The following data is collected for the decomposition of methy isonitrile at various tempertures:
Temp.(C)---{k(/s)} --- lnk---1/T
290--- {2.52*10^-5}--- ?--- ?
299--- {5.25*10^-5}--- ? --- ?
330--- {6.30*10^-4}--- ?--- ?
Complete the table above and, using your graphing calculator determine the value of the activation energy for this reaction.
To complete the table and determine the value of the activation energy for the reaction, we need to calculate the values of lnk (natural logarithm of k) and 1/T (reciprocal of temperature).
First, let's calculate lnk for each temperature using the given values of k:
Temp.(C)---{k(/s)}---lnk---1/T
290--- {2.52*10^-5}--- ?--- ?
299--- {5.25*10^-5}--- ?--- ?
330--- {6.30*10^-4}--- ?--- ?
To find lnk, you can take the natural logarithm (ln) of the given values of k. In this case, you can use your calculator's logarithm function or a scientific calculator with a natural logarithm button. Here are the calculations:
ln(2.52*10^-5) = -10.36
ln(5.25*10^-5) = -9.58
ln(6.30*10^-4) = -7.36
Now, let's calculate 1/T. This requires converting the temperatures from Celsius to Kelvin. To convert Celsius to Kelvin, add 273.15 to the given temperatures:
Temp.(C)---{k(/s)}---lnk---1/T
290--- {2.52*10^-5}--- -10.36--- 1/563.15
299--- {5.25*10^-5}--- -9.58--- 1/572.15
330--- {6.30*10^-4}--- -7.36--- 1/603.15
To calculate 1/T, divide 1 by the Kelvin temperature. Here are the calculations:
1/563.15 = 0.001775
1/572.15 = 0.001747
1/603.15 = 0.001657
Now we can complete the table:
Temp.(C)---{k(/s)}---lnk---1/T
290--- {2.52*10^-5}--- -10.36--- 0.001775
299--- {5.25*10^-5}--- -9.58--- 0.001747
330--- {6.30*10^-4}--- -7.36--- 0.001657
Now, to determine the value of the activation energy, we can plot the natural logarithm of k (lnk) against 1/T and perform a linear regression analysis using a graphing calculator.
1. Enter the values of lnk (vertical axis) and 1/T (horizontal axis) into the graphing calculator.
2. Plot the points on the graphing calculator to create a scatter plot.
3. Use the linear regression feature of the graphing calculator to calculate the equation of the line that best fits the data points.
4. The slope of the line will represent the value of the activation energy (Ea).
Please note that the exact steps to perform a linear regression analysis may vary depending on the model of your graphing calculator. Refer to the user manual or documentation for your specific calculator model for detailed instructions on how to perform a linear regression analysis.
Once you have obtained the equation of the line and its slope, the slope will represent the value of the activation energy for the reaction. This value can then be used to complete the table and answer the question.