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 $y=0\mathrm{.}85x$ 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 $550l\frac{b}{h}r$ and contains $20wt\%$ acetic acid. The desired concentration in the raffinate is $5wt\%.$ The pure solvent enters at a rate of $700l\frac{b}{h}r.$

a$.)$ What is the composition of the extract?

b$.)$ How many overall, raffinate phase transfer, units, Nox, are required?