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 streams (x₁, x₂)
3. Graphically estimate the concentration in g/kg of Z in the exiting extract streams (y₁,y₂)