Question 24.8: A pure nitrogen carrier gas flows parallel to the 0.6 m² sur...
A pure nitrogen carrier gas flows parallel to the 0.6 m² surface of a liquid acetone in an open tank. The acetone temperature is maintained at 290 K. If the average mass-transfer coefficient, k_{c}, for the mass transfer of acetone into the nitrogen stream is 0.0324 m/s, determine the total rate of acetone release in units of kg.mol/s.
The total molar rate of acetone transfer from the liquid to the gas phase can be evaluated by
W_{A}=N_{A} A=k_{c} A\left(c_{A s}-c_{A \infty}\right)The mass transfer area is specified as 0.6 m² . At 290 K, acetone exerts a vapor pressure of 161 mmHg or 2.148 \times 10^{4} \mathrm{~Pa}. Therefore, the concentration of acetone in the gas phase at the acetone surface is
c_{A s}=\frac{P_{A}}{R T}=\frac{2.148 \times 10^{4} \mathrm{~Pa}}{\left(8.314 \frac{\mathrm{Pa} \times \mathrm{m}^{3}}{\mathrm{~kg} \mathrm{~mol} \times \mathrm{K}}\right)(290 \mathrm{~K})}=8.91 \frac{\mathrm{kg} \mathrm{mol}}{\mathrm{m}^{3}}and the concentration of acetone in the nitrogen carrier gas is near zero because the molar flowrate of the carrier gas is in a large excess relative to the rate of acetone transfer. Thus
W_{A}=k_{c} A\left(c_{A s}-c_{A \infty}\right)=\left(0.0324 \frac{\mathrm{m}}{\mathrm{s}}\right)\left(0.6 \mathrm{~m}^{2}\right)\left(8.91 \frac{\mathrm{kg} \cdot \mathrm{mol}}{\mathrm{m}^{3}}-0\right)=0.1732 \frac{\mathrm{kg} \cdot \mathrm{mol}}{\mathrm{s}}