Styrene $(1kg)$ is polymerized at $20C$ in a $1L$ solution of dichloroethane by initiation with $4**{10}^{-4}MBC\frac{l_3}{H_2}O.$ The polymerization proceeds with a rate constant of $7\mathrm{.}6Lmo{l}^{-1}{s}^{-1}.$ Chain transfer occurs to monomer with a rate constant of $0\mathrm{.}12Lmo{l}^{-1}{s}^{-1}.$ Also, spontaneous termination $($rate constant $=4\mathrm{.}9**{10}^{-2}{s}^{-1})$ and combination with counter ion $($rate constant $=6\mathrm{.}7**{10}^{-3}{s}^{-1})$ occurs. Calculate the number$-$average molecular weight of the final polymer with and without the addition of isopropylbenzene $(0\mathrm{.}3M,k_{tr,\text{i}\text{s}\text{o}}=0\mathrm{.}34(L)mo{l}^{-1}{s}^{-1}).$