PROBLEM $($ please solve all parts and show all steps$)$

$30\mathrm{.}1$ Spherical pellets of $1\mathrm{.}0cm$ diameter are spray$-$painted

b$.$ Determine the minimum time to dry the painted pellet if air

with a very thin coat of paint. The paint contains a volatile

solvent. The vapor pressure of the solvent at $298K$ is $1\mathrm{.}17$

${10}^{4}Pa,$ and the diffusivity of the solvent vapor in air at $298K$ is

$0\mathrm{.}0962c\frac{m^2}{s}.$ The amount of solvent in the wet paint on the

pellet is $0\mathrm{.}12g$ solvent per $c{m}^2$ of pellet surface area. The

molecular weight of the solvent is $78\frac{g}{g}$mole.

a$.$ Determine the minimum time to dry the painted pellet if still

air at $298K$ and $1\mathrm{.}0$atm surrounds the pellet.