P$6\mathrm{.}9$ Diffusive Fluxes and Concentration Changes

Consider the concentration profile $C(x)=C_0{e}^{-ax}$ along the positive x$-$axis

where $C_0$ and a are constant positive parameters. $($a$)$ Calculate the size and

direction of the diffusive flux as a function of $x$ produced by the constant diffusivity $D.$

$($b$)$ Calculate the corresponding in situ concentration change, del$\frac{C}{d}$elt, due to diffusion.

Numbers:

$C_o=1mmol{L}^{-1}$

$a=0\mathrm{.}02m^{-1}$

$D=1{10}^{-9}{m}^2{s}^{-1}$

Evaluate flux $F$ and concentration change, del$\frac{C}{d}$elt, at $x=0,10m,100m,1km.$