A styrene$-$butadiene random copolymer rubber band was swollen in toluene. If the equilibrium

swollen volume increased by a factor or $5$ and $=0\mathrm{.}4,$ estimate the number of elastically

effective strands per volume $(\frac{v_e}{V}).$ Using $\frac{v_e}{V},$ determine the crosslink fraction. The molar

volume of toluene is $106c\frac{m^3}{m}ol,$ assume $=1,$ and that the repeat unit is comprised of a

styrene and a butadiene unit $(M_0=158\frac{g}{m}ol).$ Estimate the Young's modulus of the rubber

band in both the swollen and the dry state. $(1\mathrm{.}5$ point$)$