Problem $1.$ Assessment of Controlling Transport Resistances. Part $1(10$ points$)$

The first$-$order catalytic reaction $AR$ with an activation energy of $167k\frac{J}{m}ol$ is carefully

measured at a point where $C_{Ag}=100mo\frac{l}{m^3}$ and $T_g=500K$ in an experimental reactor

containing $6mm$ catalyst pellets $(L=1{10}^{-3}(m)).$

$(1)$ Find what factors influence the observed rate $($pore diffusion, film mass transfer, particle

and$/$or film $T.$ Also, find $T_S$ and find what fraction of the resistance is due to film mass

transfer.

$(2)$ Find the parameter $($see Chapter $22$ handout$)$ based on the isothermal pellet at TG free

of physical transport effects

$(3)$ Find the reaction rate constant $k^{,},$ at $500K.$ Also, define the complete units of $k\text{'},".$

The following thermodynamic, system and rate values are reported for this system.

$-r_A^{\text{'}},,=1{10}^{2}mo\frac{l}{m^3}$ catalyst$-s{k}_{\text{e}\text{f}\text{f}}=1{10}^{-2}\frac{W}{m}$ catalyst $-K$

$H_r=1k\frac{J}{m}ol,h=1{10}^3\frac{W}{m^2}$ catalyst$-K$

$D_{\text{e}\text{f}\text{f}}=1{10}^{-8}\frac{m^2}{s},k_g=1\frac{m^3}{m^2}$ catalyst$-s$