The adsorption behavior of a solute is well correlated by Langmuir model with qmax$=200$ ug$/$mL and Ke$=8$ mL$/$mg$/.$

a$)$ Calculate the shock wave velocity for an injection of $2$ mg$/$mL into a $50$ cm in diameter column

with a void fraction of $0\mathrm{.}36$ run at $2$ mL$/$minute$.$ The length of the column is $20$ cm$.$

b$)$ For an injection volume of $6$L calculate the elution profile $($conditions are the same as in part a$)$