Optional! (15 bonus pts). Unsteady State with Convection. An absorbent spherical silica gel bead of 0.20 cm diameter in placed in a flowing air stream (velocity = 50 cm/s, 25C, 1 atm pressure, 1.0 mole% of water vapor. Water partitions into the silica gel bead's surface, described by the linear relationship Cas=K.pa, where cas is the concentration of H2O in the silica, pa is the H20 vapor partial pressure, and K is the partition coefficient = 2.0 mol O2/(cm silica)-(atm H2O vapor) at 25C. The diffusion coefficient of H20 in the silica gel is 1.0 x 10-6 cm-/s. The diffusion coefficient of water in air is 0.260 cm/s and the kinematic viscosity of air at 25C is 0.15689 cm-/s. Assuming that the partial pressure of H20 vapor in the gas stream remains constant, what is the concentration of H20 in the center of the silica gel bead after 41.67 minutes? Initially, the silica gel bead contains no H20. Hint: you will need to use what you know about convection to calculate kc and then approach with unsteady state