For the bulk polymerization of methyl methacrylate at $77$oC with AIBN as yhe initiator, the initial rate of polymerization was $1\mathrm{.}94$ x $10^-4$ mol$/$l$-$s$.[$M$]$ and $[$I$]$ were $9$ mol$/$l and $2\mathrm{.}35$ x$10^-4$ mol$/$l respectively. To reduce the heat transfer problems the polymerization was repeated in a solution of benzene by the addition of $4\mathrm{.}5$ litre of benzene with $[$I$]=2\mathrm{.}11$ x $10^-4$ l$/$mol$.$ Assuming that the rate constants are the same for both the bulk and solution polymerization, calculate the rate of solution polymerization of methyl methacrylate.

$2$b$.)$ Water$-$soluble polymers have a wide range of applications across various industries. List three applications and highlight their advantages.