Question $1$

Water at $25C$ flows through a bed of benzoic acid spheres of size $d_p=8mm$ at a superficial velocity of

$0\mathrm{.}022m^3$ 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 $0\mathrm{.}7m.$ 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 $(\{$:$k_{\text{l}\text{l}\text{c}\text{o}\text{r}\text{n}\text{e}\text{r}}a).$

The following data are available: diffusivity of benzoic acid in water $={10}^{-5}c\frac{m^2}{s},$ kinematic viscosity of

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