Domain: Polymer kinetics

In a kinetic study of styrene polymerization, an organic peroxide was employed as a thermal initiator. Under otherwise identical conditions, the time required to achieve 20% monomer conversion was observed to be 70 minutes at 60\(°C\) and 38 minutes at 70\(°C\). In contrast, photopolymerization of styrene furnished 20% conversion in 18 minutes at 60\(°C\) and 16 minutes at 70\(°C\). Given that the peroxide half-life at 60\(°C\) is 153 hours, calculate its half-life at 90\(°C\).

Grading rubric:
criterion: Correctly defines the overall thermal activation energy as the sum of propagation, half-decomposition, and half-termination energies (\(E_p - E_t/2 + E_d/2\)). 
weight: 10
criterion: Correctly justifies the photochemical activation energy formulation (\(E_p - E_t/2\)) by explicitly setting the initiation activation energy to zero.
weight: 10
criterion: Correctly determines the apparent activation parameter for the thermal polymerization (\(E_{RP(therm)}/R\)) to be within the precise range of 6,970 K to 6,985 K.
weight: 20
criterion: Correctly determines the apparent activation parameter for the photopolymerization (\(E_{RP(photo)}/R\)) to be within the precise range of 1,340 K to 1,350 K.
weight: 20
criterion: Correctly calculates the isolated decomposition activation parameter (\(E_d/R\)) to be within the precise range of 11,260 K to 11,270 K.
weight: 20
criterion: Correctly reports the final predicted half-life at 90°C to be within the precise range of 9.35 hours to 9.45 hours.
weight: 20

Answer:
approximately 9.4 h