Final answer:
The half-life is the time needed for half of a reactant to be consumed, and it is influenced by activation energy. Without specific values or conditions, directly comparing the half-lives of Sicumyl peroxide and tert-butyl perbenzoate is not possible.
Step-by-step explanation:
The question asks for a comparison of half-life times for Sicumyl peroxide and tert-butyl perbenzoate and not the calculation of the activation energy. The half-life of a reaction is the time required for half the initial amount of a reactant to be consumed. When comparing the half-lives of two substances, we consider the reaction rates and the stability of the initiators at given temperatures.
The half-life of a reactant is significantly influenced by the activational energy barriers the molecules face. In general, a substance with a higher activation energy will have a longer half-life because the rate of reaction is slower, meaning it takes longer for half of the substance to decompose or react. Conversely, a substance with a lower activation energy will have a shorter half-life, as the reaction will proceed more quickly.
Without knowing the specific half-life values for Sicumyl peroxide and tert-butyl perbenzoate or the conditions under which these half-lives were determined, it is not possible to compare their half-lives directly. However, typically such data is found in experimental results or chemical databases. It's important to compare the half-life times at the same temperature, as the decomposition rates are temperature-dependent.