Question

An Arnold cell is to be operated as a pseudo-steady-state cell to determine the gas diffusivity of benzene in air at 308 K and 1.0 atm. The 20-cm-long tube, with an inner diameter of 1.0 cm, is initially loaded with liquid benzene to a depth of 1.0 cm from the bottom of the tube. The tube and the liquid are maintained at a constant temperature of 308 K. At this temperature, benzene exerts a vapor pressure of 0.195 atm. Air is continually blown over the top of the tube, removing any of the vaporized benzene vapor; the gas space within the tube is essentially stagnant. At 308 K, liquid benzene’s density is 0:85 g/cm3.
a. It was determined that 72.0 h were required to completely evaporate the benzene initially loaded into the tube. Estimate the binary gas-phase diffusion coefficient for benzene in air using these data.

Answer 1

Answer:

D=1.0x10^-5 m^2/s

Explanation:

the data given by the exercise are as follows:

T=308 K

d=1 cm

PA=0.195 atm

pL=0.85 g/cm^3

The expression for binary gas-phase diffusion coefficient is equal to:

$D=\frac{\frac{pL*yB}{MA(\frac{t1^{2}-t2^{2} }{2} } }{c(yA1-yA2}$

$yB=\frac{1-0.805}{ln(\frac{1}{0.805}) }=0.89$

$C=\frac{P}{RT}=\frac{1}{82.06*308}=3.95x10^{-5} mol/cm^{2}$

substituting the values ​​in the diffusion equation:

$D=9.6x10^{-6} m^{2}/s$

from Appendix J-1 from Welty:

298 K, D=9.62x10^-5 m^2/s

At 308 K, we have the following:

$D=9.62x10^{-5}(\frac{308}{298})^{3/2}=1.0x10^{-5}m^{2}/s$