$3)$ At a particular location in a distillation column, where the temperature is $350$ K and the pressure $500$ mHg$,$ the mole fraction of the more volatile component in the vapor is $0\mathrm{.}7$ at the interface with the liquid and $0\mathrm{.}5$ in the bulk of the vapor. The molar latent heat of the more volatile component is $1\mathrm{.}5$ times that of the less volatile component. The resistance to mass transfer in the vapor may be considered to lie in a stagnant film of thickness $0\mathrm{.}5$ mm at the interface. The diffusivity in the vapor mixture is $2\backslash$times $10$

$5$

m

$2$

$/$s$.($a$)$ Calculate the mass transfer rates $($in kmol per m

$2$

per second$)$ of the two components. $($b$)$ Assuming ideal gas behavior, calculate the mole fractions and concentration gradients of the two components at the mid$-$point of the film. $4)$ Water evaporates from an open bowl at $349$ K at the rate of $4\mathrm{.}11\backslash$times $10$

$3$

kg per m

$2$

per second. Assume ideal gas and neglect the partial pressure of vapor in the surrounding atmosphere. $($a$)$ What is the effective gas$-$film thickness? $($b$)$ The water is replaced by ethanol at $343$ K$.$ What will be its rate of cvaporation in kg per m

$2$

per second if the film thickness is unchanged? $($c$)$ At the surface of the ethanol, what proportion of the total mass transfer will then be attributable to bulk flow? DATA: Vapor pressure of water at $349$ K$=34$ mmHg Vapor pressure of ethanol at $343$ K$=544$ mmHg Diffusivity of water vapor in air $=2\mathrm{.}6\backslash$times $10$

$5$

m

$2$

$/$s Diffusivity of ethanol in air $=1\mathrm{.}2\backslash$times $10$

$5$

m

$2$

$/$s Density of mercury $=13\mathrm{.}6$ g$/$cm

$3$