ERT 216 HEAT & MASS TRANSFERSEM2, 2013/2014 Tutorial: Principles of Mass Transfer (Part 1) 1. A gas of CH4 and He is contained in a tube at 101.32 kPa pressure and 298 K. At one point the partial pressure of methane is p A1 = 60.79 kPa, and at the point 0.02 m distance away, pA2 = 20.26 kPa. If the total pressure is constant throughout the tube, calculate the flux of CH4 (methane) at steady state for equimolar counterdiffusion. 2. The gas CO2 is diffusing at steady state through a tube 0.20 m long having diameter of 0.01 m and containing N2 at 298 K. The total pressure is constant at 101.32 kPa. The partial pressure of CO2 is 456 mm Hg at one end and 76 mm Hg at the other end. The diffusivity DAB is 1.67 x 10-5 m2/s at 298K. Calculate the flux of CO2 in cgs and SI units for equimolar counterdiffusion. 3. Helium and nitrogen gas are contained in a conduit 5 mm in diameter and 0.1 m long at 298 K and a uniform constant pressure of 1.0 atm abs. The partial pressure of He at one end of the tube if 0.060 atm and at the other end is 0.020 atm. The diffusivity DAB is 0.687 x 10-4 m2/s. Calculate the following for steadystate equipmolar counterdiffusion: (a) Flux of He in kg mol/s.m2 and g mol/s. cm2 (b) Flux of N2 (c) Partial pressure of He at a point 0.05 m from either end. 4. Ammonia gas (A) and nitrogen (B) are diffusing in counterdiffusion through a straight glass tube 0.610m long with an inside diameter of 24.4 mm at 298 K and 101.32 kPa. Both ends of the tube are connected to large mixed chambers at 101.32 kPa. The partial pressure of NH3 is constant at 20.0 kPa in one chamber and 6.666 kPa in the other. The diffusivity at 298 K and 101.32 kPa is 2.30 x 10 -5 m2/s. (a) Calculate the diffusion of NH3 in kg mol/s. (b) Calculate the diffusion of N2. (c) Calculate the partial pressure at point 0.305m in the tube and plot p A, pB and P versus distance, z. 5. Ammonia gas is diffusing through N2 under steady-state conditions with N2 nondiffusing since it is insoluble in one boundary. The total pressure is 1.013 x 105 Pa and the temperature is 298 K. The partial pressure of NH 3 at one point is 1.333 x 104 Pa, and at the other point 20 mm away it is 6.666 x 10 3 Pa. The DAB for the mixture at 1.013 x 105 Pa and 298K is 2.30 x 10-5 m2/s. (a) Calculate the flux of NH3 in kg mol/s. m2. (b) Do the same as (a) but assume that N2 also diffuses; that is, both boundaries are permeable to both gases and the flux is equimolar counterdiffusion. In which case is the flux greater. 1 and at the other boundary at point 2 it is 6. The concentration of HCl at point 1 at one boundary of the film is 12. The sphere is in a large volume of still air at 52.ERT 216 HEAT & MASS TRANSFER 6. The diffusivity of naphthalene in air at 00C is 5.60C is 1. SEM2.9K.0 wt% HCl (density.16 x 10-6 m2/s.26 x 10-10 m2/s at 298K).26 x 10-9 m2/s at 298K.00 x10 7 T 1.173x10 16 φM B μBVA0.7 kg/m3). m2.5 x 10-9 m2/s. For a mixture of ethanol (CH3CH2OH) vapour and methane (CH4). predict the diffusivity using: 1/ 2 1.0 wt% HCl (ρ2 = 1030. Predict the diffusivity of the enzyme urease in a dilute solution in water at 298 K using the modified Polson equation (see below) and compare the result with the experimental value (4. 8.69 x10-10 m2/s at 282.0 mm thick at 283 K.01x10-11 m2/s). (a) Estimate the diffusivity at 293K using the Wilke-Chang equation. calculate the flux of HCl in kg mol/s.0mm Hg. T 1/ 2 DAB 1.75 1 M A 1 M B DAB 1/ 3 1/ 3 2 p Σν A Σν B 7. The diffusivity can be corrected using temperature correction factor using: 1/ 2 1. The diffusion coefficient of HCl in water is 2. 1.75 1 M A 1 M B DAB 1/ 3 1/ 3 2 p Σν A Σν B (a) At 1. The vapour pressure of naphthalene at 52.60C and 1atm abs pressure. 2013/2014 Mass transfer is occurring from a sphere of naphthalene having a radius of 10 mm. (b) Estimate the diffusivity at 293K by correcting the experimental value at 288K to 293K.6 10.0132 x 105 Pa and 298 and 373K (b) At 2.0265 x 105 Pa and 298K. 11.00 x10 7 T 1. The solute HCl (A) is diffusing through a thin film of water (B) 2. The diffusivity of dilute methanol in water has been determined experimentally to be 1.9K and at 298K using the Wilke-Chang method (see equation below).3 kg/m3). It is desired to predict the diffusion coefficient of dilute acetic acid (CH 3COOH) in water at 282.40 x10 15T DAB μM 1A/ 3 2 . Assuming steady-state and one boundary impermeable to water. 9. 9.Compare the predicted values with the experimental value (7. ρ1 = 1060. 1 wt% gelatin at 293K separates two solutions of sucrose.5 atm inside and 0 outside.0mm thick and polyethyelene 8.0 atm pressure is inside the container. Predict the diffusivity D AP of oxygen in a protein solution containing 11g protein / 100ml solution. Use a τ of 1. The concentration of sucrose in the solution at one surface of the gelatin is constant at 2. (b) The flux NA of H2 at steady state. 3. The gas hydrogen is diffusing through a sheet of vulcanized rubber 20 mm thick at 250C.25m and the void fraction ε is 0. Assume that the partial pressure of CO2 outside is zero. and 0.90 m3 gas (at STP of 00C and 1atm) per m3 rubber per atm pressure of CO2. 4.82 x 10-10 m3 H2O (STP)/s. The partial pressure of H2 is 1.atm/m. A layer of gelatin in water 5 mm thick containing 5. It is desired to calculate the rate of diffusion of CO2 gas in air at steady state through a loosely packed bed of sand at 276 K and a total pressure of 1. The partial pressure of CO2 is 2. Nitrogen gas at 2. Oxygen has been shown not to bind to BSA. 13. 3 . Calculate the flux of sucrose in kg sucrose/s.85 x 10-9 m2/s). Tutorial: Principles of Mass Transfer (Part 2) 1. and compare with the experimental value (0.m 2 through the gel at steady state. calculate flux NA at steady state.200 m2 when the vapour pressure of water vapour inside is 10 mm Hg and the air outside contains water vapour at a pressure of 5 mm Hg. Calculate the total leakage or diffusion of CO2 through the plug to the outside in kg mol CO2/s at steady state. 6.2g/100ml at the other surface.026 x 103 Pa at the top of the bed and 0 Pa at the bottom. Diffusivity of O 2 in water = 2. The partial pressure at the other side of the two films is 0 atm. Oxygen is diffusing through a solution of bovine serum albumin (BSA) at 298K.0 mm inside diameter and 11mm outside diameter. Assuming no other resistances.0 mm long in kg mol H2/s at steady state.41 x 10-9 m2/s.m2.30.0g sucrose / 100 ml solution. Calculate the leakage of H 2 through a tube 1. A flat plug 30mm thick having an area of 4.0 atm and 300C is diffusing through a membrane of nylon 1. Cellophane is being used to keep food moist at 38 0C. Permeability of water in cellophane is 1.013 x 105 Pa.0 mm thick in series. Hydrogen gas at 2.87.10 mm thick and an area of 0. The solubility of the CO2 gas is 0.0 atm and 270C is flowing in a neoprene tube 3. Calculate: (a) The diffusivity DAB from the permeability PM and solubility S. 2013/2014 12. 5. The gas CO 2 at 250C and 2. Calculate the loss of water vapour in g/day at steady state for a wrapping 0.0 x 10 -4 m2 and made of vulcanized rubber is used for closing an opening in a container. The bed depth is 1.ERT 216 HEAT & MASS TRANSFER SEM2. 2. 10 kg mol A/m3 and a convection coefficient kc = 2 x 10-7 m/s. 10. Use DAB = 5. calculate the concentration in the solid at the surface (x=0) and x=0. The equilibrium moisture content at the surfaces of the wood due to the drying air blown over it is held at 5 wt% moisture.8 mm thick containing 30 wt% moisture is being dried from both sides (neglecting ends and edges). (b) Plot the data.15 wt% agar gel at 278K is 10. The diffusivity of urea in the agar is 4. Diffusion occurs at all six faces.0x10-2 kg mol A/m3. The drying can be assumed to be represented by a diffusivity of 3. Calculate the concentration at the midpoint of the block after 10h. The Henry’s law equilibrium relation is pA (atm) = 609 xA (mole fraction in liquid). Helium gas at 202. The equilibrium distribution coefficient K = cLi/ci = 0.16 mm thick in z direction. Calculate the rate of absorption of H2S. 4 .0 x 10-4 m2 in area is used to view the contents of a metal vessel at 200C. A solid rectangular solid block of 5.05 atm.0 mm thick and 1.ERT 216 HEAT & MASS TRANSFER SEM2.5 x 10-14 m2/s.01m from the surface after t = 3x104s.0 x 10-5 and pA of H2S in the gas is 0.1 kg mol/m 3. (b) Calculate the permeability PM. The block is 10. A window of SiO2 2. (a) Assuming that the slab is a semi-infinite solid. The slab is suddenly immersed in pure turbulent water.50 atm abs and 300C.62 mm thick in y direction and 10. Suddenly. the convective coefficient kc is very large.72x10-10 m2/s. 9.6 kPa is contained in the vessel.16 mm thick in the x direction. (a) Calculate the loss of He in kg mol/h at steady state. In a wetted-wall tower an air-H2S mixture is flowing by a film of water that is flowing as a thin film down a vertical plate.72 x 10-8 m2/h. At a given point the mole fraction of H2S in the liquid at the liquid-gas interface is 2. The H2S is being absorbed from the air to the water at a total pressure of 1. that is. 8. Tutorial: Principles of Mass Transfer (Part 3) 1.50. the front face of the slab is exposed to a flowing fluid having a concentration c1=0. Calculate the time for the center to reach 10 % moisture. A very thick slad has a uniform concentration of solute A of c 0=1. 7. The diffusivity in the solid is DAB = 4x10-9 m2/s.16 mm thick and contains a uniform concentration of urea of 0. 2013/2014 7. so the surface resistance can be assumed to be negligible. A flat slab of Douglas fir wood 50. A value for kc’ of 9.567x10-4 m/s has been predicted for the gas-phase mass transfer coefficient. 245 x 10-9 m2/s. The diffusivity of benzoic acid is 1.10C is flowing at a velocity of 0. The physical properties of water at 26.Pa for water vapour in air at 338. DAB = 1. Assuming that the velocity profile is fully developed. The physical properties of water at 26.10C: µ = 8.20. calculate the average concentration of benzoic acid at the outlet. The water vapour concentration in the air is small. ρ = 996 kg/m3. The tube is 1.ft 2. 3.245 x 10-9 m2/s. The solubility of benzoic acid in water is 0.4 mm diameter sphere (b) A packed bed of 25. DAB = 1.20 Ib mol/hr.71 x 10-4 Pa.4 mm spheres with ε = 0.245 x 10 -9 m2/s.71 x 10-4 Pa. 5 .10C: µ = 8. Calculate the flux ratios kx0/kx’ for xA1= 0.ERT 216 HEAT & MASS TRANSFER SEM2. 0.01 to correct for high flux and plot the ratio versus xA1.66 m/s.35.10C is flowing parallel to a flat plate of solid benzoic acid. so the physical properties of air can be used. Water vapour is being transferred to the solids.65.02948 kg mol/m3. ρ = 996 kg/m3. (a) Calculate xBM (b) Calculate the flux for a water velocity of 0. 2013/2014 2.0305 m/s in a tube having an inside diameter of 6.m2. 5.6K and 101.137 m in the direction of flow.s. At a certain point the mass-transfer coefficient kx’ for very low fluxes has been estimated as 0.s. 4.35 mm. A pure water at 26.32 kPa flowing in a large duct past solids of different geometries as stated below. (a) A single 25. A large volume of pure water at 26. It is desired to estimate the mass-transfer coefficient kG in kg mol/s.22 m having the walls coated with benzoic acid.152 m/s. The velocity in the duct is 3. Toluene A is evaporating from a wetted porous slab by having inert pure air at 1 atm flowing parallel to the flat surface. and 0.829 m long with the last 1. where L = 0.