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 · P_A, where C*_A is the equilibrium concentration of H₂O in the silica, and P_A 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.