You have probably seen little packets of silica gel particles to absorb water in all kinds of food and consumer

products. Imagine that a $2mm$ diameter particle is in a rapidly flowing air stream at a velocity of $50c\frac{m}{s}$ containing

$1\mathrm{.}0$ mole$\%$ of $H2O$ vapor. The pressure of $1\mathrm{.}0$atm and temperature of $25C.$ At equilibrium, water vapor has a

linear solubility in silica gel, $c_W^{**}=S{P}_w,$ where $S=2\mathrm{.}0\frac{\text{m}\text{o}\text{l}}{c{m}^3(atm)}.$ At $25C,$ the diffusion coefficient of $H2O$ in the

silica gel is $1\mathrm{.}0{10}^{-6}cm\frac{2}{s}.$ Initally, the silica contains no $H2O.$ Assume that the partial pressure of $H2O$ vapor in

the gas stream remains constant.

a$.$ What is the mass transfer coefficient for water vapor in air?

b$.$ Use your answer to a to find the Biot number for system. Is this system limited by external convection or

internal diffusion?

c$.$ Use charts to find the concentration of $H2O$ in the center of the silica gel bead after $1hr.$