Consider the table of data collected for the reaction A → Products. . Calculate the rate constant for this reaction. Show work. Time (s) [A] M In [A] 1/[A] 0.6 -0.51083 1.666667 0.5 0.325 -1.12393 3.076923 1 0.178 -1.72597 5.617978 1.5 0.095 -2.35388 10.52632 2 0.05 -2.99573 20 2.5 0.028 -3.57555 35.71429 0.015 -4.19971 66.66667 3.5 0.008 -4.82831 125 4 0.004 -5.52146 250
Consider the table of data collected for the reaction A → Products. . Calculate the rate constant for this reaction. Show work. Time (s) [A] M In [A] 1/[A] 0.6 -0.51083 1.666667 0.5 0.325 -1.12393 3.076923 1 0.178 -1.72597 5.617978 1.5 0.095 -2.35388 10.52632 2 0.05 -2.99573 20 2.5 0.028 -3.57555 35.71429 0.015 -4.19971 66.66667 3.5 0.008 -4.82831 125 4 0.004 -5.52146 250
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![**Reaction Rate Constant Calculation**
Consider the table of data collected for the reaction \( A \rightarrow \text{Products} \):
- **Calculate the rate constant for this reaction.** Show work.
The table below provides various measurements for the reaction over time, specifically the concentration of reactant \( [A] \) in molarity (M), the natural logarithm of the concentration \( \ln[A] \), and the inverse of the concentration \( 1/[A] \):
| Time (s) | [A] (M) | ln [A] | 1/[A] |
|----------|---------|--------|-------|
| 0 | 0.6 | -0.51083 | 1.666667 |
| 0.5 | 0.325 | -1.12393 | 3.076923 |
| 1 | 0.178 | -1.72597 | 5.617978 |
| 1.5 | 0.095 | -2.35388 | 10.52632 |
| 2 | 0.05 | -2.99573 | 20 |
| 2.5 | 0.028 | -3.57555 | 35.71429 |
| 3 | 0.015 | -4.19971 | 66.66667 |
| 3.5 | 0.008 | -4.82831 | 125 |
| 4 | 0.004 | -5.52146 | 250 |
### Explanation of the Table
- **Time (s):** The time at which the measurements were taken (in seconds).
- **[A] (M):** The concentration of reactant A in molarity.
- **ln[A]:** The natural logarithm of the concentration of reactant A.
- **1/[A]:** The inverse of the concentration of reactant A.
### Steps to Calculate the Rate Constant
1. Determine the order of the reaction by analyzing which plot (linear, \( \ln[A] \) vs. time, or \( 1/[A] \) vs. time) gives a straight line.
2. Use the slope of the appropriate plot to calculate the rate constant \( k \).
### Note:
You can identify the order of reaction by finding which relationship](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1243504b-5612-4510-ba6c-7b5ec7c70d6e%2F5f38d46f-8620-44b8-aa49-f0a46ee982d0%2F5s2k8i9_processed.png&w=3840&q=75)
Transcribed Image Text:**Reaction Rate Constant Calculation**
Consider the table of data collected for the reaction \( A \rightarrow \text{Products} \):
- **Calculate the rate constant for this reaction.** Show work.
The table below provides various measurements for the reaction over time, specifically the concentration of reactant \( [A] \) in molarity (M), the natural logarithm of the concentration \( \ln[A] \), and the inverse of the concentration \( 1/[A] \):
| Time (s) | [A] (M) | ln [A] | 1/[A] |
|----------|---------|--------|-------|
| 0 | 0.6 | -0.51083 | 1.666667 |
| 0.5 | 0.325 | -1.12393 | 3.076923 |
| 1 | 0.178 | -1.72597 | 5.617978 |
| 1.5 | 0.095 | -2.35388 | 10.52632 |
| 2 | 0.05 | -2.99573 | 20 |
| 2.5 | 0.028 | -3.57555 | 35.71429 |
| 3 | 0.015 | -4.19971 | 66.66667 |
| 3.5 | 0.008 | -4.82831 | 125 |
| 4 | 0.004 | -5.52146 | 250 |
### Explanation of the Table
- **Time (s):** The time at which the measurements were taken (in seconds).
- **[A] (M):** The concentration of reactant A in molarity.
- **ln[A]:** The natural logarithm of the concentration of reactant A.
- **1/[A]:** The inverse of the concentration of reactant A.
### Steps to Calculate the Rate Constant
1. Determine the order of the reaction by analyzing which plot (linear, \( \ln[A] \) vs. time, or \( 1/[A] \) vs. time) gives a straight line.
2. Use the slope of the appropriate plot to calculate the rate constant \( k \).
### Note:
You can identify the order of reaction by finding which relationship
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