Final answer:
The question requires calculating the activation energy for dicumyl peroxide and tert-butyl perbenzoate using the provided half-life times.
Step-by-step explanation:
The student is interested in calculating the activation energy for two different initiators (dicumyl peroxide and tert-butyl perbenzoate) based on their half-life times at different temperatures. To find the activation energy, we usually use the Arrhenius equation, which relates the rate constant k of a reaction to the temperature T, the activation energy Ea, and the pre-exponential factor A, also known as the frequency factor.
The equation is given by k = A * e(-Ea/RT), where R is the ideal gas constant (8.314 J/mol·K) and T is the temperature in Kelvin.
To determine the activation energies of the reactions, the rate constants need to be determined first, which can be done through the use of the half-life data provided in the question. It is known that for a first-order reaction, the half-life t1/2 is related to the rate constant k by t1/2 = ln(2) / k.
Once k is found for multiple temperatures, a plot of ln(k) versus 1/T (in K-1) can be used to find the activation energy. The slope of this plot will be equal to -Ea/R.