1.26b. Steady-state, one-dimensional, liquid-phase flux calculation.
A crystal of Glauber's salt (Na2SO4× 10H2O) dissolves in a large tank of pure water at 288 K. Estimate the rate at which the crystal dissolves by calculating the flux of Na2SO4 from the crystal surface to the bulk solution. Assume that molecular diffusion occurs through a liquid film uniformly 0.085 mm thick surrounding the crystal. At the inner side of the film (adjacent to the crystal surface) the solution is saturated with Na2SO4, while at the outer side of the film the solution is virtually pure water. The solubility of Glauber's salt in water at 288 K is 36 g of crystal/100 g of water and the density of the corresponding saturated solution is 1,240 kg/m3 (Perry and Chilton, 1973). The diffusivity of Na2SO4 in dilute aqueous solution at 288 K can be estimated as suggested in Problem 1-20. The density of pure liquid water at 288 K is 999.8 kg/m3; the viscosity is 1.153 cP.
Solution
A = Na2SO4 B = H2O
Calculate xA1 (saturated solution)
Basis: 100 g H2O (36 g of dissolved crystal)
(Pure water)
Calculate diffusivity
1.27c, d. Molecular diffusion through a gas-liquid interface.
Ammonia, NH3, is being selectively removed from an air-NH3 mixture by absorption into water. In this steady-state process, ammonia is transferred by molecular diffusion through a stagnant gas layer 5 mm thick and then through a stagnant water layer 0.1 mm thick. The concentration of ammonia at the outer boundary of the gas layer is 3.42 mol percent and the concentration at the lower boundary of the water layer is esentially zero.The temperature of the system is 288 K and the total pressure is 1 atm. The diffusivity of ammonia in air under these conditions is 0.215 cm2/s and in liquid water is 1.77 ´ 10Ð5 cm2/s. Neglecting water evaporation, determine the rate of diffusion of ammonia, in kg/m2-hr. Assume that the gas and liquid are in equilibrium at the interface.

Solution:
Initial estimates: