The following data was collected for the reaction between ethoxide and methyl iodide T(°C) Rate (1/s) T (K) 1/T (1/K) In (rate) 168 273.15 0.00366 5.12 6 354 |279.15 0.00358 5.87 12 735 285.15 0.00351 6.60 18 1463 291.15 0.00343 7.29 24 3010 297.15 0.00337 8.01 30 6250 303.15 0.00330 8.74

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The following data was collected for the reaction between ethoxide and methyl iodide:

| T(°C) | Rate (1/s) | T (K)  | 1/T (1/K) | ln (rate) |
|-------|------------|--------|-----------|-----------|
| 0     | 168        | 273.15 | 0.00366   | 5.12      |
| 6     | 354        | 279.15 | 0.00358   | 5.87      |
| 12    | 735        | 285.15 | 0.00351   | 6.60      |
| 18    | 1463       | 291.15 | 0.00343   | 7.29      |
| 24    | 3010       | 297.15 | 0.00337   | 8.01      |
| 30    | 6250       | 303.15 | 0.00330   | 8.74      |

A plot of ln (rate) vs. 1/T using the above table was made and is shown below, with a linear regression line fitted to the data. Using the provided graph, estimate the activation energy (kJ/mol) of the reaction between ethoxide and methyl iodide. Enter your number using 2 decimal places without unit.

Gas constant is \( R = 8.3144598 \, \text{J} \cdot \text{mol}^{-1} \cdot \text{K}^{-1} \).

### Graph Description

The graph is a plot of ln(k) vs 1/T. It shows a linear relationship, as indicated by the line of best fit with the equation:

\[ y = -9930.5x + 41.445 \]

The R² value is 0.9992, indicating a very good fit to the data points. The x-axis represents 1/T (1/K), ranging from approximately 0.00330 to 0.00366. The y-axis represents ln(k), ranging from approximately 5.00 to 9.30. 

Each data point corresponds to a temperature from the table, demonstrating the rate of reaction across different temperatures. The graph helps visualize the linear relationship and calculate the activation energy using the slope of the fitted line.
Transcribed Image Text:The following data was collected for the reaction between ethoxide and methyl iodide: | T(°C) | Rate (1/s) | T (K) | 1/T (1/K) | ln (rate) | |-------|------------|--------|-----------|-----------| | 0 | 168 | 273.15 | 0.00366 | 5.12 | | 6 | 354 | 279.15 | 0.00358 | 5.87 | | 12 | 735 | 285.15 | 0.00351 | 6.60 | | 18 | 1463 | 291.15 | 0.00343 | 7.29 | | 24 | 3010 | 297.15 | 0.00337 | 8.01 | | 30 | 6250 | 303.15 | 0.00330 | 8.74 | A plot of ln (rate) vs. 1/T using the above table was made and is shown below, with a linear regression line fitted to the data. Using the provided graph, estimate the activation energy (kJ/mol) of the reaction between ethoxide and methyl iodide. Enter your number using 2 decimal places without unit. Gas constant is \( R = 8.3144598 \, \text{J} \cdot \text{mol}^{-1} \cdot \text{K}^{-1} \). ### Graph Description The graph is a plot of ln(k) vs 1/T. It shows a linear relationship, as indicated by the line of best fit with the equation: \[ y = -9930.5x + 41.445 \] The R² value is 0.9992, indicating a very good fit to the data points. The x-axis represents 1/T (1/K), ranging from approximately 0.00330 to 0.00366. The y-axis represents ln(k), ranging from approximately 5.00 to 9.30. Each data point corresponds to a temperature from the table, demonstrating the rate of reaction across different temperatures. The graph helps visualize the linear relationship and calculate the activation energy using the slope of the fitted line.
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