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We wish to extract organic compound Z from an aqueous reaction mixture. Pure extraction solvent E (with no residual amount of Z) at 1 kg/hr is to be added into two single-stage mixer settler tank combinations (in cross-flow mode) as shown in the figure. The aqueous feed stream is entering the cascade at 2 kg/hr and contains 0.8 g solute Z per kg diluent solution. Derive the generic operating line for this cross-flow system. Using a distribution coefficient of 8.333 (y/x=weight fraction of Z in E/ weight fraction of Z in aqueous phase) plot the equilibrium line in Excel or Matlab and answer the following questions:

1. Determine the slope of the operating line (both operating lines have the same slope since the flow rates of E and R are constant)
2. Graphically estimate the concentration in g/kg of Z in the exiting diluent stream of tank 1 (x1) & tank 2 (x2)
3. Graphically estimate the concentration in g/kg of Z in the exiting extract stream of tank 1 (y1) & tank 2 (y2)

R=2 kg/h Xin=0.8 E=1 kg/h 1 Y1 Vin=0 X Ez=1 kg/h 2 Y2 Yin=0 X2