At $600K$ the reversible gas reaction has rate constants of $k_1=2\mathrm{.}22\frac{f{t}^3}{\text{l}\text{b}\text{m}\text{o}\text{l}*s}$ and $k_2=0\mathrm{.}032h^{-1}.$A plug flow reactor is fed with $333\mathrm{.}33\frac{f{t}^3}{\text{m}\text{i}\text{n}}$ of gas whose composition is $60\%$ bromine, $30\%C_2{H}_4$ and $10\%$ inerts, at $600K$ and $1\mathrm{.}5$ atm. Determine:

a$)$ The composition in equilibrium.

b$)$ The number of tubes that make up the reactor, if each tube is $1in$ of diameter and $20$ ft$.$ long, if $60\%$ conversion is achieved within the reactor.