Problem $1$

The first$-$order, irreversible reaction $(AB)$ takes place in a $0\mathrm{.}30cm$ radius spherical catalyst pellet

at $T=450K.$ At a partial pressure of $A$ of $\frac{0\mathrm{.}70}{b}ar,$ the production rate of $B$ is $2\mathrm{.}510-5mo\frac{l}{gs}.$

Ignore external mass transfer limitations$.$

The catalytic pellet density is ${}_c=0\mathrm{.}85\frac{g}{c}{m}^3$

The effective diffusivity of $A$ in the pellet is $D_{A,\text{e}\text{f}\text{f}}=0\mathrm{.}0070c\frac{m^2}{s}.$

a$)$ Determine the reaction rate constant $k($in $s^{-1})$

b$)$ Determine the increase in production rate $($in $\%)$ if the pellet radius is halved.