$$

The equilibrium for acetic acid extraction from $3-$heptanol into water at $25C$ is $y=1\mathrm{.}208x,$ where $y$ is the weight fraction of acetic acid in water and $x$ is the weight fraction of acetic acid in $3-$heptanol. We have a feed with $F=R=100k\frac{g}{h}$ that is $x_0=0\mathrm{.}005wt$ frac acetic acid and $0\mathrm{.}995wt$ frac $3-$heptanol. This feed is contacted in a counter$-$current extractor with a solvent that is $y_{N+1}=0\mathrm{.}0002wt$ frac acetic acid and $0\mathrm{.}9998wt$ frac water. We desire an outlet raffinate concentration of $x_{NA}=0\mathrm{.}0005wt$ frac acetic acid and $0\mathrm{.}9995wt$ frac $3$heptanol. Assume water and $3-$heptanol are immiscible and that R and E are constant.

a$.$ If solvent flow rate $E=140k\frac{g}{h},$ calculate the exiting extract $wt$ frac $y_1$ andf determine the number of equilibrium stages $N$ required.

b$.$ What are the minimum solvent flow rate $(E_{\text{m}\text{i}\text{n}}),$ and the maximum exiting extract wt fraction.

c$.$ This question and Question $2$ in the $"$IE Tutorial" are for the same system, but $y=1\mathrm{.}208x$ in one problem and $y=0\mathrm{.}828x$ in the other problem. Explain why.