An aqueous process stream of 100 gal/h at 20°C contains 8 wt% Na₂SO₄ and 6 wt% of a high-molecular-weight substance (A). This stream is processed in a continuous countercurrent-flow dialyzer using a pure water sweep of the same flow rate. The membrane is a microporous cellophane with pore volume  50%, wet thickness 0.0051 cm, tortuosity  4.1, and pore diameter  31A. The molecules to be separated have the following properties:

Calculate the membrane area in m² for only a 10% transfer of A through the membrane, assuming no transfer of water. What is the % recovery of the Na₂SO₄ in the diffusate? Use log-mean concentration-driving forces and assume the mass-transfer resistances on each side of the membrane are each 25% of the total mass-transfer resistances for Na₂SO₄ and A.

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Molecular weight Molecular diameter, Å Diffusivity, cm²/s x 105 Na₂SO4 142 5.5 0.77 A 1,000 15.0 0.25