Using GAC to remove contaminants

Consider a drinking water source that is contaminated with herbicides. To remove the herbicides, a drinking water treatment plant uses a granular activated carbon $($GAC$)$ column. Estimate the break though time, $t_b,$ for the compound to pass through the GAC column, given the data below and in the Table.

a$.$ Do the analysis for atrazine, assuming that the inlet concentration to the GAC column is $0\mathrm{.}03m\frac{g}{L},$ which is $10$ times the maximum contaminant level $($MCL$)$ for this compound.

b$.$ Do the analysis for carbofuran, assuming that the inlet concentration to the GAC column is $0\mathrm{.}4m\frac{g}{L},$ which is $10$ times the MCL for this compound.

Data:

$Q=22\frac{m^3}{s}$ total water flow rate of wastewater that the municipal system must treat

Problems originate from Dr$.$ Lauren Kennedy, Dr$.$ Eric Bell, Dr$.$ Ali Boehm, and Nazaroff & Alvarez$-$Cohen $2000$

EBCT$=10$ min empty bed contact time $=\frac{V}{Q}$ for the column without GAC $($see pg $338)$

${}_c=500k\frac{g}{m^3}$ density of granular activated carbon

$D=1\mathrm{.}5m$ depth of the GAC bed

$\backslash$table$[[$Compound$,$MCL $(m\frac{g}{L}),C_{in}(m\frac{g}{L}),\backslash$table$[[K_f($Freundlich$],[$Isotherm$],[$parameter$)]],\backslash$table$[[\frac{1}{n}($Freundlich$],[$Isotherm$],[$parameter$)]]],[$Atrazine$,0\mathrm{.}003,0\mathrm{.}03,289,0\mathrm{.}291],[$Carbofuran$,0\mathrm{.}04,0\mathrm{.}4,275,0\mathrm{.}408]]$