As part of the manufacturing process for the fabrication of titanium-oxide-based solar panels, a layer of nonporous titanium oxide must be reduced to metallic titanium, Ti, by hydrogen gas as shown in...

As part of the manufacturing process for the fabrication of titanium-oxide-based solar panels, a layer of nonporous titanium oxide must be reduced to metallic titanium, Ti, by hydrogen gas as shown in the following figure.

The reaction at the Ti/TiO₂
boundary is given by

Pure H₂
gas flows rapidly over the surface of the nanoporous TiO₂
slab. As TiO₂(s) is reduced to Ti (molecualr weight
), the path length for mass transfer of H₂
and H₂O gas through the porous slab from the surface to the Ti/TiO₂
boundary increases with time. You may assume that (1) the process operates at 1.0 atm and 900 K; (2) the reaction is very fast so that the concentration of H₂
gas at the Ti/TiO₂
boundary is zero and the reduction of TiO₂(s) is limited by the diffusion of TiO₂(g) away from the Ti(s)/TiO₂
boundary; (3) the diffusion process is pseudo-steady state along the diffusion path; and (4) the effective gas-phase diffusion coefficient of H₂
within the porous Ti(s) containing a mixture of H₂(g) and H₂O(g) is 0.031 cm²/s at the temperature and pressure of the process, whereas the effective diffusion coefficient of H₂O(g) within the nanoporous Ti(s) containing a mixture of H₂(g) and H2O(g) is 0.01 cm²/s at the temperature and pressure of the process. The density of the nanoporous Ti(s) is 2.6 g/cm³.

a. Determine the flux of H₂
to the Ti/TiO₂
boundary when
, assuming

b. Determine the number of hours necessary for all the TiO₂
to be converted to Ti(s).

c. At
, determine the concentration profile for H₂(g).