In a study, a $2\%$ hydrazine and $98\%$ of helium mixture is to be passed over a packed bed of cylindrical particles of $0\mathrm{.}25$ cm in diameter and $0\mathrm{.}5$ cm in length at a gas$-$phase velocity of $15\frac{m}{s}$ and a temperature of $750$ K $.$ The kinematic viscosity of helium at this temperature is $4\mathrm{.}5x{10}^{-4}\frac{m}{s}.$ The hydrazine decomposition reaction is believed to be externally mass transfer limited under this condition. If the packed bed is $0\mathrm{.}05$ m in length,

Given;

$D_{AB}=3\mathrm{.}47{10}^{-4}\frac{m}{s}$ at $298$ K

Bed porosity $=30\%$

a$)$ Calculate the mass transfer coefficient using Colburn $J_D$ factor.

b$)$ Determine the conversion could be expected. Assume isothermal operation.

$x=1-e^{-(\frac{k{a}_s}{U})L}$