Water at $25\backslash$deg C flows through a bed of benzoic acid spheres of size dp$=8$ mm at a superficial velocity of

$0\mathrm{.}022$ m$3$

per second per square meter of bed cross$$section$.$ The fractional void volume of the bed is $0\mathrm{.}4$

and the depth of the acid is $0\mathrm{.}7$ m$.$ If the inlet water is free from benzoic acid, calculate the mass transfer

coefficient in terms of the area for mass transfer per unit volume of packed bed a $($kLa$).$

The following data are available: diffusivity of benzoic acid in water $=105$ cm$2$

$/$s$,$ kinematic viscosity of

the liquid $=0\mathrm{.}95$ cSt$,$ solubility of benzoic acid in water at the given temperature $=3\mathrm{.}01$ kg$/$m$3$