A first-order isomerization reaction is taking place in a non-isothermal, spherical catalyst pellet. Determine the effectiveness factor and the maximum temperature rise in the pellet for the following conditions:

\[\begin{array}{ll}\Delta H=-750 \mathrm{~kJ} / \mathrm{mol} \quad D_{\text {eff }}=1 \times 10^{-7} \mathrm{~m}^{2} / \mathrm{s} \quad c_{a s}=15 \mathrm{~mol} / \mathrm{m}^{3} \\T_{s}=425 \mathrm{~K} & E_{a}=125 \mathrm{~kJ} / \mathrm{mol} \quad k_{e f f}=0.025 \mathrm{~W} / \mathrm{m} \mathrm{K} \\d=0.01 \mathrm{~m} & k_{s}^{\prime \prime}=0.01 \mathrm{~m} / \mathrm{s} @ 425 \mathrm{~K}\end{array}\]