Problem $1(10$ pts$).($The quintessential problem of Module $3,$ a problem found everywhere

online and one which you will likely see again.$)$ Atrazine seeps out of a solid into wet soil at the

soil surface. Soil typically has several layers, including the O$-$horizon $("$organics$"),$ the A$-$horizon

$("$topsoil$"),$ the B$-$horizon, etc. down until the bedrock layer. We will consider two$-$layer soil with

only the topsoil $(20cm)$ and the clay or bedrock below. The atrazine does not penetrate the

clay$/$bedrock or the soil solids in this example. The soil is saturated with water and the water

fraction is $0\mathrm{.}60.$ For the pore diffusivity of atrazine through this wet soil, make a simplifying

assumption that Dae' $=DA{B}^{***}$ epsilon$^2$ without calculating DAK. The solubility of atrazine in

water at $20C$ is $30m\frac{g}{L},$ its molar mass is $216\frac{g}{m}ol,$ the temperature is $20C,$ and the rate

constant is $5e-4h{r}^{{?}^{{?}^{?}}}-1$ at $20C.$

$($a$)$ Calculate the diffusivity of atrazine in pure water at $20C$ using the Wilke$-$Chang model.

Viscosity of water at $20C$ is $1cP,$ the association parameter for water is $2\mathrm{.}6($dimensionless$),$

and the molal volume of atrazine at its boiling point is $170cm\frac{3}{m}ol.$

$($b$)$ What is the flux at the soil$/$clay interface, which occurs at a depth of $20cm?$

$($c$)$ Convert the solubility of atrazine in water to units of $mo\frac{l}{L}$ and the rate constant to units of

$s^{{?}^{{?}^{?}}}-1.$ The diffusion coefficient $(c{m}^{{?}^{{?}^{?}}}\frac{2}{s})$ and the depth $(cm)$ can remain in the given units.

$($d$)$ Calculate the diffusion coefficient for atrazine in the soil, starting with your answer from $($a$),$

which should have been between $6$ and $7{10}^{{?}^{{?}^{?}}}-6c{m}^{{?}^{{?}^{?}}}\frac{2}{s}.$

$($e$)$ What is the concentration of atrazine at a depth of $6cm?$