times 8.314 \]
Calculating \( E_a \) gives the activation energy for the reaction.
---
This exercise helps to understand the relationship between reaction rate, reaction order, and activation energy in chemical kinetics.
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