$.$ 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 $15$ m$/$s and a temperature of $750$K$.$ The kinematic viscosity of helium at this temperature is $4\mathrm{.}5$ x$104$ 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;

DAB $=3\mathrm{.}47$ x$104$ m$/$s at $298$K

Bed porosity $=30\%$

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

kC $=$ D$\_$AB$/$d$\_$p $($Sh$)$

Sh $=$ Sc$1/3$ Re $($JD$)$ ; Sc $=$ v$/$D$\_$AB

$$J$\_$D$=0\mathrm{.}765/$Re$^0\mathrm{.}82+0\mathrm{.}365/$Re$^0\mathrm{.}386$

Re $=($d$\_$p U$)/$v ; v$=\backslash$mu $/\backslash$rho $\_$b

dp $=($A$/\backslash$pi $)=((\backslash$pi dL$\_$p$+2\backslash$pi $($d$^2/4))/\backslash$pi $)$

a$\_$c$=(6(1-))/$d$\_$p

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

X $=1-$e$^(-(($k$\_$c a$\_$c$)/$U$)$L$)$