The equilibrium for extraction of acetic acid from water into 3heptanol at \(25^{\circ} \mathrm{C}\) is \(\mathrm{y}=0.828 \mathrm{x}\), where \(\mathrm{y}\) is weight fraction acetic acid in 3-heptanol and \(x=\) weight fraction acetic acid in water. \(400 \mathrm{~kg} / \mathrm{h}\) of feed with \(\mathrm{x}_{0}=0.5 \mathrm{wt} \%\) acetic acid and \(99.5 \mathrm{wt} \%\) water is contacted in a countercurrent extractor with \(\mathrm{E}=560 \mathrm{~kg} / \mathrm{h}\) of solvent that is \(\mathrm{y}_{\mathrm{N}+1}=\) \(0.01 \mathrm{wt} \%\) acetic acid and \(99.99 \mathrm{wt} \%\) 3-heptanol. Outlet raffinate concentration is \(\mathrm{x}_{\mathrm{N}}=0.03 \mathrm{wt} \%\) acetic acid and \(99.97 \mathrm{wt} \%\) water. Assume water and 3-heptanol are immiscible and that \(\mathrm{R}\) and \(\mathrm{E}\) are constant.

a. Determine number of equilibrium stages \(\mathrm{N}\) required.

b. What is minimum solvent flow rate, \(\mathrm{E}_{\text {min }}\) ?