$(25$ pts$)$ In organic chemistry, alcohols undergo oxidation to yield aldehydes, which in turn can undergo

further oxidation to produce the corresponding carboxylic acids. In the presence of strong base like

potassium hydroxide $(KOH),$ two moles of aldehydes can undergo a reaction with the base yielding one

mole of alcohol and one mole of carboxylate. This reaction is known as the Cannizzaro Reaction. It is

worth noting that from an engineering standpoint, this reaction is generally undesired due to the higher

value typically associated with aldehydes compared to the resultant alcohols and carboxylic acids,

although this aspect will be overlooked for the purpose of this problem.

You are going to design a flow reactor to convert benzaldehyde $($A$)$ into benzyl alcohol $($B$)$ and benzoic

acid $($C$).$

$2A+BC+D$

The reaction kinetics

established as second order $\text{'}$

respect to the aldehyde spe

and first order with respect tc

strong base species $($i$.$e$.,-1$

$k{C}_A^2{C}_B).$ For the sake

simplicity, the reaction

considered irreversible in

problem.

To estimate the rate constant of the reaction, a lab$-$scale steady$-$state isothermal ideal CSTR setup was

established as above. $0\mathrm{.}10M$ benzaldehyde liquid$-$phase solution and $1\mathrm{.}0$MKOH liquid$-$phase solution

are supplied to the mixer, with the same volumetric flow rate of $1\mathrm{.}0m\frac{L}{s}$ respectively, and the mixed

reactants $(2\mathrm{.}0m\frac{L}{s})$ were fed to the $500mL$ ideal isothermal CSTR running steady$-$state at $60C.$ No

reaction was observed in the region between the mixer and the reactor.

$($a$)(6$ pts$)$ Establish the stoichiometric table for this setup.

$($b$)(7pts)$ The outlet concentration of benzaldehyde was determined to be $7\mathrm{.}5{10}^{-3}mo\frac{l}{L}.$ What are

$($i$)$ the conversion of benzaldehyde $(x),($ii$)$ the rate of consumption $(-r_A),$ and $($iii$)$ the rate constant

under this condition?

$($c$)(6$ pts$)$ Consider replacing the reactor with an ideal Plug Flow Reactor $($PFR$)$ operating at the same

temperature. Determine the volume of the ideal PFR necessary to achieve the same conversion as

described in part $1-($b$).$

$($d$)(6$ pts$)$ The lab$-$scale CSTR system has undergone scaling up to a pilot$-$scale system, resulting in a

$100-$fold increase in both all volumetric flow rates and the volume of the CSTR$.$ The initial

concentrations of the reactants remained same. What is the anticipated conversion from this pilot$-$

scale setup?