X - products plot of In[ X ] vs. time -0.2 -0.4 -0.6 y = -0.2967x-0.1621 -0.8 -1.2 -1.4 -1.6 -1.8 time / minutes [X] was measured over time, and the plot shown above was constructed from that data. The plot is linear (R² = 0.999), with the slope = -0.2967. .... If this reaction has a constant “half-life", what is the half-life ? minutes [x ]u
X - products plot of In[ X ] vs. time -0.2 -0.4 -0.6 y = -0.2967x-0.1621 -0.8 -1.2 -1.4 -1.6 -1.8 time / minutes [X] was measured over time, and the plot shown above was constructed from that data. The plot is linear (R² = 0.999), with the slope = -0.2967. .... If this reaction has a constant “half-life", what is the half-life ? minutes [x ]u
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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![### Reaction Kinetics: Understanding the Decomposition of X
#### Reaction Overview:
\[ X \rightarrow \text{products} \]
#### Data Analysis:
A time-dependent measurement of the concentration of \( [X] \) was conducted. The corresponding data was used to create the linear plot as shown below.
#### Graph Description:
**Title:** plot of ln([X]) vs. time
**X-axis:** time / minutes (ranging from 0 to 6)
**Y-axis:** ln([X]) (values ranging from -1.8 to -0.2)
**Line Equation:** \( y = -0.2967x - 0.1621 \)
The plot is linear, characterized by a high correlation coefficient of \( R^2 = 0.999 \), indicating a strong linear relationship between the natural logarithm of the concentration of \( [X] \) and time. The slope of the line is -0.2967.
![Graph of ln([X]) vs. time](#)
- **X-axis (time / minutes):** The horizontal axis represents the time in minutes, with equally spaced intervals.
- **Y-axis (ln([X])):** The vertical axis denotes the natural logarithm of the concentration of \( [X] \).
- **Trendline and Equation:** A trendline is plotted to show the linear relationship between the ln([X]) and time, with the equation \( y = -0.2967x - 0.1621 \).
#### Calculation of Reaction Half-Life:
The half-life of a reaction can be determined from the slope of the linear plot.
**Question:**
If this reaction has a constant "half-life", what is the half-life?
\[ \text{Half-life} = \_\_\_\_\_\_\_\_\_\_ \text{ minutes} \]
### Further Instructions:
To derive the half-life from the slope of the plot above, use the following formula:
\[ t_{1/2} = \frac{\ln(2)}{-\text{slope}} \]
Apply this to find the specific half-life time for the reaction depicted.
---
For further discussion and detailed step-by-step solutions, please refer to the relevant sections in your course materials or reach out to your instructor.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f7442e5-ed1a-4154-ba5d-4813abad6cff%2Fc86515ee-aacf-4492-a9f4-c615d91d3145%2F51i5m6m.png&w=3840&q=75)
Transcribed Image Text:### Reaction Kinetics: Understanding the Decomposition of X
#### Reaction Overview:
\[ X \rightarrow \text{products} \]
#### Data Analysis:
A time-dependent measurement of the concentration of \( [X] \) was conducted. The corresponding data was used to create the linear plot as shown below.
#### Graph Description:
**Title:** plot of ln([X]) vs. time
**X-axis:** time / minutes (ranging from 0 to 6)
**Y-axis:** ln([X]) (values ranging from -1.8 to -0.2)
**Line Equation:** \( y = -0.2967x - 0.1621 \)
The plot is linear, characterized by a high correlation coefficient of \( R^2 = 0.999 \), indicating a strong linear relationship between the natural logarithm of the concentration of \( [X] \) and time. The slope of the line is -0.2967.
![Graph of ln([X]) vs. time](#)
- **X-axis (time / minutes):** The horizontal axis represents the time in minutes, with equally spaced intervals.
- **Y-axis (ln([X])):** The vertical axis denotes the natural logarithm of the concentration of \( [X] \).
- **Trendline and Equation:** A trendline is plotted to show the linear relationship between the ln([X]) and time, with the equation \( y = -0.2967x - 0.1621 \).
#### Calculation of Reaction Half-Life:
The half-life of a reaction can be determined from the slope of the linear plot.
**Question:**
If this reaction has a constant "half-life", what is the half-life?
\[ \text{Half-life} = \_\_\_\_\_\_\_\_\_\_ \text{ minutes} \]
### Further Instructions:
To derive the half-life from the slope of the plot above, use the following formula:
\[ t_{1/2} = \frac{\ln(2)}{-\text{slope}} \]
Apply this to find the specific half-life time for the reaction depicted.
---
For further discussion and detailed step-by-step solutions, please refer to the relevant sections in your course materials or reach out to your instructor.
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