A + B → C [A](M)[B](M) Initial Rate (M/h) 0.137 0.277 193 0.428 0.277 1,470 0.137 0.679 547 Find the order with respect to B. Round to the nearest whole number.
A + B → C [A](M)[B](M) Initial Rate (M/h) 0.137 0.277 193 0.428 0.277 1,470 0.137 0.679 547 Find the order with respect to B. Round to the nearest whole number.
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...
Related questions
Question
![### Chemical Kinetics: Determining Reaction Order
#### Reaction: \( \text{A} + \text{B} \rightarrow \text{C} \)
The following table summarizes the concentrations of reactants A and B, along with the initial rate of formation of product C:
| \([A] (\text{M})\) | \([B] (\text{M})\) | Initial Rate (\(\text{M/h}\)) |
|---------------|---------------|---------------------|
| 0.137 | 0.277 | 193 |
| 0.428 | 0.277 | 1,470 |
| 0.137 | 0.679 | 547 |
**Objective:** Determine the order of the reaction with respect to \( \text{B} \). Round to the nearest whole number.
### Explanation of the Data:
1. By comparing experiments 1 and 3, where \([A]\) is constant:
- Experiment 1: \([A] = 0.137 \text{ M}\), \([B] = 0.277 \text{ M}\), Rate = 193 \(\text{ M/h}\)
- Experiment 3: \([A] = 0.137 \text{ M}\), \([B] = 0.679 \text{ M}\), Rate = 547 \(\text{ M/h}\)
2. The ratio of \([B]\) in experiments 1 and 3 is:
\[
\frac{0.679}{0.277} \approx 2.45
\]
3. The ratio of the rates in experiments 1 and 3 is:
\[
\frac{547}{193} \approx 2.83
\]
4. The order of reaction with respect to \( \text{B} \) (denoted as \( n \)) is determined by the formula:
\[
\left(\frac{[\text{B}]_2}{[\text{B}]_1}\right)^n = \frac{\text{Rate}_2}{\text{Rate}_1}
\]
Substituting the values:
\[
(2.45)^n = 2.83
\]
5. Solving for \( n \):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c8d8a42-8de4-4466-9c46-ae253053e314%2Fd4d58618-ff8a-43f9-a979-901e97d85307%2Fmyxq4xp.png&w=3840&q=75)
Transcribed Image Text:### Chemical Kinetics: Determining Reaction Order
#### Reaction: \( \text{A} + \text{B} \rightarrow \text{C} \)
The following table summarizes the concentrations of reactants A and B, along with the initial rate of formation of product C:
| \([A] (\text{M})\) | \([B] (\text{M})\) | Initial Rate (\(\text{M/h}\)) |
|---------------|---------------|---------------------|
| 0.137 | 0.277 | 193 |
| 0.428 | 0.277 | 1,470 |
| 0.137 | 0.679 | 547 |
**Objective:** Determine the order of the reaction with respect to \( \text{B} \). Round to the nearest whole number.
### Explanation of the Data:
1. By comparing experiments 1 and 3, where \([A]\) is constant:
- Experiment 1: \([A] = 0.137 \text{ M}\), \([B] = 0.277 \text{ M}\), Rate = 193 \(\text{ M/h}\)
- Experiment 3: \([A] = 0.137 \text{ M}\), \([B] = 0.679 \text{ M}\), Rate = 547 \(\text{ M/h}\)
2. The ratio of \([B]\) in experiments 1 and 3 is:
\[
\frac{0.679}{0.277} \approx 2.45
\]
3. The ratio of the rates in experiments 1 and 3 is:
\[
\frac{547}{193} \approx 2.83
\]
4. The order of reaction with respect to \( \text{B} \) (denoted as \( n \)) is determined by the formula:
\[
\left(\frac{[\text{B}]_2}{[\text{B}]_1}\right)^n = \frac{\text{Rate}_2}{\text{Rate}_1}
\]
Substituting the values:
\[
(2.45)^n = 2.83
\]
5. Solving for \( n \):
Expert Solution
Step 1
Since the rate of reaction depends only on the concentration of reactants
Hence for the above reaction we can write rate as
Rate = K [A]a [B]b
where a = order with respect to A
b = order with respect to B
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY