Dibutyl phthalate $($DBP$),$ a plasticizer, has a potential market of $12$millionl$\frac{b}{y}r$ and is to be produced by reaction of n$-$butanol with monobutyl phthalate $($MBP$).$ The reaction follows an elementary rate law and is catalyzed by $H_{2}S{O}_4.$ A stream containing MBP and butanol is to be mixed with $H_{2}S{O}_4$ the catalyst immediately before the stream enters the reactor. The concentration of MBP in the stream enters in the reactor is $0\mathrm{.}2$lbmo$\frac{l}{f}{t}^3,$ and the molar feed rate of butanol is five times that of MBP$.$ The specific reaction rate at $100F$ is $1\mathrm{.}2f\frac{t^3}{l}bmo{l}^{**}h.$ There is a $1000$ gallon CSTR and associated peripheral equipment available for use on this project for $30$ days a year $($operating $24$ h$/$dav$).$

a$)$ Determine the exit conversion in the available $1000-$gallon reactor if you were to produce $33\%$ of the share $($i$.$e$.,4$ million $l\frac{b}{y}r)$ of the predicted market.

b$)$ How might you increase the conversion for the same $F_{A_0}?$ For example, what conversion would be achieved if a second $1000-$gal CSTR were placed either in series or in parallel with the CSTR$?$

c$)$ For the same temperature as part $($a$),$ what CSTR volume would be necessary to achieve a conversion of $85\%$ for a molar feed rate of MBP of $1$lbmo$\frac{l}{m}in?$

d$)$ How would your results for parts $($a$)$ and $($b$)$ change if the temperature were raised to $150F$ where $k$ is now $5\mathrm{.}0f\frac{t^3}{l}b$ mol$*$h but the reaction is reversible with $Kc=0\mathrm{.}3?$

e$)$ What generalizations can you make about what you learned in this problem that would apply to other problems?

f$)$ Write a question that requires critical thinking and then explain why your question requires critical thinking.