At a certain temperature this reaction follows second-order kinetics with a rate constant of 23.M¹s¹: 2N₂O5 (g) 2N₂O4 (g) + O₂(g) Suppose a vessel contains N₂O, at a concentration of 1.04M. Calculate how long it takes for the concentration of N₂O5 to decrease to 8.0% of its initial value. You may assume no other reaction is important. do Round your answer to 2 significant digits. m s X ? 5

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### Reaction Kinetics Problem

At a certain temperature, this reaction follows second-order kinetics with a rate constant of \( 23. \text {M}^{-1} \text{s}^{-1} \):

\[ 2 \text{N}_2\text{O}_5(\text{g}) \rightarrow 2\text{N}_2\text{O}_4(\text{g}) + \text{O}_2(\text{g}) \]

#### Problem Statement

Suppose a vessel contains \( \text{N}_2\text{O}_5 \) at a concentration of \( 1.04 \text{M} \). Calculate how long it takes for the concentration of \( \text{N}_2\text{O}_5 \) to decrease to 8.0% of its initial value. You may assume no other reaction is important.

Round your answer to 2 significant digits.

#### Solutions and Explanations

*To calculate the time needed for a second-order reaction to reach a certain concentration, the following formula is applicable:*

\[
\frac{1}{[\text{A}]} = kt + \frac{1}{[\text{A}_0]}
\]

Where:
- \([\text{A}_0]\) is the initial concentration.
- \([\text{A}]\) is the final concentration.
- \(k\) is the rate constant.
- \(t\) is the time.

Substitute the known values into the formula to find the amount of time.

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Transcribed Image Text:### Reaction Kinetics Problem At a certain temperature, this reaction follows second-order kinetics with a rate constant of \( 23. \text {M}^{-1} \text{s}^{-1} \): \[ 2 \text{N}_2\text{O}_5(\text{g}) \rightarrow 2\text{N}_2\text{O}_4(\text{g}) + \text{O}_2(\text{g}) \] #### Problem Statement Suppose a vessel contains \( \text{N}_2\text{O}_5 \) at a concentration of \( 1.04 \text{M} \). Calculate how long it takes for the concentration of \( \text{N}_2\text{O}_5 \) to decrease to 8.0% of its initial value. You may assume no other reaction is important. Round your answer to 2 significant digits. #### Solutions and Explanations *To calculate the time needed for a second-order reaction to reach a certain concentration, the following formula is applicable:* \[ \frac{1}{[\text{A}]} = kt + \frac{1}{[\text{A}_0]} \] Where: - \([\text{A}_0]\) is the initial concentration. - \([\text{A}]\) is the final concentration. - \(k\) is the rate constant. - \(t\) is the time. Substitute the known values into the formula to find the amount of time. ### Interactive Element Below the problem statement, an interactive element is present where users can input their answer: ```html [ ] s ``` Users are prompted to enter their answer in seconds with options to: - **Check** if the answer is correct (by clicking the checkbox icon) - **Reset** (by clicking the undo arrow icon) - **Get Help** (by clicking the question mark icon)
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