${1\mathrm{.}25}^b.$ Steady$-$state, one$-$dimensional, liquid$-$phase flux calculation

A crystal of Glauber's salt $(N{a}_{2}S{O}_4*10H_{2}O)$ dissolves in a large tank of pure water at $288K.$ Estimate the rate at which the crystal dissolves by calculating the flux of $N{a}_{2}S{O}_4$ from the crystal surface to the bulk solution. Assume that molecular diffusion occurs through a liquid film $0\mathrm{.}085mm$ thick surrounding the crystal. At the inner side of the film$-$adjacent to the crystal surface$-$the solution is saturated with $N{a}_{2}S{O}_4,$ while at the outer side of the film the solution is virtually pure water. The solubility of Glauber's salt in water at $288K$ is $36g$ of crysta$\frac{l}{100}g$ of water and the density of the corresponding saturated solution is $1240k\frac{g}{m^3}($Perry and Chilton, $1973).$ The diffusivity of $N{a}_{2}S{O}_4$ in dilute aqueous solution at $288K$ can be estimated as suggested in Problem $1\mathrm{.}19.$ The density of pure liquid water at $288K$ is $999\mathrm{.}8k\frac{g}{m^3}$; the viscosity is $1\mathrm{.}153cP.$

Answer: $12\mathrm{.}9kg$ of crysta$\frac{l}{m^2}*h$