A size exclusion chromatograph has \(\varepsilon_{\mathrm{e}}=0.42, \varepsilon_{\mathrm{p}}=0.7, \mathrm{~K}_{\mathrm{d}}=1.0\) for sugars, and \(\mathrm{K}_{\mathrm{d}}=0\) for proteins. There is no adsorption ( \(\mathrm{q}=\mathrm{Kc}, \mathrm{K}=0\) ). Column has length \(\mathrm{L}=1.0 \mathrm{~m}\), diameter \(\mathrm{d}\) \(=0.1 \mathrm{~m}\), and volumetric flow rate \(\mathrm{Q}=0.4 \mathrm{~L} / \mathrm{min}\). Feed pulse starts at \(\mathrm{t}=0\) and continues for \(\mathrm{t}_{\mathrm{F}}=5 \mathrm{~min}\), and then is followed by water at same flow rate.

a. At what time does protein first exit, and when is it finished exiting? At what time does sugar first exit, and when is it finished exiting?

b. At what time can we input the second feed pulse and have the same separation between first and second pulses as between protein and sugar in first pulse?

c. If sugar adsorbs (protein does not) with isotherm \(\mathrm{q}=\mathrm{Kc}\) with \(\mathrm{q}\) and \(\mathrm{c}\) in \(\mathrm{g} / \mathrm{L}\) and \(\mathrm{K}_{\text {sugar }}\) \(=0.73\), is the second feed pulse still separated from the \(1^{\text {st }}\) ?