Neco Model Questions Vol1 2022 Chemistry Question 40

In a free‑radical polymerisation, the initiator decomposes with a first‑order rate constant \(k_d = 1.0\times10^{-5}\ \text{s}^{-1}\). The initial initiator concentration is \([I_0]=0.01\ \text{mol L}^{-1}\) and the efficiency factor is \(f = 0.6\). The propagation rate constant is \(k_p = 500\ \text{L mol}^{-1}\text{s}^{-1}\) and termination occurs by combination with \(k_t = 1.0\times10^{7}\ \text{L mol}^{-1}\text{s}^{-1}\). The monomer concentration at the start is \([M_0]=2.0\ \text{mol L}^{-1}\). Assuming a steady‑state radical concentration, the radical concentration is given by \([R^{\bullet}] = \sqrt{\dfrac{2 f k_d [I_0]}{k_t}}\). Using the integrated rate law \(\dfrac{d[M]}{dt} = -k_p [M][R^{\bullet}]\), calculate the time required to reach 90 % conversion (i.e., \([M]=0.1[M_0]\)). Express your answer in seconds (to two significant figures).