A concentrated brine solution (aqueous sodium chloride) contains magnesium as an impurity. A membrane with surface...

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A concentrated brine solution (aqueous sodium chloride) contains magnesium as an impurity. A membrane with surface area 106 m² is used to remove 75% of the impurity, but also removes some sodium chloride. The feed contains spherical NaCl(s) crystals with a diameter of 350 nm. As the salt crystals flow through the membrane with thickness, Im, they dissolve to maintain a saturated solution (S = 1). The feed side is maintained at constant NaCl solubility (Ksp = 102 kmol/L², y₁ = 1.0). Given the diagram below, calculate (i) the molar flow rate of Na* and CI in the permeate and (ii) the size of NaCl crystals in the retentate (assume the total number of crystals is constant). De,Mg²+ = 5.3 x 10-⁹ m²/hr De,Na+ = De,Cl- = 2.7 x 10-⁹ m²/hr NaCl(s) 110 kmol/hr Soluble Na+ (aq), Cl(aq) Mg2+ (aq) 40 kmol/hr Feed H₂O = 300 L/hr Pure H₂O H₂O = 300 L/hr NaCl S=1 Membrane O O O Retentate H₂O=300L/hr Permeate H₂O = 300 L/hr NaCl(s) = ? Soluble Nat (aq), Cl(aq) Mg2+ (aq) 10 kmol/hr Na+ (aq)=Cl(aq) = ? Mg2+ (aq)= 30 kmol/hr A concentrated brine solution (aqueous sodium chloride) contains magnesium as an impurity. A membrane with surface area 106 m² is used to remove 75% of the impurity, but also removes some sodium chloride. The feed contains spherical NaCl(s) crystals with a diameter of 350 nm. As the salt crystals flow through the membrane with thickness, Im, they dissolve to maintain a saturated solution (S = 1). The feed side is maintained at constant NaCl solubility (Ksp = 102 kmol/L², y₁ = 1.0). Given the diagram below, calculate (i) the molar flow rate of Na* and CI in the permeate and (ii) the size of NaCl crystals in the retentate (assume the total number of crystals is constant). De,Mg²+ = 5.3 x 10-⁹ m²/hr De,Na+ = De,Cl- = 2.7 x 10-⁹ m²/hr NaCl(s) 110 kmol/hr Soluble Na+ (aq), Cl(aq) Mg2+ (aq) 40 kmol/hr Feed H₂O = 300 L/hr Pure H₂O H₂O = 300 L/hr NaCl S=1 Membrane O O O Retentate H₂O=300L/hr Permeate H₂O = 300 L/hr NaCl(s) = ? Soluble Nat (aq), Cl(aq) Mg2+ (aq) 10 kmol/hr Na+ (aq)=Cl(aq) = ? Mg2+ (aq)= 30 kmol/hr