A→products What would be the final concentration of A after 37.3 minutes, if in this first order reaction you started with 13 M of A? The half life of A is 3,573 seconds.
A→products What would be the final concentration of A after 37.3 minutes, if in this first order reaction you started with 13 M of A? The half life of A is 3,573 seconds.
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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![### First Order Reaction Problem Statement
**Reaction:**
A → products
**Problem:**
What would be the final concentration of A after 37.3 minutes, if in this first-order reaction you started with 13 M of A? The half-life of A is 3,573 seconds.
**Solution Steps:**
To find the final concentration of A, we need to use the first-order kinetics formula:
\[ [A]_t = [A]_0 \times e^{-kt} \]
Where:
- \([A]_t\) is the concentration of A at time \(t\)
- \([A]_0\) is the initial concentration of A
- \(k\) is the rate constant
- \(t\) is the time
First, we need to determine the rate constant, \(k\), using the half-life of a first-order reaction:
\[ t_{1/2} = \frac{0.693}{k} \]
Given, \(t_{1/2} = 3,573\) seconds:
\[ k = \frac{0.693}{3,573 \, \text{seconds}} \]
Now, convert 37.3 minutes to seconds:
\[ 37.3 \, \text{minutes} \times 60 \, \text{seconds/minute} = 2,238 \, \text{seconds} \]
We can now substitute these values into the first-order kinetics formula to find \([A]_t\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdddcaf98-1498-4874-b480-699455f18f4b%2F2a3f764a-5789-46af-a300-e591317cbb59%2Frj4j0fa_processed.png&w=3840&q=75)
Transcribed Image Text:### First Order Reaction Problem Statement
**Reaction:**
A → products
**Problem:**
What would be the final concentration of A after 37.3 minutes, if in this first-order reaction you started with 13 M of A? The half-life of A is 3,573 seconds.
**Solution Steps:**
To find the final concentration of A, we need to use the first-order kinetics formula:
\[ [A]_t = [A]_0 \times e^{-kt} \]
Where:
- \([A]_t\) is the concentration of A at time \(t\)
- \([A]_0\) is the initial concentration of A
- \(k\) is the rate constant
- \(t\) is the time
First, we need to determine the rate constant, \(k\), using the half-life of a first-order reaction:
\[ t_{1/2} = \frac{0.693}{k} \]
Given, \(t_{1/2} = 3,573\) seconds:
\[ k = \frac{0.693}{3,573 \, \text{seconds}} \]
Now, convert 37.3 minutes to seconds:
\[ 37.3 \, \text{minutes} \times 60 \, \text{seconds/minute} = 2,238 \, \text{seconds} \]
We can now substitute these values into the first-order kinetics formula to find \([A]_t\).
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