The rate constant for this first-order reaction is 0.450 s⁻¹ at 400 °C. A → products How long, in seconds, would it take for the concentration of A to decrease from 0.800 M to 0.250 M? \[ t = \] There is a blank space provided for input. ### Explanation: The problem requires using the first-order reaction integrated rate law to calculate the time it takes for the concentration of reactant A to decrease from 0.800 M to 0.250 M. For a first-order reaction, the integrated rate law is given by: \[ t = \frac{1}{k} \ln \left(\frac{[A]_0}{[A]}\right) \] where: - \( t \) is the time, - \( k \) is the rate constant, - \([A]_0\) is the initial concentration, - \([A]\) is the concentration at time \( t \). In this problem: - \( k = 0.450 \, \text{s}^{-1} \), - \([A]_0 = 0.800 \, \text{M} \), - \([A] = 0.250 \, \text{M} \). The box labeled "TOOLS x10⁷" may be a utility for calculations or converting numbers to scientific notation.
The rate constant for this first-order reaction is 0.450 s⁻¹ at 400 °C. A → products How long, in seconds, would it take for the concentration of A to decrease from 0.800 M to 0.250 M? \[ t = \] There is a blank space provided for input. ### Explanation: The problem requires using the first-order reaction integrated rate law to calculate the time it takes for the concentration of reactant A to decrease from 0.800 M to 0.250 M. For a first-order reaction, the integrated rate law is given by: \[ t = \frac{1}{k} \ln \left(\frac{[A]_0}{[A]}\right) \] where: - \( t \) is the time, - \( k \) is the rate constant, - \([A]_0\) is the initial concentration, - \([A]\) is the concentration at time \( t \). In this problem: - \( k = 0.450 \, \text{s}^{-1} \), - \([A]_0 = 0.800 \, \text{M} \), - \([A] = 0.250 \, \text{M} \). The box labeled "TOOLS x10⁷" may be a utility for calculations or converting numbers to scientific notation.
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 rate constant for this first-order reaction is 0.450 s⁻¹ at 400 °C.
A → products
How long, in seconds, would it take for the concentration of A to decrease from 0.800 M to 0.250 M?
\[ t = \]
There is a blank space provided for input.
### Explanation:
The problem requires using the first-order reaction integrated rate law to calculate the time it takes for the concentration of reactant A to decrease from 0.800 M to 0.250 M. For a first-order reaction, the integrated rate law is given by:
\[ t = \frac{1}{k} \ln \left(\frac{[A]_0}{[A]}\right) \]
where:
- \( t \) is the time,
- \( k \) is the rate constant,
- \([A]_0\) is the initial concentration,
- \([A]\) is the concentration at time \( t \).
In this problem:
- \( k = 0.450 \, \text{s}^{-1} \),
- \([A]_0 = 0.800 \, \text{M} \),
- \([A] = 0.250 \, \text{M} \).
The box labeled "TOOLS x10⁷" may be a utility for calculations or converting numbers to scientific notation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04d91ec5-5dc8-475a-a219-706d13e893d1%2F89c4346e-e406-45a7-a04d-9800add93f2f%2Fyhoi2lu.jpeg&w=3840&q=75)
Transcribed Image Text:The rate constant for this first-order reaction is 0.450 s⁻¹ at 400 °C.
A → products
How long, in seconds, would it take for the concentration of A to decrease from 0.800 M to 0.250 M?
\[ t = \]
There is a blank space provided for input.
### Explanation:
The problem requires using the first-order reaction integrated rate law to calculate the time it takes for the concentration of reactant A to decrease from 0.800 M to 0.250 M. For a first-order reaction, the integrated rate law is given by:
\[ t = \frac{1}{k} \ln \left(\frac{[A]_0}{[A]}\right) \]
where:
- \( t \) is the time,
- \( k \) is the rate constant,
- \([A]_0\) is the initial concentration,
- \([A]\) is the concentration at time \( t \).
In this problem:
- \( k = 0.450 \, \text{s}^{-1} \),
- \([A]_0 = 0.800 \, \text{M} \),
- \([A] = 0.250 \, \text{M} \).
The box labeled "TOOLS x10⁷" may be a utility for calculations or converting numbers to scientific notation.
Expert Solution
Step 1
Initial concentration = 0.800 M
Final concentration = 0.250 M
Step by step
Solved in 3 steps with 1 images
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