$(40$ points$)$ Component I in an aqueous media is purified using a chromatography column in

length $2\mathrm{.}5cm$ in diameter$)$ packed with $75m$ diameter porous particles with a bed porosity of $0\mathrm{.}38.$

The partition coefficient for I is $0\mathrm{.}5.$ The retention time and base width data obtained for three different

linear velocities of the eluent are as follows:

$($a$)$ Determine the constants of the Van Deemter Equation and plot the height of theoretical plate as a

function of linear velocity. Determine the optimum linear velocity and minimum height of

theoretical plate graphically and compare it to the result obtained from Example $4-3.$

$($b$)$ Calculate the number of theoretical plates for a linear velocity of $2c\frac{m}{m}in.$