A industrial waste treatment facility receiving $1$ MGD of flow needs to build a new reactor to

treat chromium$($VI$)$ waste from an electroplating operation. Cr$($VI$),$ present in water as HCrO$4-$ can be treated

by chemical reduction with bisulfite, HSO$3-$

$,$ yielding Cr$($OH$)3($s$)$ that can be removed by gravity sand filtration

and sulfate $($SO$42-$

$),$ an inert anion species.

$3$ HSO$3-+2$ HCrO$4-+$ H $2$ O $2$ Cr$($OH$)3($s$)+3$ SO$42-+$ H$+$

Information from the literature shows that HCrO$4-$ reduction by this reaction follows a pseudo$-$first$-$order rate

with k$1=0\mathrm{.}1$ s $-1$ at pH $7\mathrm{.}5$ when treating with $1$ mM HSO$3-$

$.$ If the wastewater initially has a HCrO$4-$

concentration of $100\backslash$mu M$,$ determine the minimum reactor volume $($in gallons$)$ needed to ensure that the

HCrO$4-$ concentration drops to $0\mathrm{.}1\backslash$mu M if $($a$)$ reaction is conducted in an ideal CSTR$,($b$)$ reaction is conducted

in an ideal PFR$,$ or $($c$)$ reaction is conducted in a PRF with dispersion that can be modeled as $5$ CSTR

reactors$-$in$-$series.

Time $[$Dia$]$

$($min$)($M$)($

$17\mathrm{.}48$E$-05$

$2\mathrm{.}54\mathrm{.}88$E$-05$

$43\mathrm{.}29$E$-05$

$5\mathrm{.}51\mathrm{.}95$E$-05$

$71\mathrm{.}16$E$-05$

$8\mathrm{.}56\mathrm{.}38$E$-06$

$103\mathrm{.}98$E$-06$