A large plate, \(0.25 \mathrm{~m}\) in diameter, is coated with a \(1 \mathrm{~mm}\) layer of zeolite catalytic material. A gas containing a noxious compound is slowly flowing over the catalytic material. Experiments have shown that the intrinsic, pseudo-first-order rate constant for the destruction of the compound is \(1 \times 10^{-6} \mathrm{~s}^{-1}\) and the effective diffusivity of the compound in the zeolite is \(1 \times 10^{-12} \mathrm{~m}^{2} / \mathrm{s}\). The overall effectiveness factor for catalyst was found to be 0.5 and the gas can be approximated as air at \(300 \mathrm{~K}\).

a. Estimate at what velocity the fluid is flowing over the surface of the catalyst.

b. What is the maximum effectiveness factor that could be achieved in this system?