In an experimental agitated contactor pure

carbon dioxide is being absorbed in water at $25C$

and $2$atm presure. Water is pumped into the

contactor at a rate of $1$ liter per minute.

Water is pumped into the

contactor at a rate of

$1$ litre per minute and

the carbonated water

leaves the vessel

continuously so that

a constant volume

is maintained in the

contactor. The ontlet

water contains $2\mathrm{.}3g$

$C{O}_2$ per liter. The specific area of gas$-$liquid contact

is $80\frac{m^2}{m^3}$ of the gas$-$liquid dispersion;

the volume of gas$-$liquid dispersion is $8$ litres. The liquid

phase can be assumed to be well mixed. The solubility

of $C{O}_2$ in water can be calculated using Henry's$/$aw$.$

At $25C,$ the Henry's law constant for $C{O}_2$ is

$1640\frac{\text{a}\text{t}\text{m}}{\text{m}\text{o}\text{l}\text{f}\text{r}\text{a}\text{c}\text{t}\text{i}\text{o}\text{m}}$ and its diffusivity in water is

$1\mathrm{.}92{10}^{-9}\frac{m^2}{s}.$ Calculate

$($a$)$ thickness of the liquid film if the film theory is applicable.

$($b$)$ the contact time betweren a liquid element with the

gas if the penetration theory is applicable.

$($c$)$ the fractional renewal rate if surface renewal

theory is applicable.