The following rates were observed for a first-order, irreversible reaction, carried out on a spherical catalyst:

\[\begin{array}{lr}d_{p 1}=0.625 \mathrm{~cm} & r_{o b s, 1}=0.09 \mathrm{~mol} / \mathrm{gcat} \cdot \mathrm{hr} \\d_{p 2}=0.1 \mathrm{~cm} & r_{o b s, 2}=0.275 \mathrm{~mol} / \mathrm{gcat} . \mathrm{hr}\end{array}\]

Strong diffusional limitations were observed in both cases. Determine the true rate of reaction. Is the diffusional resistance still important when \(d_{p}=0.05 \mathrm{~cm}\) ?