CHE425: Problem set #21. A 3-ft depth of stagnant water at 25oC lies on top of a 0.10-in. thickness of NaCl. At time t< 0, the water is pure. At time t = 0, the salt begins to dissolve into the water. If theconcentration of salt in the water at the solid-liquid interface is maintained at saturation(0.00544 mol NaCl/cm3) and the diffusivity of NaCl is 1.2×10-5 cm2/s, independent ofconcentration, estimate, by assuming the water to act as a semi-infinite medium, the time andof salt in the water when: (a) 10% of the salt has dissolved; (b) 50% of the salt has dissolved;and (c) 90% of the salt has dissolved. Density of NaCl = 2.165 g/cm3. Molecular weight ofNaCl = 58.44 g/mol.Part Moles transferred Time, s Time, h(a) 10% transferred 0.000941 1,960 0.544(b) 50% transferred 0.004705 48,900 13.6(c) 90% transferred 0.008469 159,000 44.02. A slab of dry wood of 4-inch thickness and sealed edges is exposed to air of 40% relativehumidity. Assuming that the two unsealed surfaces of the wood immediately jump to anequilibrium moisture content of 10 lb H2O per 100 lb of dry wood, determine the time for themoisture content at the center of the slab to reach 1% of the equilibrium value. Assume adiffusivity of water of 8.3×10-6 cm2/s. x t, s Time, h0.01 1.82 234,000 653) Dry air at 1 atm flows at 2 m/s across the surface of a 2-inch-long surface that is coveredwith a thin film of water. If the air and water are at 25oC and the diffusivity of water in air is0.25 cm2/s, estimate the water flux in kmol/sm2 for the evaporation of water at the middle ofthe surface, assuming laminar boundary-layer flow. Air at 25oC,  = 0.018 cP = 1.8 x 10-5kg/m-s.2H O5 2(0.016)[0.00128 0 2.05 10 kmol/s-] m-= - = �nA4. Air at 1 atm and 100oC flows across a thin, flat plate of subliming naphthalene that is 1 mlong. The Reynolds number at the trailing edge of the plate is at the upper limit for a laminarboundary layer. Estimate: (a) the average rate of sublimation in kmol/sm2; and (b) the localrate of sublimation 0.5 m from the leading edge. Vapor pressure of naphthalene = 10 torr;viscosity of air = 0.0215 cP; molar density of air = 0.0327 kmol/m3; and diffusivity ofnaphthalene in air = 0.94×10-5 m2/s.Solutionn AA,B2 kmol / s - m/ . . .     0 0059 4 3 10 0 2 54 102 4ch( ) ( )( )2A A4 2A,B0.00417 4.3/ 1.79 10 km10 ol/s m0 ---� �= - = � - = �� �xci okn c cA5. Water at 25oC flows turbulently at 5 ft/s through a straight, cylindrical tube cast frombenzoic acid, of 2-in inside diameter. If the tube is 10 ft long, and fully developed, turbulentis assumed, estimate the average concentration of acid in the water leaving the tube. Theproperties are: solubility of benzoic acid in water = 0.0034 g/cm3; viscosity of water = 0.89cP = 0.0089 g/cms; and diffusivity of benzoic acid in water at infinite dilution = 9.18×10-6cm2/s.outA(0.00367)(4,870)=0.0034 1 exp(152)(20.2 = 0.00005)20 � �� �- -� �� �� �� �cg/cm3Therefore, the concentration of benzoic acid in the exiting water is way below the solubility value.6.2 Air at 1 atm flows at a Reynolds number of 50,000 normal to a long, circular, 1-indiameter made of naphthalene. Calculate the average sublimation flux in kmol/sm2. Vaporpressure of naphthalene = 10 torr; viscosity of air = 0.0215 cP; molar density of air = 0.0327kmol/m3; and diffusivity of naphthalene in air = 0.94×10-5 m2/s.( )4A A5A(0.080)(4.3 10 3.44 10) 0�--= - = =- ��sckN c c kmol/s-m27. Carbon dioxide is stripped from water by air in a wetted-wall tube. At a location wherepressure is 10 atm and temperature 25oC, the flux of CO2 is 1.62 lbmol/hft2. The partialpressure of CO2 is 8.2 atm at the interface and 0.1 atm in the bulk gas. The diffusivity of CO2in air at these conditions is 1.6×10-2 cm2/s. Assuming turbulent flow, calculate by film theorythe mass-transfer coefficient kc for the gas phase and the film thickness.( )(0.00022)(0.475)(0.000409) 0.82 0.010.315=-=ck cm/s = DAB / kc = 1.6 x 10-2/0.315 = 0.051 cm8. Water is used to remove CO2 from air by absorption in a column packed with Pall rings. Ata region of the column where the partial pressure of CO2 at the interface is 150 psia and theconcentration in the bulk liquid is negligible, the absorption rate is 0.017 lbmol/hft2. TheCO2 diffusivity in water is 2.0×10-5 cm2/s. Henry’s law for CO2 is p = Hx, where H = 9,000psia. Calculate by film theory the mass-transfer coefficient kc in cm/s for the gas phase andthe film thickness in cm.( )62.31 10(0.0556) 0.0167 00.0025-=�=-ck cm/s = DAB /kc = 2 x 10-5/0.0025 = 0.0080 cmRef: J. D. Seader and E. J. Henley, Separation Process Principles , Wiley,