Adsorption of anthracene from cyclohexane on activated alumina follows a Langmuir isotherm, \(\mathrm{q}=22 \mathrm{c} /(1+375 \mathrm{c})\), where \(\mathrm{c}\) is in mol anthracene/L and \(\mathrm{q}\) is in mol anthracene \(/ \mathrm{kg}\) adsorbent. A \(40.0 \mathrm{~cm}\) long column is initially clean \((c=0, \mathrm{q}=0)\). A feed that is \(\mathrm{c}_{\text {feed }}=0.0008\) is fed at \(\mathrm{t}=0\) until column is totally saturated. Superficial velocity is 16.0 \(\mathrm{cm} / \mathrm{min}\). Data: See Examples 20-6 and 20-7.

a. How long does it take to saturate column (what is breakthrough time)?

b. Saturated column is eluted with pure cyclohexane at a superficial velocity of 20.0 \(\mathrm{cm} / \mathrm{min}\). Reset \(\mathrm{t}=0\) and predict times it takes for anthracene concentrations of 0.0008 \(\mathrm{mol} / \mathrm{L}, 0.0004 \mathrm{~mol} / \mathrm{L}\), and \(0.0000 \mathrm{~mol} / \mathrm{L}\) to exit column.

Example 20-6

Example 20-7

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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.