_______________________ Last Name, First CHE425: Problem set #11. The gas CO2 is diffusing at steady state through a tube 0.20 m long having a diameter of0.01 m and containing N2 at 298oK. The total pressure is constant at 101.32 kPa. The partialpressure of CO2 at one end is 456 mmHg and 76 mm Hg at the other end. The diffusivity DABis 1.67×10-5 m2/s at 298oK. Calculate the flux of CO2 in cgs and SI units for equimolarcounterdiffusion.2. Helium and nitrogen gas are contained in a conduit 5 mm in diameter and 0.1 m long at298oK and a uniform constant pressure of 1.0 atm abs. The partial pressure of He at one endof the tube is 0.060 atm and 0.020 atm at the other end. The diffusivity of Helium in nitrogenat 298oK is 6.87×10-5 m2/s. Calculate the following for steady-state equimolarcounterdiffusion.a) Flux of he in kmol/s∙m2.b) Flux of N2.c) Partial pressure of He at a point of 0.05 from either end.3. A long glass capillary tube, of diameter 0.01 cm, is in contact with water at one end anddry air at the other. Water vapor evaporates at the wet end within the capillary, and the vapordiffuses through the capillary toward the dry end. How long is required for one gram of waterto evaporate through this system? The vapor pressure of water is 17.5 mmHg at 20oC, thetemperature at which the entire system is maintained. Take the diffusivity of water vapor inair at 20oC to be 0.3 cm2/s, and assume that the dry air is at a pressure of 760 mmHg. Assumethat the distance from the wet interface within the capillary to the dry end is always 10 cm.Gas constant R = 82.057 cm3atm/(molK)4.2Find the initial evaporation rate of water, in units ofcentimeters per second of surface velocity, for the Arnold celloperating at 1 atm and 25oC as shown. The inside diameter of thetube is 1 mm. Dry air is blow over the top of the tube. Thesaturated humidity of water in air at 25oC is 0.0189 lb H2O/lb dryair. Diffusivity of water vapor in air at 25oC is 0.22 cm2/s.5.2 A process is carried out under ultrahigh vacuum in a reactor whose walls are a glass tubeof inside diameter 10 cm and wall thickness 1 cm. We do not want H2 to “leak” across thetube wall by diffusion and there by reduce the quality of the vacuum environment for theprocess. The diffusivity of H2 in glass at the process temperature, 700oK, is 10-8 cm2/s. Themolar solubility ratio of H2 in glass is 0.2 (mol/cm3) H2 in glass/(mol/cm3) H2 in air. Supposethe tube is one meter long, and the end plates and fittings of the tube are impermeable tohydrogen. Suppose further that at some instant of time the vacuum pump had bought thesystem to a pressure of 10-6 torr. The glass tube is surrounded by atmospheric air, and thepartial pressure of hydrogen in air is 3.810-4 torr. Estimate the partial pressure of H2 insidethe glass tube after 1 hour.Pure water10 cm6.2 A liquid A evaporates at one end of a capillary tube and the vapor diffuses toward theother end, which is open to a large gas space B that is essentially free of A. Assume that the gas B is insoluble in liquid A, and work with the following conditionsand properties:Total pressure P = 1 atmVapor pressure of A Pvap = 550 torrTemperature T = 25oCCapillary length L = 10 cmMolecular weights MwA = 100, MwB = 28Binary diffusivity DAB = 0.25 cm2/sa) Find the magnitude of the molar average velocity vM.b) What is the factor by which you would be in error if you assume that yA << 1?c) Is vM constant along the capillary axis? Explain your answer.d) Is vm (the mass average velocity) constant along the capillary axis? Explain youranswer.7. A water droplet having a diameter of 0.16 mm is suspended in still air at 50oC, 1.0132×105Pa (1 atm), and 30% relative humidity. The droplet temperature can be assumed to be at 50oCand its vapor pressure at 50oC is 7.38 kPa. 1) Calculate the initial rate of evaporation of water if DAB of water vapor in air is 0.288 cm2/s.2) Determine the time for the water droplet to evaporate completely.8. A lime (CaO) slurry droplet having a diameter Dd of 0.20 mm is suspended in a gascontaining SO2 at 50oC, 1.0132×105 Pa (1 atm). The mole fraction of SO2 in the gas phase is10-4. Rate of diffusion of SO2 from the gas to the droplet surface is given byNs = kd(πDd2) c (yg,s − yd,s)In this equation c is the total gas concentration and kd is the mass transfer coefficient for SO2in the gas phase given bykd = 22SO gasdDD-Rate of diffusion of SO2 from the droplet surface into the interior droplet is given byNs = kLf(πDd2) C*SO2In this equation C*SO2 is the equilibrium SO2 concentration at the droplet surface kLf is themass transfer coefficient for SO2 in the liquid phase given bykLf = kL2 2*lime lime*SO SO1D CD C� �+� �� �� �, wherekL = 2SODd and the liquid film thickness δ at the surface is estimated to be 1 μm. f = 2 2*lime lime*SO SO1D CD C� �+� �� �� �= the enhancement factor of the liquid film coefficient kL due tothe very fast reaction of dissolved SO2 with dissolved lime in the bulk liquid. The gas- and liquid-phase surface concentrations are related by Henry’law as follows:c yd,s = HC*SO2The Henry’law constant for the solubility of SO2 in water at 50oC is given byH = 0.054 33mol/cm in gas phasemol/cm in liquid phaseOther data at 50oC: Equilibrium concentration of lime, C*lime = 1.35×10-5 mol/cm3. Diffusivityof SO2 and lime in water: Dlime = DSO2 = 2×10-5 cm2/s. Diffusivity of SO2 in gas: DSO2-gas = 0.20cm2/sEstimate the rate of diffusion of SO2,