Benzene and trimethylamine (TMA) are to be separated in a three-equilibrium-stage liquid–liquid extraction column using pure water as the solvent. If the solvent-free extract and raffinate products are to contain, respectively, 70 and 3 wt% TMA, find the original feed composition and the water-to-feed ratio with a right-triangle diagram. There is no reflux. Equilibrium data are as follows:

The tie-line data are:

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TRIMETHYLAMINE-WATER-BENZENE COMPOSITIONS ON PHASE BOUNDARY ΤΜΑ 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 Extract, wt% H₂O 94.6 89.4 84.0 78.0 72.0 66.4 58.0 47.0 Benzene 0.4 0.6 1.0 2.0 3.0 3.6 7.0 13.0 ΤΜΑ 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 Raffinate, wt% H₂O 0.0 0.0 1.0 2.0 4.0 7.0 15.0 34.0 Benzene 95.0 90.0 84.0 78.0 71.0 63.0 50.0 26.0