Water is evaporating from a pool exposed to a breeze of ambient air at $300$ K$,1\mathrm{.}0132$ bar and $25\%$ relative humidity. Assuming that mass transfer is due to molecular diffusion through a stagnant film of air of $80$ mm determine the following:

A$)$ The diffusivity of water in air using Hirschfeldre's equation

B$)$ The model to evaluate the rate of evaporation of water

C$)$ The initial rate of evaporation of water as a molar flux in Kmol$/$Cm$^2-$s

D$)$ The time in hours for the water level to drop $1$ cm

Given:

$-$ Mass air: $29$ g$/$mol

$-$ Water vapor pressure $($@$300$K$)=35\mathrm{.}31$ kPa

$-$ Collision diameter $($air$)=3\mathrm{.}620$ Anstrong

$-$ Collision diameter $($water$)=2\mathrm{.}640$ Anstrong

$-$ E$/$K $($air$)=97$ K

$-$ E$/$K $($water$)=809\mathrm{.}1$ K

$-$ Water density$=1$ g$/$cm$^3$

$-1$ atm $=1\mathrm{.}0132$ bar $=101\mathrm{.}3$ kPa

$-$ R $=8\mathrm{.}134$ kPa m$^3/$kmol$-$K

Hint: Relative humidity is the ratio of the partial Pressure of water to the equilibrium vapor pressure at the same temperature.