The thickness of the liquid film, if the Film theory is applicable. H$./$ The contact time between the liquid with the gas if the Penetration theory is applicable.

A magnetic stirrer agitated vessel is used to absorb CO$2$ in water at $298$ K and $2$

atm pressure. Water is fed at a rate of $1$ L$/$min$,$ and the carbonated water leaves the vessel continuously so that a constant volume is maintained in the contactor. The outlet water contains $2\mathrm{.}3,$g CO$/$L$.($The interfacial area of gas$-$liquid contact is $80$ m$^2/$ m$^2$; the volume of gas$-$Iigud dispersion is$8$L The solubility of CO$2$ in water can be found using Henry's law. At $298$ K$,$ Henry's law constant for CO$2$ is $1640$ atm$/$mole fraction, and its diffusivity in water is$,1\mathrm{.}92$x$10$ m$/$s$.$ The density of the liquid is $997$ kg$/^2.$Calculate:

i$$i$/$ The surface renewal rate if the Surface$-$renewal theory is applicable.