An impurity is to be removed from an aqueous solution by adsorption on a selective adsorbent in a batch system. The solution, at 25°C and containing 0.1 kg/m3 of the impurity, will be loaded into a 1 m diameter baffled cylindrical tank to a 1 m height agitated by a 0.33 m diameter sixblade turbine at 30 rpm. The adsorbent particles are 0.05 cm in diameter, have a density of 1,100 kg/m3, and are completely suspended in the liquid. The diffusivity of the impurity in the solution at 25°C is 6.6 × 10⁻¹⁰ m²/s.

(a) Estimate the mass transfer coefficient for transport of the impurity to the surface of the adsorbent particles.

(b) Predict the time needed to remove 90% of the impurity if 1 kg of adsorbent particles is added to the tank and the adsorption process is controlled by the external mass transfer resistance. Assume that the impurity concentration at the particle surface is kept at zero because the adsorption is very favorable.