The ethanol dehydration reaction in Figure $1$ is carried out with the feed entering at $300C.$ The feed contains $90$ mole$\%$ ethanol and the balance acetaldehyde and enters the reactor at a rate of $150mo\frac{l}{s}.$ To keep the temperature from dropping too far $($the reaction is endothermic$)$ and thereby decreasing reaction rate to an unacceptably low level, heat is transferred to the reactor. When heat addition $(Q)$ is $2440kW,$ the outlet temperature is $253C.$ Calculate the fractional conversion of ethanol achieved in the reactor.

Dr$.$ Richards of the Montana State University Department of Chemical and Biological Engineering has hired you to solve this problem using a python code and using Excel.

Here is what else you need to know...

This problem is solved by writing a material balance on two of the atoms $($she suggests carbon and hydrogen$)$ and an energy balance on the reactor. A material balance is simply a mathematical statement that all the hydrogen $($for example$)$ going into the process has come out again. The following hydrogen balance is shown as an example:

Hydrogen in inlet $C_2{H}_{5}OH+$ Hydrogen in inlet $C{H}_3$CHO

$=$ Hydrogen in outlet $C_2{H}_{5}OH+$ Hydrogen in outlet $C{H}_3$CHO

Hydrogen in outlet $H_2$

$0\mathrm{.}9**150\frac{\text{m}\text{o}\text{l}\text{e}\text{s}}{S}**6\frac{H}{\text{m}\text{o}\text{l}\text{e}}+0\mathrm{.}1**150\frac{\text{m}\text{o}\text{l}\text{e}\text{s}}{s}**4\frac{H}{\text{m}\text{o}\text{l}\text{e}}=6n_1^{}+4n_2^{}+2n_3^{}$

$6n_1^{}+4n_2^{}+2n_3^{}=435$mol$\frac{H}{s}$

The equation above is your first linear equation, now write a linear equation that describes the material balance of carbon.

Write a linear equation that describes the energy balance, using Table $1$ and the same concept that energy in must equal energy out.

$Q+{\displaystyle \underset{?}{\overset{?}{}}}{n}_{in}$widehat$(H_{in})={\displaystyle \underset{?}{\overset{?}{}}}{n}_{\text{o}\text{u}\text{t}}$widehat$(H_{\text{o}\text{u}\text{t}})$

Table $1.$ Substance Enthalpies $($accounting for difference in stream temperatures and changes of state$)$

$\backslash$table$[[$Substance$,\backslash$table$[[n_{in}$