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 activation energy for the reaction, we need to calculate the values of ln(k) and 1/T.
To calculate ln(k), take the natural logarithm of the given values of k.
For example, if we take the first temperature (290°C) and k value of 2.52*10^-5, we can calculate ln(k) as follows:
ln(2.52*10^-5) ≈ -10.84
Similarly, calculate ln(k) for the other two temperatures.
To calculate 1/T, convert the temperature from Celsius to Kelvin by adding 273.15 to each value. Then take the reciprocal of the resulting temperature.
For example, for the first temperature (290°C), convert it to Kelvin:
290°C + 273.15 ≈ 563.15K
Now, calculate 1/T:
1/563.15 ≈ 0.001778
Similarly, calculate 1/T for the other two temperatures.
Now that we have the values for ln(k) and 1/T, we can plot a graph of ln(k) versus 1/T on a graphing calculator.
Once the graph is plotted, we can use the graphing calculator's methods to determine the activation energy. One common method is to perform linear regression on the data points to obtain the equation of the line. The activation energy (Ea) can be obtained by using the Arrhenius equation:
ln(k) = -Ea/RT + ln(A)
Here, R is the gas constant (8.314 J/K·mol) and A is the pre-exponential factor.
By comparing the equation of the line obtained from linear regression with the Arrhenius equation, we can determine the value of Ea.
Please note that the specific steps for using a graphing calculator may vary depending on the model and software used. Make sure to consult the user manual or online resources specific to your graphing calculator for detailed instructions on how to perform linear regression and calculate the activation energy.