1. Given the following data, determine the orders with respect to the concentrations of substances A and B in the reaction [A] initial 0.10 M 0.20 M 0.30 M 0.20 M 0.10 M A + B [B]initial 0.10 M 0.10 M 0.10 M 0.20 M 0.20 M products Time for reaction 262 s 131 s 87 s 66 s 131 s
1. Given the following data, determine the orders with respect to the concentrations of substances A and B in the reaction [A] initial 0.10 M 0.20 M 0.30 M 0.20 M 0.10 M A + B [B]initial 0.10 M 0.10 M 0.10 M 0.20 M 0.20 M products Time for reaction 262 s 131 s 87 s 66 s 131 s
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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What other two trials give me the same overall order of 2, using the same method as the one shown below..
![### Reaction Rate Data Analysis
**Problem Statement:**
Given the following data, determine the orders with respect to the concentrations of substances A and B in the reaction:
\[ A + B \rightarrow \text{products} \]
**Experimental Data:**
| \([A]_{\text{initial}}\) | \([B]_{\text{initial}}\) | Time for Reaction (s) |
|--------------------------|--------------------------|----------------------|
| 0.10 M | 0.10 M | 262 s |
| 0.20 M | 0.10 M | 131 s |
| 0.30 M | 0.10 M | 87 s |
| 0.20 M | 0.20 M | 66 s |
| 0.10 M | 0.20 M | 131 s |
**Analysis:**
In this table, the initial concentrations of reactants A and B are varied to observe their effect on the reaction time. By comparing these variables, one can determine the order of the reaction with respect to each reactant:
1. **Effect of \([A]\)**:
- As \([A]\) increases from 0.10 M to 0.20 M (while \([B]\) is constant at 0.10 M), the reaction time halves from 262 seconds to 131 seconds.
- With \([A]\) increased to 0.30 M, the reaction time further reduces to 87 seconds.
- This suggests a first-order relationship in terms of \([A]\).
2. **Effect of \([B]\)**:
- Holding \([A]\) constant at 0.10 M, when \([B]\) increases from 0.10 M to 0.20 M, the reaction time decreases from 262 seconds to 131 seconds.
- A similar pattern is noted when both are at 0.20 M; the reaction time is consistent at 66 seconds, confirming the first-order dependency on \([B]\).
By carefully analyzing the concentration vs. time relationship, one can infer the reaction order for each reactant. In this case, the reaction is first order with respect to both \([A]\) and \([B]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08bb2a94-da17-43f2-90ab-4ad444df37b3%2Fc3825469-cf5b-49ef-a52a-85b64646e057%2Foimldsu_processed.png&w=3840&q=75)
Transcribed Image Text:### Reaction Rate Data Analysis
**Problem Statement:**
Given the following data, determine the orders with respect to the concentrations of substances A and B in the reaction:
\[ A + B \rightarrow \text{products} \]
**Experimental Data:**
| \([A]_{\text{initial}}\) | \([B]_{\text{initial}}\) | Time for Reaction (s) |
|--------------------------|--------------------------|----------------------|
| 0.10 M | 0.10 M | 262 s |
| 0.20 M | 0.10 M | 131 s |
| 0.30 M | 0.10 M | 87 s |
| 0.20 M | 0.20 M | 66 s |
| 0.10 M | 0.20 M | 131 s |
**Analysis:**
In this table, the initial concentrations of reactants A and B are varied to observe their effect on the reaction time. By comparing these variables, one can determine the order of the reaction with respect to each reactant:
1. **Effect of \([A]\)**:
- As \([A]\) increases from 0.10 M to 0.20 M (while \([B]\) is constant at 0.10 M), the reaction time halves from 262 seconds to 131 seconds.
- With \([A]\) increased to 0.30 M, the reaction time further reduces to 87 seconds.
- This suggests a first-order relationship in terms of \([A]\).
2. **Effect of \([B]\)**:
- Holding \([A]\) constant at 0.10 M, when \([B]\) increases from 0.10 M to 0.20 M, the reaction time decreases from 262 seconds to 131 seconds.
- A similar pattern is noted when both are at 0.20 M; the reaction time is consistent at 66 seconds, confirming the first-order dependency on \([B]\).
By carefully analyzing the concentration vs. time relationship, one can infer the reaction order for each reactant. In this case, the reaction is first order with respect to both \([A]\) and \([B]\).
![### Reaction Order Determination
#### Part (a)
\[
\frac{262}{131} = \frac{k[0.10M]^a [0.10M]^b}{k[0.20M]^a [0.10M]^b}
\]
The terms \([0.10M]^b\) cancel out, resulting in:
\[
\frac{2}{0.5^a} = \frac{0.5^a}{0.5^a} = 4
\]
Thus, we have:
\[
\left(\frac{1}{262}\right)\bigg/\left(\frac{1}{131}\right) = 0.5^a
\]
This simplifies to:
\[
\frac{0.5}{0.5} = \frac{0.5^a}{0.5^a}
\]
Therefore, \(1 = a\).
#### Part (b)
\[
\frac{262}{131} = \frac{k[0.10M]^a [0.10M]^b}{k[0.10M]^a [0.20M]^b}
\]
The terms \([0.10M]^a\) cancel out, resulting in:
\[
\frac{2}{0.5^b} = \frac{0.5^b}{0.5^b} = 4
\]
Thus, we have:
\[
\left(\frac{1}{262}\right)\bigg/\left(\frac{1}{131}\right) = 0.5^b
\]
This simplifies to:
\[
\frac{0.5}{0.5} = \frac{0.5^b}{0.5^b}
\]
Therefore, \(1 = b\).
### Conclusion
The overall reaction order is determined as:
\[
\text{Overall order} = 2
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08bb2a94-da17-43f2-90ab-4ad444df37b3%2Fc3825469-cf5b-49ef-a52a-85b64646e057%2F931vtrw_processed.png&w=3840&q=75)
Transcribed Image Text:### Reaction Order Determination
#### Part (a)
\[
\frac{262}{131} = \frac{k[0.10M]^a [0.10M]^b}{k[0.20M]^a [0.10M]^b}
\]
The terms \([0.10M]^b\) cancel out, resulting in:
\[
\frac{2}{0.5^a} = \frac{0.5^a}{0.5^a} = 4
\]
Thus, we have:
\[
\left(\frac{1}{262}\right)\bigg/\left(\frac{1}{131}\right) = 0.5^a
\]
This simplifies to:
\[
\frac{0.5}{0.5} = \frac{0.5^a}{0.5^a}
\]
Therefore, \(1 = a\).
#### Part (b)
\[
\frac{262}{131} = \frac{k[0.10M]^a [0.10M]^b}{k[0.10M]^a [0.20M]^b}
\]
The terms \([0.10M]^a\) cancel out, resulting in:
\[
\frac{2}{0.5^b} = \frac{0.5^b}{0.5^b} = 4
\]
Thus, we have:
\[
\left(\frac{1}{262}\right)\bigg/\left(\frac{1}{131}\right) = 0.5^b
\]
This simplifies to:
\[
\frac{0.5}{0.5} = \frac{0.5^b}{0.5^b}
\]
Therefore, \(1 = b\).
### Conclusion
The overall reaction order is determined as:
\[
\text{Overall order} = 2
\]
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