Water at $20$oC flows at a rate of $5\mathrm{.}5$ x $10-7$ m$3/$s through a packed bed of

benzoic acid particles in a column with an inner diameter of $2\mathrm{.}5$ inches.

The particles are spheres with a diameter of $$ inches, the bed voidage is

$0\mathrm{.}40$ and the surface area of the particles is $0\mathrm{.}1$ m$2.$ The solubility of

benzoic acid in water is $2\mathrm{.}948$ x $10-2$ kg mol$/$m$3.$ The diffusivity of benzoic

acid in water at $25$oC is $1\mathrm{.}21$ x $10-9$ m$2/$s$.$ The density of water at $20$oC is

$998\mathrm{.}2$ kg$/$m$3$ and its viscosity is $1$ x $10-3$ Pa s$.$

Determine the concentration of benzoic acid exiting this packed bed column