Consider the first-order reaction described by the equation H,C– CH, H-C- -с —н H H Cyclopropane Propene At a certain temperature, the rate constant for this reaction is 5.84 × 104s-!. Calculate the half-life of cyclopropane at this temperature. - מו4 Given an initial cyclopropane concentration of 0.00700 M, calculate the concentration of cyclopropane that remains after 1.70 hours. concentration:
Consider the first-order reaction described by the equation H,C– CH, H-C- -с —н H H Cyclopropane Propene At a certain temperature, the rate constant for this reaction is 5.84 × 104s-!. Calculate the half-life of cyclopropane at this temperature. - מו4 Given an initial cyclopropane concentration of 0.00700 M, calculate the concentration of cyclopropane that remains after 1.70 hours. concentration:
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ISBN:9781305957404
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Chapter1: Chemical Foundations
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**Cyclopropane** (C₄H₆) transforms into **Propene** (C₃H₆) as shown in the chemical equation below:
\[ \text{Cyclopropane} \rightarrow \text{Propene} \]
At a certain temperature, the rate constant for this reaction is given as \( 5.84 \times 10^{-4} \, \text{s}^{-1} \).
#### Calculate the half-life of cyclopropane at this temperature:
The half-life ( \( t_{1/2} \) ) of a first-order reaction is calculated using the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
where:
- \( t_{1/2} \) is the half-life,
- \( k \) is the rate constant.
\[ t_{1/2} = \]
[**Input box for the half-life calculation in seconds**]
---
#### Given an initial cyclopropane concentration of 0.00700 M, calculate the concentration of cyclopropane that remains after 1.70 hours.
For a first-order reaction, the relationship between the concentration of the reactant at a given time \( t \) and the rate constant \( k \) is given by:
\[ [A]_t = [A]_0 e^{-kt} \]
where:
- \([A]_t\) is the concentration at time \( t \),
- \([A]_0\) is the initial concentration,
- \( k \) is the rate constant,
- \( t \) is the time.
Convert 1.70 hours to seconds (since \( k \) is in \( \text{s}^{-1} \)):
\[ t = 1.70 \, \text{hours} \times 3600 \, \text{s/hour} \]
Then calculate:
[**Input box for the concentration calculation in Molarity (M)**]
#### Explanation of Diagrams:
- **Cyclopropane (structure on the left)**: Three carbon atoms form a triangle with each carbon bonded to two hydrogen atoms (\( C_3H_6 \)).
- **Reaction Arrow**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ba7c6ed-fa43-414f-84dd-b449df297bc7%2Fc5e9d74a-4a29-4921-ab1e-64b3e1acf543%2F2wldslf_processed.png&w=3840&q=75)
Transcribed Image Text:### First-Order Reaction: Cyclopropane to Propene
**Consider the first-order reaction described by the equation:**
**Cyclopropane** (C₄H₆) transforms into **Propene** (C₃H₆) as shown in the chemical equation below:
\[ \text{Cyclopropane} \rightarrow \text{Propene} \]
At a certain temperature, the rate constant for this reaction is given as \( 5.84 \times 10^{-4} \, \text{s}^{-1} \).
#### Calculate the half-life of cyclopropane at this temperature:
The half-life ( \( t_{1/2} \) ) of a first-order reaction is calculated using the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
where:
- \( t_{1/2} \) is the half-life,
- \( k \) is the rate constant.
\[ t_{1/2} = \]
[**Input box for the half-life calculation in seconds**]
---
#### Given an initial cyclopropane concentration of 0.00700 M, calculate the concentration of cyclopropane that remains after 1.70 hours.
For a first-order reaction, the relationship between the concentration of the reactant at a given time \( t \) and the rate constant \( k \) is given by:
\[ [A]_t = [A]_0 e^{-kt} \]
where:
- \([A]_t\) is the concentration at time \( t \),
- \([A]_0\) is the initial concentration,
- \( k \) is the rate constant,
- \( t \) is the time.
Convert 1.70 hours to seconds (since \( k \) is in \( \text{s}^{-1} \)):
\[ t = 1.70 \, \text{hours} \times 3600 \, \text{s/hour} \]
Then calculate:
[**Input box for the concentration calculation in Molarity (M)**]
#### Explanation of Diagrams:
- **Cyclopropane (structure on the left)**: Three carbon atoms form a triangle with each carbon bonded to two hydrogen atoms (\( C_3H_6 \)).
- **Reaction Arrow**
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