$3.$ Acetic acid is to be extracted from water with $3-$heptanol as the solvent in a countercurrent packed extraction column. Water and $3-$heptanol can be considered completely

immiscible. The equilibrium relationship is y $=0\mathrm{.}85$ x where y and x are the weight

fractions of the acetic acid in the extract and raffinate phases respectively. The feed

enters at a rate of $550$ lb$/$hr and contains $20$ wt$\%$ acetic acid. The desired concentration

in the raffinate is $5$ wt$\%.$ The pure solvent enters at a rate of $700$ lb$/$hr$.$

a$.)$ What is the composition of the extract? $($The answer is $0\mathrm{.}11,$ while Raffinate stream is $463\mathrm{.}157$ lb$/$hr$,$ extract is $786\mathrm{.}84$ lb$/$hr$).$

b$.)$ Using Numerical integration determine How many overall, raffinate phase transfer, units, NOX, are required?