The catalytic oxidation reaction of hydrogen with oxygen is carried out in a packed$-$bed reactor

filled with catalyst pellets $(d=1mm,Pt$ on alumina$).$ The catalytic rate law measured as $r=k_r{C}_{H2}$

with $k_0={1\mathrm{.}4}^{**}{10}^{3}cm.s^{-1}(T_0=0(K)),E_{ac}=14\mathrm{.}9k\frac{J}{m}ol.$ Assuming a linear gas velocity of $u=1\frac{m}{s},$

a diffusion coefficient $D_{AB}=1c\frac{m^2}{s},$ a kinematic viscosity $v={10}^{-4}\frac{m^2}{s}$ and a temperature of $T=600$

$K,$ what is the effective transport coefficient? Is the overall reaction is limited by external diffusion

or internal diffusion? Assume $D_{AB}=D_{ef},S_A=100\frac{m^2}{g}-$cat and ${}_c=2\frac{g}{c}{m}^3.$

$k(T)=k(T_0)exp[\frac{\text{E}\text{a}\text{c}\text{t}}{R}**(\frac{1}{T_0}-\frac{1}{T})]$

$coth(x)=\frac{e^x+e^{-x}}{e^x-e^{-x}}$