Acetic acid is to be removed from an aqueous solution by allowing droplets of the acetic acid-water solution to fall through a column of benzene. The droplets initially contain 1.0 weight % of acetic acid and this has to be reduced to 0.2%. The droplets have a diameter of 1 mm and the temperature is 25°C. At this temperature, the diffusivity of acetic acid in water is 0.88 × 10⁻⁹ m²/s while the diffusivity of acetic acid in benzene is 1.92 × 10⁻⁹ m²/s, both in dilute conditions. The distribution coefficient of acetic acid between water and benzene is 45.5, defined as the weight fraction of acetic acid in water divided by the weight fraction of acetic acid in benzene.

(a) Determine the distance the drops must fall if they are treated as solid spheres and both internal and external mass transfer resistances are considered.

(b) Repeat part

(a) assuming that the droplets fall at the same velocity as in part

(a) but that now they are completely mixed by internal recirculation so that the external mass transfer resistance is controlling.

Assume that the volume of benzene is very large so that the weight fraction of acetic acid in the bulk benzene phase remains zero in both part

(a) and part (b).