Problem $1$: Fick's Law. Some graduate students work on the hydrothermal liquefaction of

sewage sludge to produce renewable fuels and chemicals. However, the students may cause an

unpleasant odor in the lab! Calculate whether Parafilm is sufficient to keep the room below $1$

ppm $($the detection level for the human nose$).$

a$.$ Calculate the flux of the aromatic, A$,$ through a $100m$ thick polymer film given a

diffusion coefficient of $D_{AB}={10}^{-5}c\frac{m^2}{s}.$ The concentration in the headspace inside

the beaker is $1000ppm$ and the HVAC in the building ensures the concentration near the

outside of the film is always nearly zero. $(N_A[=]\frac{\text{m}\text{o}\text{l}}{c{m}^2(s)}).$

b$.$ If the beaker is $10cm$ in diameter, what is the total flux exiting the beaker

$(W_A[=]mo\frac{l}{s})?$

c$.$ If the room is $101010ft,$ well mixed and the fume hoods, doors and windows are all

sealed, how long before you accumulate to the nasty $1ppm?$

d$.$ Would doubling up on the parafilm increase this time, or have no effect? $($calculation not

required$)$