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
![**The Decomposition of Dinitrogen Pentoxide**
**Reaction Overview:**
The decomposition of dinitrogen pentoxide (N₂O₅) in carbon tetrachloride solution at 30 °C proceeds according to the following reaction:
\[ \text{N}_2\text{O}_5 \rightarrow 2 \text{NO}_2 + \frac{1}{2} \text{O}_2 \]
**Rate Law:**
This reaction is first order with respect to N₂O₅, having a rate constant (k) of \(4.10 \times 10^{-3}\) min⁻¹.
**Problem Statement:**
If the initial concentration of N₂O₅ is 0.417 M, determine the time required (in minutes) for the concentration of N₂O₅ to decrease to \(5.25 \times 10^{-2}\) M.
**Action Required:**
- Input the calculated time in the blank provided.
- Two options for interaction:
- Submit Answer
- Retry Entire Group
**Additional Information:**
- The display shows there are 9 more group attempts remaining.
**Explanation of the Reaction Order:**
For a first-order reaction, the rate of decomposition can be expressed using the integrated first-order rate law formula:
\[ [\text{N}_2\text{O}_5] = [\text{N}_2\text{O}_5]_0 e^{-kt} \]
Where:
- \([\text{N}_2\text{O}_5]\) is the concentration of N₂O₅ at time t.
- \([\text{N}_2\text{O}_5]_0\) is the initial concentration of N₂O₅.
- \(k\) is the rate constant.
- \(t\) is the time elapsed.
This formula can be rearranged to solve for time \(t\) when the concentration at time \(t\) and the rate constant are known.
**Example Calculation:**
Given:
- Initial concentration, \([\text{N}_2\text{O}_5]_0 = 0.417\) M
- Final concentration, \([\text{N}_2\text{O}_5] = 5.25 \times 10^{-2}\) M
- Rate constant, \(k = 4.10 \times](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60358686-21d1-41ff-a93a-9ba59c7b6516%2F3e32a10e-01f6-49f8-9d01-5d6b152d9562%2F2iqkdw_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:**The Decomposition of Dinitrogen Pentoxide**
**Reaction Overview:**
The decomposition of dinitrogen pentoxide (N₂O₅) in carbon tetrachloride solution at 30 °C proceeds according to the following reaction:
\[ \text{N}_2\text{O}_5 \rightarrow 2 \text{NO}_2 + \frac{1}{2} \text{O}_2 \]
**Rate Law:**
This reaction is first order with respect to N₂O₅, having a rate constant (k) of \(4.10 \times 10^{-3}\) min⁻¹.
**Problem Statement:**
If the initial concentration of N₂O₅ is 0.417 M, determine the time required (in minutes) for the concentration of N₂O₅ to decrease to \(5.25 \times 10^{-2}\) M.
**Action Required:**
- Input the calculated time in the blank provided.
- Two options for interaction:
- Submit Answer
- Retry Entire Group
**Additional Information:**
- The display shows there are 9 more group attempts remaining.
**Explanation of the Reaction Order:**
For a first-order reaction, the rate of decomposition can be expressed using the integrated first-order rate law formula:
\[ [\text{N}_2\text{O}_5] = [\text{N}_2\text{O}_5]_0 e^{-kt} \]
Where:
- \([\text{N}_2\text{O}_5]\) is the concentration of N₂O₅ at time t.
- \([\text{N}_2\text{O}_5]_0\) is the initial concentration of N₂O₅.
- \(k\) is the rate constant.
- \(t\) is the time elapsed.
This formula can be rearranged to solve for time \(t\) when the concentration at time \(t\) and the rate constant are known.
**Example Calculation:**
Given:
- Initial concentration, \([\text{N}_2\text{O}_5]_0 = 0.417\) M
- Final concentration, \([\text{N}_2\text{O}_5] = 5.25 \times 10^{-2}\) M
- Rate constant, \(k = 4.10 \times
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