Neco Model Questions Vol1 2017 Chemistry Question 43

In the free‑radical polymerisation of methyl methacrylate (MMA, $M=100\,$g mol$^{-1}$) the following kinetic data are given at 25 °C: propagation rate constant $k_{p}=1.0\times10^{4}\,$L mol$^{-1}$ s$^{-1}$, termination rate constant $k_{t}=5.0\times10^{7}\,$L mol$^{-1}$ s$^{-1}$, initiator decomposition constant $k_{d}=1.0\times10^{-5}\,$s$^{-1}$, initiator efficiency $f=0.6$, initiator concentration $[I]=1.0\times10^{-4}\,$mol L$^{-1}$, monomer concentration $[M]=2.0\,$mol L$^{-1}$, solvent concentration $[S]=10\,$mol L$^{-1}$ and chain‑transfer constant to solvent $C_{s}=0.02$. Assuming steady‑state, (a) calculate the number‑average degree of polymerisation $DP_{n}$ using $DP_{n}=\frac{k_{p}[M]}{2k_{t}[R\cdot]+k_{p}C_{s}[S]}$, where $[R\cdot]=\sqrt{\frac{2fk_{d}[I]}{k_{t}}}$. (b) Determine the number‑average molecular weight $M_{n}$. (c) If the initiator concentration is doubled, how does $DP_{n}$ change?