b$)$ The thermal decomposition of dimethyl ether is to be carried out in an isothermal reactor at $500C.$ The reactor is operated at a pressure of $1$ atm $.$ The reaction of the process is

$(C{H}_3{)}_2{O}_{(g)}C{H}_{4(g)}+H_{2(g)}+C{O}_{(g)}$

$150mo\frac{l}{h}$ of dimethyl ether is entering the reactor at $100C$ and the product gas exits at $500C$ contains $120mo\frac{l}{h}$ of methane $(C{H}_4).$ Given heat of formation of dimethyl ether is $-184\mathrm{.}1k\frac{J}{m}ol$ and heat capacity, Cp of dimethyl ether is

$Cp[\frac{J}{\text{m}\text{o}\text{l}\text{.}K}]=26\mathrm{.}86+0\mathrm{.}1659T-4\mathrm{.}179{10}^{-5}{T}^2$

i$)$ Draw and label this process.

$(2$ marks$)$

ii$)$ Compute the percent conversion of dimethyl ether.

$(2$ marks$)$

iii$)$ Construct an inlet and outlet enthalpy table using the reference state: $C(s),O2(g),H2(g)$ at $25C,$ and $1$ atm $.$

$(3$ marks$)$

iv$)$ Evaluate the rate at which heat $(kW)$ must be transferred to or from the reactor by using the heat of formation method.

$(12$ marks$)$