$($Multiple reactions with heat effects$).$ Styrene can be produced from ethylbenzene by the following reaction: ethylbenzene $+$ styrene$+$H$2(1)$ However, several irreversible side reactions also occur: ethylbenzene $->$ benzene $+$ ethylene $(2)$ ethylbenzene$+$H$,->$ toluene $+$ methane $(3)[$J$.$ Snyder and B$.$ Subramaniam, Chem. Eng. Sci., $49,5585(1994)].$ Ethylbenzene is fed at a rate of $0\mathrm{.}00344$ kmol$/$s to a $10\mathrm{.}0-$m$$ PFR reactor along with inert steam at a total pressure of $2\mathrm{.}4$ atm. The steam$/$ethylbenzene molar ratio is initially $[$i$.$e$.,$ parts $($a$)$ to $($c$)]14\mathrm{.}5$:$1$ but can be varied. Given the following data, find the exiting molar flow rates of styrene, benzene, and toluene for the following inlet temperatures when the reactor is operated adiabatically. $($a$)$ To $=800$ K $($b$)$ To $=930$ K $($c$)$ To $=1100$ K $($d$)$ Find the ideal inlet temperature for the production of styrene for a steam$/$ethyl benzene ratio of $58$:$1.($Hint: Plot the molar flow rate of styrene versus To$.$ Explain why your curve looks the way it does$).($e$)$ Find the ideal steam$/$ethyl benzene ratio for the production of styrene at $900$ K$.($Hint: See part $($d$)$ Additional information: Heat capacity at $900$ K Methane: $68$ J$/$mol$.$K Styrene: $273$ J$/$mol$.$K Ethylene: $90$ J$/$mol$.$K Ethylbenzene: $299$ J$/$mol$.$K Benzene: $201$ J$/$mol$.$K Hydrogen: $30$ J$/$mol$.$K Toluene: $249$ J$/$mol$.$K Steam: $40$ J$/$mol$.$K p$=2137$ kg$/$m$^2$ of pellet $0=0\mathrm{.}4=$ AH$1$s $=118,000$ kJ$/$kmol ethylbenzene AH$,2$E $105,200$ kJ$/$kmol ethylbenzene $=$ AH$13$E $=-53,900$ kJ$/$kmol ethylbenzene $=$ KI $=$exp, b$.$ bz $)[$Tb$)$ T $+$b$,$ h$($T$)+[$b$.$ T$+)$ T$+$bo$]$I$\}$ atm bi $=-17\mathrm{.}34$ b$4=-2\mathrm{.}314$x$10-10$ b$2=-1\mathrm{.}302$x$104$ bs $=1\mathrm{.}302$x$10-6=$ b$3=5\mathrm{.}051$ bo$=-4\mathrm{.}931$x$10-3=$ The kinetic rate laws for the formation of styrene $($St$),$ benzene $($B$),$ and toluene $($T$),$ respectively, are as follows. $10,925(-0\mathrm{.}08511.=$ P$(1-0)$ exp $-0\mathrm{.}08539-$ P: PH$2($kmol$/$m$$s$)$ T $().$ PEB $25,000138=$ P$(1-0)$ exp $13\mathrm{.}2392-$ T $($PEB$)($kmol$/$m$$s$)17=$ P$(1-6)$ exp$(0\mathrm{.}2961-411,000($PEB PH$2)$ T $($kmol$/$m$$s$)($f$)$ The temperature T is in Kelvin. $[$Hint: this is a problem with multiple reactions. Do not use design equation $($i$.$e$.$ do not use conversion$).$ Solve for the flow rates of each species $($i$.$e$.$ system of ordinary differential equations$)]$ can you write the matlab