An ion exchange column is used to capture a protein from a very dilute solution. Band broadening is controlled by intraparticle pore diffusion. The adsorption isotherm is essentially rectangular. The adsorption capacity is very high. Be as quantitative as possible in answering the following questions. Include sketches of the breakthrough curves for each case.

a. What happens to the time at which the mid point of the breakthrough curve exits the column if the feed concentration is halved?

b. What happens to the time at which the mid point of the breakthrough curve exists the column if the particle size is halved but the adsorption isotherm and column size stay the same?