The second-order decomposition reaction A → B + 2C is carried out in a tubular reactor packed with catalyst pellets 0.4 cm in diameter. The reaction is internal-diffusion-limited. Pure A enters the reactor at a superficial velocity of 3 m/s, a temperature of 250°C, and a pressure of 500 kPa. Experiments carried out on smaller pellets where surface reaction is limiting yielded a specific reaction rate of 0.05 m6/mol·g-cat·s. Calculate the length of bed necessary to achieve 80% conversion. Critique the numerical answer.
Additional information:

Effective diffusivity: 2.66 x 108 m/s Pellet density: 2 x 106 g/m Ineffective diffusivity: 0.00 m/s Bed porosity: 0.4 Internal surface area: 400 m/g