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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Using the kinetics data below, determine the Rate Law and the rate law constant
![### Reaction Rate Equations and Rate Constants
#### Please review the following reaction rate equations and their corresponding rate constants. Select the correct option as per the given choices.
1. **Option 1**
\[
\text{rate} = k[A]^1[B]^0[C]^1, \quad k = 1,600 \, M^{-1}s^{-1}
\]
2. **Option 2**
\[
\text{rate} = k[A]^1[B]^1[C]^1, \quad k = 6,400 \, M^{-2}s^{-1}
\]
3. **Option 3**
\[
\text{rate} = k[A]^1[B]^0[C]^2, \quad k = 32,000 \, M^{-2}s^{-1}
\]
4. **Option 4**
\[
\text{rate} = k[A]^1[B]^1[C]^2, \quad k = 128,000 \, M^{-3}s^{-1}
\]
### Explanation
The rate equation for a reaction indicates how the rate is affected by the concentration of the reactants. It is typically written in the form:
\[
\text{rate} = k[A]^m[B]^n[C]^p
\]
Where:
- \(\text{rate}\) is the reaction rate.
- \(k\) is the rate constant.
- \([A]\), \([B]\), and \([C]\) are the concentrations of reactants A, B, and C.
- \(m\), \(n\), and \(p\) are the orders of the reaction with respect to each reactant.
The rate constant \(k\) has units that depend on the overall order of the reaction.
**Task:** Based on the given reaction rate equations and their respective rate constants, determine which set of parameters is correct according to the chemical context provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8466b748-e672-4c61-893b-8156cddfafb1%2F7ae27c03-4eab-4200-9ac3-fb36b124dc56%2F1whstit_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Reaction Rate Equations and Rate Constants
#### Please review the following reaction rate equations and their corresponding rate constants. Select the correct option as per the given choices.
1. **Option 1**
\[
\text{rate} = k[A]^1[B]^0[C]^1, \quad k = 1,600 \, M^{-1}s^{-1}
\]
2. **Option 2**
\[
\text{rate} = k[A]^1[B]^1[C]^1, \quad k = 6,400 \, M^{-2}s^{-1}
\]
3. **Option 3**
\[
\text{rate} = k[A]^1[B]^0[C]^2, \quad k = 32,000 \, M^{-2}s^{-1}
\]
4. **Option 4**
\[
\text{rate} = k[A]^1[B]^1[C]^2, \quad k = 128,000 \, M^{-3}s^{-1}
\]
### Explanation
The rate equation for a reaction indicates how the rate is affected by the concentration of the reactants. It is typically written in the form:
\[
\text{rate} = k[A]^m[B]^n[C]^p
\]
Where:
- \(\text{rate}\) is the reaction rate.
- \(k\) is the rate constant.
- \([A]\), \([B]\), and \([C]\) are the concentrations of reactants A, B, and C.
- \(m\), \(n\), and \(p\) are the orders of the reaction with respect to each reactant.
The rate constant \(k\) has units that depend on the overall order of the reaction.
**Task:** Based on the given reaction rate equations and their respective rate constants, determine which set of parameters is correct according to the chemical context provided.
![### Experimental Data on Reaction Rates
The table below represents data from an experiment to determine the reaction rates for different trials with varying concentrations of reactants A, B, and C. The rate of the reactions has been measured in M/sec (molarity per second).
#### Table of Experimental Results
| Trial | [A] | [B] | [C] | Rate (M/sec) |
|--------|------|------|--------|----------------|
| Trial 1| 0.50 | 0.25 | 0.050 | 4.0 x 10¹ |
| Trial 2| 0.25 | 0.25 | 0.050 | 2.0 x 10¹ |
| Trial 3| 0.50 | 0.50 | 0.15 | 3.6 x 10² |
| Trial 4| 0.50 | 0.50 | 0.050 | 4.0 x 10¹ |
#### Explanation of Graphs and Diagrams
**Graphical Representation** (not shown due to limitations, described here):
- **X-Axis:** Represents the concentration of reactant [A], [B], or [C].
- **Y-Axis:** Represents the reaction rate in M/sec.
- Each point on the graph corresponds to one of the trials and its respective rate.
#### Rate Equations
- The rate law equations derived from the experimental data are presented below:
\[
\text{rate} = k[\text{A}]^{1}[\text{B}]^{0}[\text{C}]^{1}, \quad k = 1,600 \, M^{-1}s^{-1}
\]
\[
\text{rate} = k[\text{A}]^{1}[\text{B}]^{1}[\text{C}]^{1}, \quad k = 6,400 \, M^{-2}s^{-1}
\]
### Analysis
- **Trial 1 and 2 Comparison:** Decreasing the concentration of A by half (0.50 to 0.25) while keeping B and C constant decreases the rate from 4.0 x 10¹ to 2.0 x 10¹, suggesting that the rate is directly proportional to [A].
- **Trial](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8466b748-e672-4c61-893b-8156cddfafb1%2F7ae27c03-4eab-4200-9ac3-fb36b124dc56%2F2yxr0e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Experimental Data on Reaction Rates
The table below represents data from an experiment to determine the reaction rates for different trials with varying concentrations of reactants A, B, and C. The rate of the reactions has been measured in M/sec (molarity per second).
#### Table of Experimental Results
| Trial | [A] | [B] | [C] | Rate (M/sec) |
|--------|------|------|--------|----------------|
| Trial 1| 0.50 | 0.25 | 0.050 | 4.0 x 10¹ |
| Trial 2| 0.25 | 0.25 | 0.050 | 2.0 x 10¹ |
| Trial 3| 0.50 | 0.50 | 0.15 | 3.6 x 10² |
| Trial 4| 0.50 | 0.50 | 0.050 | 4.0 x 10¹ |
#### Explanation of Graphs and Diagrams
**Graphical Representation** (not shown due to limitations, described here):
- **X-Axis:** Represents the concentration of reactant [A], [B], or [C].
- **Y-Axis:** Represents the reaction rate in M/sec.
- Each point on the graph corresponds to one of the trials and its respective rate.
#### Rate Equations
- The rate law equations derived from the experimental data are presented below:
\[
\text{rate} = k[\text{A}]^{1}[\text{B}]^{0}[\text{C}]^{1}, \quad k = 1,600 \, M^{-1}s^{-1}
\]
\[
\text{rate} = k[\text{A}]^{1}[\text{B}]^{1}[\text{C}]^{1}, \quad k = 6,400 \, M^{-2}s^{-1}
\]
### Analysis
- **Trial 1 and 2 Comparison:** Decreasing the concentration of A by half (0.50 to 0.25) while keeping B and C constant decreases the rate from 4.0 x 10¹ to 2.0 x 10¹, suggesting that the rate is directly proportional to [A].
- **Trial
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