In Example 19-3, why is it better to guess (theta) instead of (F_{p}) ? Example 19-3 A

In Example 19-3, why is it better to guess \(\theta\) instead of \(F_{p}\) ?

Example 19-3

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A perfectly mixed GP unit is separating a mixture that is 20.0 mol% carbon dioxide, 5.0 mol% oxygen, and 75.0 mol% nitrogen using a poly(dimethylsiloxane) membrane at 25.0C. Feed flow rate Fin = 20,000 cm (STP)/s. Membrane thickness is 1.0 mil (0.00254 cm). Feed pressure is 3.0 atm, and permeate pressure is 0.40 atm. Membrane area = 150.0 m. Find cut 0 = Fp/Fin and the outlet mole fractions of permeate and retentate.