A test column containing $2$m depth of $50$mm Raschig rings is used to separate CO$2$ from an air stream at $25$ C and $1$ atm pressure to recover $90\%$ of the CO$2.$ The gas stream contains $18\%$ CO$2$ and is fed at $10$ m$3$s$-1$ to the column. It is scrubbed with pure water.

$1)$ Given the Henry$$s constant for CO$2$ in water is $1680$ on a mol fraction basis

which film is controlling the separation and is the choice of a packed column

appropriate?

$2)$ Calculate the minimum water flow rate needed to achieve this separation.

$3)$ The column is operated at $3$ times the minimum flowrate. Calculate the HTU

for this arrangement.

$4)$ From the HTU, explain in detail, how you would calculate the mass transfer

coefficient.