$(30$ points$)$ Analyze the concentration profile of a dissolving spherical particle composed of

material A suspended in a quiescent solvent with $0$ initial concentration of $A.$ Assume that

the dissolution rate and saturated concentration of A are both very small, hence the change

in particle diameter is negligible. Also calculate the concentration of $A$ at $r=2R_0,$ and $t=$

$\frac{R_0^2}{4}t.$ The saturated concentration of $A$ is $C_{A0},$ the radius of the sphere is $R_0,$ and diffusivity

is $D.$