Question $3($Total: $32$ marks$)$

Polylactic acid, $(C_3{H}_4{O}_2{)}_n,$ is widely used in food packaging and medical applications due to its

biocompatibility, and good mechanical and optical properties. A recycling company runs the

following process to valorise the waste PLA:

Stage $1$: thermal decomposition of PLA at $400C$ to $C{O}_2$ and $C_2{H}_4.C{O}_2$ released is captured by

CaO to form limestone which can be used as a construction material.

Step $2$: $C_2{H}_4$ is cracked to $H_2$ and solid carbon at $800C.$ The latter can be used as an additive in

tyre production.

Calculate the heat requirement for the two reactors $($excluding the $C{O}_2$ capture process$)$ for

treating $1$ ton$/$day of waste PLA with a feeding temperature of $25C,$ assuming complete reaction

takes place in both reactors operated at $1$atm, and products exit the reactors at the reaction

temperatures.

Data:

${?}^i{H}_{2}O($v$)$ as the combustion product; ${?}^{\text{i}\text{i}\text{p}\text{e}\text{r}}$ mol of monomer

Melting point of PLA $=180C$; Heat of fusion $=6\mathrm{.}55k\frac{J}{m}ol$ monomer