Please solve for E

MB for lake with suspended sediments

a$.)$ A new manufacturing plant begins discharging their waste stream into Yates Lake $($V$=10,000m^3,A=2000m^2)$ on December $31,2009.$ The treated waste stream contains trichlorobenzene $($TCB$).$ In water, TCB degrades with a rate constant $k=\frac{0\mathrm{.}06}{?}$ day. To ensure compliance with regulations, the plant wants to keep the concentration of TCB in the lake at $0\mathrm{.}05m\frac{g}{L}.$ How much TCB can the plant release to the lake $(k\frac{g}{?}$ day$)?$ Note that water from Yates Lake flows into the Tallapoosa river at a rate of $80,000\frac{L}{?}$ day. $0\mathrm{.}034k\frac{g}{?}$ day

b$.)$ On April $9,2010,$ the waste storage tanks and secondary containment containers fail, releasing the contents of the storage tanks into the lake. Derive an expression for the change in TCB concentration in the lake after the spill.

$C(t)=\frac{\frac{W}{V}}{\frac{1}{}+k}+(C(t_{\text{s}\text{p}\text{i}\text{l}\text{l}})-\frac{\frac{W}{V}}{\frac{1}{}+k})e^{-(\frac{1}{}+k)(t-t_{\text{s}\text{p}\text{i}\text{t}})}$

c$.)$ If the spill contained $1kg$ of TCB$,$ how many days will it take until the concentration of TCB in the lake is below the drinking water standard $($note that the drinking water standard is NOT $0\mathrm{.}05m\frac{g}{L})?$ What is the dominant loss mechanism for TCB in the lake?

$t=124$ days

reaction is the dominat loss mechanism

d$.)$ In an effort to remediate the spill, sediments are added to the lake at a sediment loading rate, $W_s,$ of $100k\frac{g}{d}ay.$ Assuming the particles settle at a velocity of $0\mathrm{.}2\frac{m}{?}$ day, what is the steady state concentration of particulate matter in the lake?

$208m\frac{g}{L}$

e$.)$ If the $K_D$ for sorption of TCB on the sediment is ${10}^{4}m\frac{L}{g},$ will sorption be a significant removal process $($and thus needs to be considered$)?$

Yes, the value is substantially greater than unity and thus sorption must be accounted for.

f$.)$ Dredging of the lake sediment was scheduled to begin July $19,2010.$ Assuming steady$-$state has been reached, what is the new steady$-$state total concentration of TCB in the lake $($including sorption of TCB to the sediments$)?$ Compare this to the concentration on July $19,2010$ if sediments had not been added. Based on your analysis, what remediation strategy do you recommend?

$C_{ss}=0\mathrm{.}062m\frac{g}{L}$

This concentration is larger than the concentration prior to adding suspended sediment.