A calorimetric analysis of a reactive system reveals the following results:

Detected onset temperature: \(350 \mathrm{~K}\)

Final temperature: \(450 \mathrm{~K}\)

Assuming a reaction order of 1 , a plot of \(\ln \left[\frac{d T / d t}{T_{F}-T}ight]\) versus \(\left(T-T_{o}ight) / T\) produces a straight line with slope of 30 and intercept of -10.0 . The \(R^{2}\) fit for this straight line is 0.99 .

a. What is the value of the dimensionless adiabatic temperature rise, \(B\) ?

b. What is the value of the dimensionless parameter \(\Gamma\) ?

c. What is the value of the rate coefficient at the detected onset temperature, \(k\left(T_{o}ight)\) ?

d. What is the activation energy, in \(\mathrm{kJ} / \mathrm{mol}\), and the pre-exponential factor \(A\), in \(\mathrm{s}^{-1}\) ?

e. At what temperature, in \(\mathrm{K}\), does the maximum self-heat rate occur?