Problem $2[25$ points$].$

A mixture of albumen and lysozyme is separated by a column chromatography with a $1m$ length,

which is filled with $500$ grams of resins. The resin having a $1\mathrm{.}2\frac{g}{c}{m}^3$ density and $0\mathrm{.}5$ fractional

participle porosity $(E_p=0\mathrm{.}5).$ Assume the resin has cylindrical pores and an average pore diameter

is $25A({10}^{-10}(m)).$ Albumin peak is detected after $5,000$ seconds having a width of $600$ seconds

and a $0\mathrm{.}3$ absorbance peak $(C_{\text{m}\text{a}\text{x}}).$ Lysozyme peak is detected after $5,500$ seconds having a width

of $800$ seconds and a $0\mathrm{.}8$ absorbance peak $(C_{\text{m}\text{a}\text{x}}).$ Both peaks follow Gaussian distribution with

standard deviations.

$2\mathrm{.}1.$ What were the individual velocities of albumen and lysozyme?

$2\mathrm{.}2.$ What is the resolution?

$2\mathrm{.}3.$ What is the mass fraction of albumin in the feed mixture?

$($Assume there exist only albumin and lysozyme proteins in the feed.$)$