$(25$pts$)$

$2.$ Consider a $2-$stage $($mixer$-$settlen$)$ solvent extraction arrangement, as shown.

The organic $($org$)$ feed solution contains $3\mathrm{.}0$ moles$/$liter $U($hexavalent$)$ and $0\mathrm{.}1$ moles$/$liter tetravalent $)$ ions. The aqueous $($aq$)$ nitric acid solution does not contain any solutes but contains a reducing agent that reduces the tetravalent $Pu$ to trivalent $(P{u}^{3+})$ while keeping $U$ as hexavalent. $P{u}^3$ is relatively inextractable; so that most of the Pu in the organic feed is washed to the aqueous raffinate phase, and thus, $U$ and $Pu$ are partitioned. Flow rates into and out of the system are equa and remain constant.

Distribution coefficients are, for each stage:

$D(U)=8$

$D(P{u}^{3+})=0\mathrm{.}2.$

For this U$-$Pu partitioning process:

a$)$ Calculate $U$ and $Pu$ concentrations in the organic product and aqueous raffinate phas

b$)$ Determine the Partitioning Factor $($PF$),$ which can be defined as:

$PF=\frac{\text{R}\text{e}\text{c}\text{o}\text{v}\text{e}\text{r}\text{y}ofU\text{i}\text{n}\text{t}\text{o}\text{t}\text{h}\text{e}\text{o}\text{r}\text{g}\text{a}\text{n}\text{i}\text{c}\text{p}\text{r}\text{o}\text{d}\text{u}\text{c}\text{t}}{\text{R}\text{e}\text{c}\text{o}\text{v}\text{e}\text{r}\text{y}ofPu\text{i}\text{n}\text{t}\text{o}\text{t}\text{h}\text{e}\text{o}\text{r}\text{g}\text{a}\text{n}\text{i}\text{c}\text{p}\text{r}\text{o}\text{d}\text{u}\text{c}\text{t}}$