Estimate the mass-transfer coefficient for the dissolution of sodium chloride from a cast sphere, \(1.5 \mathrm{~cm}\) in diameter, if placed in a flowing water stream. The velocity of the \(291 \mathrm{~K}\) water stream is \(1.0 \mathrm{~m} / \mathrm{s}\). Assume that the kinematic viscosity at the average liquid film conditions is \(1.02 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\), and the mass diffusivity is \(1.25 \times 10^{-9} \mathrm{~m}^{2} / \mathrm{s}\). The solubility of \(\mathrm{NaCl}\) in water at \(291 \mathrm{~K}\) is \(0.35 \mathrm{~g} / \mathrm{cm}^{3}\), and the density of the saturated solution is \(1.22 \mathrm{~g} / \mathrm{cm}^{3}\) (Perry and Chilton, 1973).