to a small reservoir. The surface area, average depth and outflow rate from the lake are given as $7\mathrm{.}5{10}^5{m}^2,6m$ and $2\frac{m^3}{sec},$ spectively. After the dump, toluene is expected to be removed from the lake primarily by washout and by a first$-$order removal reaction th a rate coefficient of $0\mathrm{.}1/$day$.$

a$.$ Draw a diagram and write the mass balance equation for toluene in the lake. As part of your answer, specify the initial condition $($immediately after the accident$).$

b$.$ Develop a solution for the toluene concentration as a function of time.

c$.$ Calculate the toluene concentration in the lake immediately after the spill, at $5$ days after the spill and at $10$ days after the spill.

d$.$ What would be the steady$-$state concentration of toluene in the lake? Briefly explain.