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For a spherical catalyst particle, the diffusion-reaction equation is given by:
\[ \frac{d^2C_A}{dr^2} + \frac{2}{r}\frac{dC_A}{dr} = \frac{k}{D_e}C_A^2 \]
where \(C_A\) is the concentration of A, \(r\) is the radial position within the particle, \(k\) is the
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