A spherical silica gel adsorbent particle of 0.20 cm diameter

A spherical silica gel adsorbent particle of 0.20 cm diameter in placed in a rapidly flowing air stream at a velocity of 50 cm/s containing 1.0 mole% of H2O vapor at total system pressure of 1.0 atm and temperature of 25°C. At 25°C, the equilibrium of H2O vapor with silica gel is described by the linear relationship C*A = S · PA, where C*A is the equilibrium concentration of H2O in the silica, and PA is the H2O vapor partial pressure, and S is the partitioning coefficient, with S = 2.0 gmole O2/(cm3 silica) (atm H2O vapor) at 25°C. At 25°C, the diffusion coefficient of H2O in the silica gel is 1.0 × 10-6 cm2/s. Assuming that the partial pressure of H2O vapor in the gas stream remains constant, what is the concentration of H2O in center of the silica gel bead after 2.78 hr? Initially, the silica gel bead contains no H2O.