A $1mm$ cube of $MgS{O}_4-7H_{2}O$ crystal falls through a tank of pure water at $10C.$ The solubility of $MgS{O}_4$ in water is $10C$ is $0\mathrm{.}232$ weight fraction and solutions density is $1200\frac{k}{m^3}.$ The molecular weight of $MgS{O}_4$ is $120\mathrm{.}0\frac{g}{\text{m}\text{o}\text{l}}$ and the density of the crystal is

$p_c=2200\frac{kg}{m^3}.$ Assume the molecular diffusion occurs through a film of water uniformly $0\mathrm{.}100mm$ thick, surrounding the crystal. The diffusivity of $MgS{O}_4$ in water is

$8\mathrm{.}40{10}^{-10}\frac{m^2}{(s)}.$

b$)$ Calculate the initial flux of $MgS{O}_4$

c$)$ Derive the expression for the size of crystal as a function of time