$(20pts)$ An open well contains water contaminated with volatile benzene at the bottom of the

well, with dimensions shown in the figure below. The concentration of dissolved benzene in

water is $156\frac{g}{m^3},$ and remains constant. The system is isothermal at $25C.$ We are interested

in determining the emission of benzene, a carcinogen, into the atmosphere from the well.

Assume the solubility of air into water is zero and under steady state condition.

a$.(3$ pts$)$ Three species are transferred in the well: $A=$ water, $B=$ benzene, and $C=$air. State the

boundary conditions and their numerical values in the unit of mole fraction, $y_i(i=A,B,C).$

b$.(3$ pts$)$ For each of the three species, what is the mass balance equation $($in the unit of

mole$)?$

c$.(3$ pts$)$ For each of the three species, what is the expression for the total molar flux?

d$.$ pts$)$ One of the boundary conditions gives $N_C(z)=0.$ Obtain the expressions for $y_C(z)$

and $N_{AB}=N_A+N_B.$

e$.(4$ pts$)$ Species B $($benzene$)$ is diluted in the system. In this case, you can assume that the

total molar flux $(N_B)$ is determined by only the diffusive flux. Obtain the value of $N_B.$

f$.(3$ pts$)$ What is the emission rate of benzene from the well in the unit of mole$/$day$?$

$$ Use these properties $>$

The molecular diffusivity of air is $0\mathrm{.}2c\frac{m^2}{s}$ at $1\mathrm{.}0$atm and $25C.$

The molecular diffusivity of benzene vapor in air is $0\mathrm{.}093c\frac{m^2}{s}$ at $1\mathrm{.}0$atm and $25C.$

The Henry's law constant for benzene in water is $H=4\mathrm{.}84{10}^{-3}{m}^3*at\frac{m}{m}$ole at $25C.$

The vapor pressure of liquid water is $0\mathrm{.}031$atm.

The humidity of the air flowing over the well hole is $40\%$ at $25C.$

The molecular weight of benzene is $78\frac{g}{m}$ole.

The gas constant is $R=8\mathrm{.}21{10}^{-5}{m}^3-at\frac{m}{K}-$mol.