A feed stream $(200$ kg$/$h$)$ containing $20\%$ mass of acetone in water is extracted in a counter current extractor with a solvent containing $100\%$ MIBK. The ratio of solvent to feed is $0\mathrm{.}25$:$1.$

Calculate

$($i$)$ Calculate the number of stages required if acetone in Raffinate $($R$)$ phase is $5\%$ by mass.

$($ii$)$ Calculate the flow rates of Extract $($E$)$ and Raffinate $($R$).$

$($iii$)$ Show graphically the construction of stages and difference point

Please use the following ternary diagram for the calculations.