Domain: Polymer kinetics

A solution-phase polymerization of a monomer (M) was carried out using a peroxide initiator (P) at two different temperatures under identical initial concentrations of (M) and (P). The experimental data collected for the conversion of M after 60 minutes revealed the following:Run #1 (50 °C): 20% conversion of M; initial polymer molecular weight = 100,000.Run #2 (65 °C): 58% conversion of M; initial polymer molecular weight = 60,000.Calculate the energy of activation (\(E_d\)) for the thermal decomposition of P.  (Assume termination by coupling)

Grading rubric:
criterion: Correctly explicitly applies the Steady State Approximation (SSA) to equate initiation and termination rates (\(R_i = R_t\)).
weight: 20
criterion: Correctly identifies that the number average molecular weight (\(\overline{M}_n\)) is inversely proportional to the square root of the initiator concentration (\([I]^{-1/2}\)) in the derivation of the governing equation. 
weight: 10
criterion: Correctly explicitly includes the factor of 2 in the termination rate equation (\(2k_t\)) specifically for the termination by coupling mechanism.
weight: 20
criterion: Correctly reports the intermediate kinetic parameter value at \(323 \text{ K}\) as \(2.231 \times 10^{-6}\).
weight: 20
criterion: Correctly reports the intermediate kinetic parameter value at \(338 \text{ K}\) as \(1.446 \times 10^{-5}\).
weight: 20
criterion: Reports the final activation energy (\(E_d\)) within the range of \(112.5 \text{ kJ mol}^{-1}\) to \(113.5 \text{ kJ mol}^{-1}\).
weight: 10

Answer:
approximately 113 kJ mol^-1