A sphere of solid material A $($potassium permanganate$)$ is suspended in a stationary body of liquid

$B($water$).$ A is very slightly soluble in $B.$ For the steady$-$state dissolution of A into B$,$ derive the

following expressions. State your assumptions clearly.

$\frac{x_A(r)-x_A}{x_{AR}-x_A}=\frac{R}{r}$

Where, $x_{AR}$ is the mole fraction of $A$ at the sphere surface, $r=R$ and $r.$

Where, $x_A$ is the mole fraction of A far away into the liquid from the sphere surface, $r.$

Also find an expression of molar flux at the sphere surface.