Penicillin is extracted from the aqueous fermentation broth based on a liquid$-$liquid

extraction process. The process uses the fact that penicillin is more soluble in organic

solvents compared to water at low $pH(2-3)$ while it is more soluble in water than organic

solvents at high pH $(8-9).$ Therefore, multiple liquid$-$Liquid extraction steps are used to

improve the purity of the penicillin. The heavy phase flow $(H,$ Containing the penicillin$)$

is $100\frac{L}{m}in$ and the light phase flow $(L)$ is $10\frac{L}{m}in.$ The distribution coefficient

between the light and heavy phases is $50.$ The penicillin concentration is $20\frac{g}{L}$ and it

must be reduced to $0\mathrm{.}1\frac{g}{L}$ in the heavy phase $($fermentation broth$)$ after extraction. $(10$

points$)$

a$.$ What is the extraction factor, $E?$

b$.$ What is the rejection coefficient, $R?$

c$.$ How many stages $(N)$ will be required to reduce the penicillin concentration to $0\mathrm{.}1$

g$/$L$?$

d$.$ Imagine that the fermentation broth contains impurities at $10\frac{g}{L}$ concentration. The

light phase also extracts the impurities. The selectivity coefficient $(\frac{K_{\text{p}\text{e}\text{n}\text{i}\text{c}\text{i}\text{l}\text{i}\text{n}}}{K_{\text{i}\text{m}\text{p}\text{u}\text{r}\text{i}\text{t}\text{i}\text{e}\text{s}}})$

is $2\mathrm{.}0.$ Estimate the concentration of the impurities in the final light phase after

extraction using the same number of stages as you determined in part $c$ of this

question?

e$.$ If the selectivity coefficient changes to $20($i$.$e$.$ it is a highly selective solvent for

penicillin$)$ instead of $2\mathrm{.}0,$ what is the concentration of the impurities in the light phase

after extraction?

$K_D=\frac{Y_L}{x_H},{}_{ij}=\frac{K_i}{K_j}$

$E=\frac{L{K}_D}{H},R=\frac{E(E^N-1)}{(E-1)}$