An initially clean \(60.0 \mathrm{~cm}\) long column contains activated carbon. At \(t=0\), we feed a dilute aqueous solution of acetic acid \(\left(\mathrm{c}=0.010 \mathrm{kmol} / \mathrm{m}^{3}\right)\) at \(4^{\circ} \mathrm{C}\) in an upward direction. Superficial velocity of feed is \(15.0 \mathrm{~cm} / \mathrm{min}\). After a very long time ( \(1200 \mathrm{~min}\) ) and when the column is certainly totally saturated ( \(c=0.010\) everywhere), feed is stopped, flow direction is reversed, and the column is eluted with pure water at \(60^{\circ} \mathrm{C}\) at a superficial velocity of \(15.0 \mathrm{~cm} / \mathrm{min}\). This elution continues for another 1200 minutes.

Data: Equilibrium at \(4^{\circ} \mathrm{C}, \mathrm{q}=0.08943 \mathrm{c}\); equilibrium at \(60^{\circ} \mathrm{C}, \mathrm{q}=0.045305 \mathrm{c}\), with \(\mathrm{c}\) in \(\mathrm{kmol} / \mathrm{m}^{3}\) and \(\mathrm{q}\) in \(\mathrm{kmol} / \mathrm{kg}\) carbon; \(ho_{\mathrm{f}}=1000\) and \(ho_{\mathrm{s}}=1820.0 \mathrm{~kg} / \mathrm{m}^{3} ; \mathrm{K}_{\mathrm{d}}=1.0 ; \varepsilon_{\mathrm{e}}=0.434\); \(\varepsilon_{\mathrm{p}}=0.57 ;\) and \(\mathrm{C}_{\mathrm{Ps}}=0.25\) and \(\mathrm{C}_{\mathrm{Pf}}=1.00 \mathrm{cal} /\left(\mathrm{g}^{\circ} \mathrm{C}\right)\). Ignore wall heat capacity effects.

a. From \(t=0\) to 1200 minutes, predict outlet concentration profile (top of column).

b. Predict outlet concentration profile (bottom of column) for the 1200 minutes of elution.