Fermentation broth enters a continuous mixer settler extraction unit at a flow rate of $100$ L$/$min$.$ This contains $20$ g$/$L antibiotic and its pH has been adjusted to $3\mathrm{.}0.$ Butyl acetate which is used as the extracting solvent enters the extractor at a flow rate of $10$ L$/$min$.$ At pH $3\mathrm{.}0$ the equilibrium relationship is given by CE $=40$CR$,$ where CR and CE are the antibiotic concentrations in the raffinate and extract respectively and are expressed in g$/$L$.$

Calculate:

a$)$ The antibiotic concentration in the extract and the raffinate.

b$)$ The fraction of antibiotic extracted.

The organic extract from the first extraction step enters a second continuous mixer settler extraction unit. An aqueous extracting solvent phase at pH $7\mathrm{.}0$ is fed into this extractor at a flow rate of $5$ L$/$min$.$ At pH $7\mathrm{.}0,$ the equilibrium relationship is given by CE $=37$CR $,$ where CE is the antibiotic concentration in the aqueous extract phase while CR is the concentration in the organic raffinate phase.

Calculate:

c$)$ The concentration of the antibiotic in the extract and raffinate from second extraction.

d$)$ The overall fraction of antibiotic extracted.