A column packed with alumina initially contains pure cyclohexane liquid. At time zero a stream containing \(0.010 \mathrm{gmol} / \mathrm{L}\) of anthracene in cyclohexane is fed to an initially clean column at \(\mathrm{v}_{\text {super }}=30 \mathrm{~cm} / \mathrm{min}\). After 10 minutes, the first feed is replaced with a second feed that contains \(0.020 \mathrm{gmol} / \mathrm{L}\) anthracene in cyclohexane at \(\mathrm{v}_{\text {super }}=30 \mathrm{~cm} / \mathrm{min}\).

a. If the column length is \(\mathrm{L}_{1}=75 \mathrm{~cm}\), plot the anthracene outlet concentration profile.

b. If the column length is \(\mathrm{L}_{1}=150 \mathrm{~cm}\), plot the anthracene outlet concentration profile.

c. Suppose that for some unexplained reason you decide to linearize the isotherm at the value \(\mathrm{c}_{\mathrm{A}}=0.020\). At this concentration, the Langmuir form gives \(\mathrm{q}_{\mathrm{A}}=0.0512\). Then, in the linear form \(\mathrm{q}=\mathrm{Kc}, \mathrm{K}=0.512 / 0.02=2.56\). Resolve parts \(\mathrm{a}\) and \(\mathrm{b}\) with the linear isotherm. Compare your results with the results using the Langmuir isotherm. Data: See Examples 20-6 and 20-7.

Example 20-6

Example 20-7

A 100.0 cm long column is packed with activated alumina. Column is initially totally saturated at C = 0.011 mol/L anthracene in cyclohexane solvent. It is then eluted with pure cyclohexane solvent (C = 0) at a superficial velocity of 30.0 cm/min. Predict and plot outlet concentration profile using solute movement theory with the single porosity model. Data: = 0.42, Kd = 1.0, pf (cyclohexane) = 0.78 kg/L, Pp 22CA 1+375 CA = 1.465 kg/L, equilibrium q = where q mol anthracene/kg adsorbent and CA = mol anthracene/L solution. Assume operation is isothermal.