Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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I need help finding the rate law for each graph. The first graph is in order zero, the middle is in order first and the last is in order second. 

### Analysis of Absorbance vs Time in a Chemical Reaction

This image showcases three different graphical analyses of absorbance (Abs) against time, as part of a kinetic study in a chemical reaction. Each graph provides insights into the reaction order and helps to understand the relationship between absorbance and time.

#### Graph 1: Abs vs Time Trial 1
- **Description**: This graph plots direct absorbance against time.
- **Equation**: The line of best fit is provided by the equation \( y = -0.0012x + 0.3231 \).
- **R-squared Value**: \( R^2 = 0.9771 \), indicating a strong linear correlation.
- **Interpretation**: The negative slope suggests a decrease in absorbance over time.

#### Graph 2: Ln(Abs) vs Time Trial 1
- **Description**: This plot presents the natural logarithm of absorbance against time.
- **Equation**: The linear relationship is described by \( y = -0.0095x - 1.0624 \).
- **R-squared Value**: \( R^2 = 0.9993 \), showing an excellent fit.
- **Interpretation**: The ln(absorbance) plot suggests a first-order reaction, given the strong linearity and the high R-squared value.

#### Graph 3: 1/Abs vs Time Trial 1
- **Description**: Here, the inverse of absorbance is plotted against time.
- **Equation**: The best fit line is represented by \( y = 0.0297x + 2.4262 \).
- **R-squared Value**: \( R^2 = 0.989 \), also indicating a strong linear fit.
- **Interpretation**: This graph suggests a second-order reaction based on the linearity observed when plotting 1/absorbance.

### Conclusion
The analysis of these graphs supports kinetic modeling of the reaction. The Ln(Abs) vs Time graph, with its highly linear fit, suggests a first-order reaction. This detailed graphical analysis aids in understanding underlying reaction dynamics and is essential for predicting reaction behavior over time.
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Transcribed Image Text:### Analysis of Absorbance vs Time in a Chemical Reaction This image showcases three different graphical analyses of absorbance (Abs) against time, as part of a kinetic study in a chemical reaction. Each graph provides insights into the reaction order and helps to understand the relationship between absorbance and time. #### Graph 1: Abs vs Time Trial 1 - **Description**: This graph plots direct absorbance against time. - **Equation**: The line of best fit is provided by the equation \( y = -0.0012x + 0.3231 \). - **R-squared Value**: \( R^2 = 0.9771 \), indicating a strong linear correlation. - **Interpretation**: The negative slope suggests a decrease in absorbance over time. #### Graph 2: Ln(Abs) vs Time Trial 1 - **Description**: This plot presents the natural logarithm of absorbance against time. - **Equation**: The linear relationship is described by \( y = -0.0095x - 1.0624 \). - **R-squared Value**: \( R^2 = 0.9993 \), showing an excellent fit. - **Interpretation**: The ln(absorbance) plot suggests a first-order reaction, given the strong linearity and the high R-squared value. #### Graph 3: 1/Abs vs Time Trial 1 - **Description**: Here, the inverse of absorbance is plotted against time. - **Equation**: The best fit line is represented by \( y = 0.0297x + 2.4262 \). - **R-squared Value**: \( R^2 = 0.989 \), also indicating a strong linear fit. - **Interpretation**: This graph suggests a second-order reaction based on the linearity observed when plotting 1/absorbance. ### Conclusion The analysis of these graphs supports kinetic modeling of the reaction. The Ln(Abs) vs Time graph, with its highly linear fit, suggests a first-order reaction. This detailed graphical analysis aids in understanding underlying reaction dynamics and is essential for predicting reaction behavior over time.
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