A crystal of Glauber's salt (left(mathrm{Na}_{2} mathrm{SO}_{4} cdot 10 mathrm{H}_{2} mathrm{O} ight)) dissolves in a large tank

Question:

A crystal of Glauber's salt \(\left(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\right)\) dissolves in a large tank of pure water at \(288 \mathrm{~K}\). Estimate the rate at which the crystal dissolves by calculating the flux of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) from the crystal surface to the bulk solution. Assume that molecular diffusion occurs through a liquid film \(0.085 \mathrm{~mm}\) thick surrounding the crystal. At the inner side of the film-adjacent to the crystal surface-the solution is saturated with \(\mathrm{Na}_{2} \mathrm{SO}_{4}\), while at the outer side of the film the solution is virtually pure water. The solubility of Glauber's salt in water at \(288 \mathrm{~K}\) is \(36 \mathrm{~g}\) of crystal \(100 \mathrm{~g}\) of water and the density of the corresponding saturated solution is \(1240 \mathrm{~kg} / \mathrm{m}^{3}\) (Perry and Chilton, 1973). The diffusivity of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) in dilute aqueous solution at \(288 \mathrm{~K}\) can be estimated as suggested in Problem 1.19. The density of pure liquid water at \(288 \mathrm{~K}\) is \(999.8 \mathrm{~kg} / \mathrm{m}^{3}\); the viscosity is \(1.153 \mathrm{cP}\).