**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

The first order integrated rate law is,

Answered: The decomposition of dinitrogen…

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The decomposition of dinitrogen pentoxide in carbon tetrachloride solution at 30 °C N2O5 2 N02 +½ 02

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

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