SMITH CHEMICAL ENGINEERING KINETICS.

$12-2$ A tank reactor and separator $($Fig$.12-6)$ are used to study the heterogeneous reaction between pure liquid $A($phase $1)$ and reactant $B$ dissolved in phase $2($also liquid$).$ The solvent in phase $2,$ reactant $B,$ and the products of reactior are all insoluble in liquid $A.$ No reaction occurs in the separator. The reacton operates isothermally at $25C,$ and at this temperature A has a limited solubility in phase $2,$ the value being $2\mathrm{.}7{10}^{-5}g$ mole$/$liter$.$ Phase $2$ is dispersed as bubbles in continuous phase $1,$ which is recycled. There is excellent stirring in the reactor, but the tluid motion within the bubbles of phase $2$ is insufficient to prevent some mass$-$transfer resistance. From independent measurements it is estimated that at average conditions the reaction resistance within the bubbles is $75\%$ of the total resistance $($mass$-$transfer plus reaction resistance$)$

$($a$)$ Derive a relationship between the concentration of reactant $B$ entering

the reactor in phase $2$ and the concentration leaving the separator.

$($b$)$ In one experiment the following data were obtained:

Feed rate of phase $2=0\mathrm{.}2\frac{c{m}^3}{sec}$

Total liquid volume in reactor $=1,500c{m}^3$

Fraction of volume in dispersed phase in reactor $=24\%$

Conctentration of $B$ entering reactor ia phase $2=0\mathrm{.}02g$ mole$/$liter

Concentration of $B($in phase $2)$ leaving irparator $=0\mathrm{.}0125g$ mole firer

Calculate the rave constant $k$ for the socond$-$order irreversible resction of the

form

$A+BP$

Assume that the average value of the reaction resistance may be used and that

equilibrium exists at the interface betwetn plase $1$ and phase $2$