Acetone $($A$)$ containing $50$ wt$\%$ acetone in a continuous countercurrent extraction system $-$ MIK

$($Methyl isobutyl ketone$)($B$)$ is extracted from the mixture using acetone, water. Process,

the amount of acetone held by $1$ kg of solvent in the extract phase obtained, the amount of acetone that $1$ kg of solvent can hold

is carried out at $70\%$ of the maximum amount of acetone. Operation

slope of the line was determined as $0\mathrm{.}65.$ Methyl isobutyl ketone $($MIK$)$ and water in each other

Assuming no dissolution, find the theoretical number of equilibrium steps required for the process.

Equilibrium values of Acetone $($A$)-$ MIK $($B$)-$ Water $($S$)$ system under process conditions:

X $($kg A$/$kg B$)($Raffinate Phase$)0\mathrm{.}000\mathrm{.}100\mathrm{.}350\mathrm{.}350\mathrm{.}630\mathrm{.}911\mathrm{.}18$

Y $($kg A$/$kg S$)($Extract Phase$)0\mathrm{.}000\mathrm{.}050\mathrm{.}180\mathrm{.}350\mathrm{.}611\mathrm{.}00$