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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![**Understanding Reaction Rates: Example Problem**
**Problem Statement:**
A rate is equal to 0.0200 M/s. If [A] = 0.100 M and the rate equation is given by rate = k[A]^2, what is the new rate if the concentration of [A] is increased to 0.200 M?
**Possible Answers:**
- ☐ 0.0200 M/s
- ☐ 0.100 M/s
- ☐ 0.0400 M/s
- ☐ 0.0600 M/s
- ☐ 0.0800 M/s
**Explanation:**
To solve this problem, you need to understand how the rate of a reaction changes with the concentration of a reactant. The given rate law is rate = k[A]^2, indicating that the rate of reaction is directly proportional to the square of the concentration of [A].
Given:
- Initial rate = 0.0200 M/s
- Initial concentration, [A] = 0.100 M
- Rate = k[A]^2
Firstly, determine the rate constant (k) using the provided data:
\[ 0.0200 \text{ M/s} = k \times (0.100 \text{ M})^2 \]
\[
0.0200 \text{ M/s} = k \times 0.0100 \text{ M}^2
\]
\[
k = \frac{0.0200 \text{ M/s}}{0.0100 \text{ M}^2}
\]
\[
k = 2 \text{ M}^{-1}\text{s}^{-1}
\]
Now, use this rate constant to find the new rate when [A] = 0.200 M:
\[
\text{New rate} = k \times (0.200 \text{ M})^2
\]
\[
\text{New rate} = 2 \text{ M}^{-1}\text{s}^{-1} \times (0.200 \text{ M})^2
\]
\[
\text{New rate} = 2 \text{ M}^{-1}\text{s}^{-1} \times 0.0400 \text{ M}^2
\]
\[
\text{New rate} = 0.080](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F560885b1-95a6-46a1-8479-9132da42c8bd%2Fe2f6cc1a-1961-41e4-b5c0-b5db35a25cba%2Fvpkf9ml_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Reaction Rates: Example Problem**
**Problem Statement:**
A rate is equal to 0.0200 M/s. If [A] = 0.100 M and the rate equation is given by rate = k[A]^2, what is the new rate if the concentration of [A] is increased to 0.200 M?
**Possible Answers:**
- ☐ 0.0200 M/s
- ☐ 0.100 M/s
- ☐ 0.0400 M/s
- ☐ 0.0600 M/s
- ☐ 0.0800 M/s
**Explanation:**
To solve this problem, you need to understand how the rate of a reaction changes with the concentration of a reactant. The given rate law is rate = k[A]^2, indicating that the rate of reaction is directly proportional to the square of the concentration of [A].
Given:
- Initial rate = 0.0200 M/s
- Initial concentration, [A] = 0.100 M
- Rate = k[A]^2
Firstly, determine the rate constant (k) using the provided data:
\[ 0.0200 \text{ M/s} = k \times (0.100 \text{ M})^2 \]
\[
0.0200 \text{ M/s} = k \times 0.0100 \text{ M}^2
\]
\[
k = \frac{0.0200 \text{ M/s}}{0.0100 \text{ M}^2}
\]
\[
k = 2 \text{ M}^{-1}\text{s}^{-1}
\]
Now, use this rate constant to find the new rate when [A] = 0.200 M:
\[
\text{New rate} = k \times (0.200 \text{ M})^2
\]
\[
\text{New rate} = 2 \text{ M}^{-1}\text{s}^{-1} \times (0.200 \text{ M})^2
\]
\[
\text{New rate} = 2 \text{ M}^{-1}\text{s}^{-1} \times 0.0400 \text{ M}^2
\]
\[
\text{New rate} = 0.080
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