Q$\mathrm{.}1.(10$ marks$)$

A spherical ball of solid, nonporous naphthalene, is suspended in still air. The naphthalene ball slowly sublimes, releasing the naphthalene vapor into the surrounding air by molecular diffusion$-$limited process. Estimate the time required to reduce the diameter from $2\mathrm{.}0$ to $0\mathrm{.}50cm$ when the surrounding air is at $347K$ and $1\mathrm{.}0$atm. Naphthalene has a molecular weight of $128\frac{g}{m}ol,$ a solid density of $1\mathrm{.}145\frac{g}{c}{m}^3,$ and a diffusivity in air of ${8\mathrm{.}1910}^{-4}\frac{m^2}{s},$ and exerts a vapor pressure of $5\mathrm{.}0$ Torr $(666Pa)$ at $347K.R=8\mathrm{.}314{10}^{6}c{m}^3*P\frac{a}{g}$mol.$K$