How did my teacher get the 1st order row and the ln k row The table provided contains data for the first-order decomposition of penicillin, as referenced from Swintosky et al.| Temp (°C) | Temp (K) | 1/Temp (1/K) | 1st-order k (hr⁻¹) | ln k ||-----------|----------|--------------|---------------------|--------|| 54 | 327 | 3.06 x 10⁻³ | 0.119 | -2.129 || 43 | 316 | 3.16 x 10⁻³ | 0.0403 | -3.211 || 37 | 310 | 3.23 x 10⁻³ | 0.0216 | -3.835 |The task is to plot the results and calculate the activation energy (Eₐ) and the Arrhenius factor (A).The graph is a plot of ln k versus 1/T (K), showing a straight line that represents the relationship described by the Arrhenius equation:\[ \ln k = \frac{-E_a}{RT} + \ln A \]**Graph Details:**- The x-axis represents \( 1/T \) in units of \( \text{K}^{-1} \), ranging from approximately 0.003 to 0.00325.- The y-axis represents \( \ln k \), ranging from -4 to 0.- The plot shows a linear trend with a line fitted through the data points, suggesting that the relationship follows the expected linear form of the Arrhenius equation.**Equation of the Line:**\[ y = -10820x + 28.987 \]\[ R^2 = 1 \]The equation suggests a perfect linear fit, signified by \( R^2 = 1 \). The slope of the line (-10820) can be used to calculate the activation energy \( E_a \), and the intercept (28.987) corresponds to \( \ln A \).

Arhenius Equation: ln k =-EaRT +ln A

3. The following data for the first-order decomposition of penicillin are obtained from Swintosky et al. Temp (°C) Тemp (К) 1/Тemp (1/K) 1st-order k (hr') In k 54 327 3.06 х 10-3 0.119 - 2.129 43 316 3.16 x 10-3 0.0403 - 3.211 37 310 3.23 х 10-3 0.0216 - 3.835 a) Plot the results and calculate the activation energy (E,) and the Arrhenius factor (A). 1/T (K)

3. The following data for the first-order decomposition of penicillin are obtained from Swintosky et al. Temp (°C) Тemp (К) 1/Тemp (1/K) 1st-order k (hr') In k 54 327 3.06 х 10-3 0.119 - 2.129 43 316 3.16 x 10-3 0.0403 - 3.211 37 310 3.23 х 10-3 0.0216 - 3.835 a) Plot the results and calculate the activation energy (E,) and the Arrhenius factor (A). 1/T (K)

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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