In order to extract acetic acid from a dilute aqueous solution with isopropyl ether, the two immiscible phases are passed counter$-$currently through a packed column $3m$ in length and $75mm$ in diameter. It is found that if $0\mathrm{.}5k\frac{g}{m^2}.s$ of the pure ether is used to extract $0\mathrm{.}25k\frac{g}{m^2}.s$ of $4\mathrm{.}0$ per cent acid by mass, then the ether phase leaves the column with a concentration of $1\mathrm{.}0$ per cent acid by mass. Calculate:

a$)$ the number of overall transfer units, based on the raffinate phase, and

b$)$ the overall extraction coefficient, based on the raffinate phase.

The equilibrium relationship is given by:

acid $\frac{?}{kg}$ isopropyl ether