Equilibrium for extraction of acetic acid from 3-heptanol into water at \(25^{\circ} \mathrm{C}\) is \(\mathrm{y}=1.208 \mathrm{x}\), where \(\mathrm{y}=\) weight fraction acetic acid in water and \(\mathrm{x}=\) weight fraction acetic acid in 3-heptanol. \(100 \mathrm{~kg} / \mathrm{h}\) of feed with \(\mathrm{x}_{0}\) \(=0.005\) is contacted in a countercurrent extractor with solvent with \(\mathrm{y}_{\mathrm{N}+1}=0.0002\). Outlet raffinate concentration is \(\mathrm{x}_{\mathrm{N}}=0.0005\). Assume water and 3 -heptanol are immiscible and that \(\mathrm{R}\) and \(\mathrm{E}\) are constant. Note that parts \(\mathrm{a}, \mathrm{b}\), and \(\mathrm{c}\) can be solved independently, or value of \(\mathrm{y}_{1}\) from part a can be used in part \(b\).

a. If solvent flow rate \(\mathrm{E}=140 \mathrm{~kg} / \mathrm{h}\), calculate exiting extract weight fraction \(y_{1}\).

b. If solvent flow rate \(\mathrm{E}=140 \mathrm{~kg} / \mathrm{h}\), determine number of equilibrium stages \(\mathrm{N}\).

c. What are minimum solvent flow rate and maximum exiting extract weight fraction?

d. Problems 13.D5 and 13.D6 are for same system, but \(\mathrm{y}=1.208 \mathrm{x}\) in one problem and \(y=0.828 x\) in the other problem. Explain why.

Data From Problems 13.D5

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, \(\mathrm{E}_{\text {min }}\) ?