An entrance section of process piping is fouled with calcium carbonate scale. Specifically, the inner surface of the pipe is coated with 0.1 cm film of solid calcium carbonate (species A) that is sparingly soluble in water. The length of the pipe containing the calcium carbonate is 1 m, and the inner diameter of the pipe is 2 cm.
In an attempt to dissolve the scale from the pipe surface, ''clean'' water containing no soluble calcium carbonate flows through the pipe at a volumetric flow rate of 314 cm3/s and a temperature of 293 K.
Determine the time in hours that it will take for the calcium carbonate coating to completely dissolve from the inner surface of the tube, assuming that bulk concentration of solute A in the liquid stream is essentially zero throughout the 1 m length of the scaled section. The following potentially useful data are available:
MA the molecular weight of solute A = 100 kg/kg mol.
PA, the density of solid A = 2.7 x 103 kg/m3.
DAB, the diffusivity of solute A in water = 1.2 x 10-9 m2/s.
C*A, the solubility of solute A in water = 0.14 mol/m3.