ERT 216 HEAT & MASS TRANSFER SEM2, 2013/2014

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Wesley Richards
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1 ERT 16 HET & MSS TRNSFER SEM, 01/014 Tutorial: Principles of Mass Transfer (Part 1) gas of CH 4 and He is contained in a tube at 10 kpa pressure and 98 K. t one point the partial pressure of methane is p 1 = kpa, and at the point 0.0 m distance away, p = 0.6 kpa. If the total pressure is constant throughout the tube, calculate the flux of CH 4 (methane) at steady state for equimolar counterdiffusion.. The gas CO is diffusing at steady state through a tube 0.0 m long having diameter of 0.01 m and containing N at 98 K. The total pressure is constant at 10 kpa. The partial pressure of CO is 456 mm Hg at one end and 76 mm Hg at the other end. The diffusivity D is 67 x 10-5 m /s at 98K. Calculate the flux of CO in cgs and SI units for equimolar counterdiffusion.. Helium and nitrogen gas are contained in a conduit 5 mm in diameter and 0.1 m long at 98 K and a uniform constant pressure of 0 atm abs. The partial pressure of He at one end of the tube if atm and at the other end is 0.00 atm. The diffusivity D is x 10-4 m /s. Calculate the following for steadystate equipmolar counterdiffusion: (a) Flux of He in kg mol/s.m and g mol/s. cm (b) Flux of N (c) Partial pressure of He at a point 0.05 m from either end. 4. mmonia gas () and nitrogen () are diffusing in counterdiffusion through a straight glass tube 0.610m long with an inside diameter of 4.4 mm at 98 K and 10 kpa. oth ends of the tube are connected to large mixed chambers at 10 kpa. The partial pressure of NH is constant at 0.0 kpa in one chamber and kpa in the other. The diffusivity at 98 K and 10 kpa is.0 x 10-5 m /s. (a) Calculate the diffusion of NH in kg mol/s. (b) Calculate the diffusion of N. (c) Calculate the partial pressure at point 0.05m in the tube and plot p, p and P versus distance, z. 5. mmonia gas is diffusing through N under steady-state conditions with N nondiffusing since it is insoluble in one boundary. The total pressure is 01 x 10 5 Pa and the temperature is 98 K. The partial pressure of NH at one point is x 10 4 Pa, and at the other point 0 mm away it is x 10 Pa. The D for the mixture at 01 x 10 5 Pa and 98K is.0 x 10-5 m /s. (a) Calculate the flux of NH in kg mol/s. m. (b) Do the same as (a) but assume that N 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

2 ERT 16 HET & MSS TRNSFER SEM, 01/ Mass transfer is occurring from a sphere of naphthalene having a radius of 10 mm. The sphere is in a large volume of still air at C and 1atm abs pressure. The vapour pressure of naphthalene at C is 0mm Hg. The diffusivity of naphthalene in air at 0 0 C is 5.16 x 10-6 m /s. The diffusivity can be corrected using temperature correction factor using: x10 T 1 M 1 M D 1 / 1 / p Σν Σν 7. For a mixture of ethanol (CH CH OH) vapour and methane (CH 4 ), predict the diffusivity using: x10 T 1 M 1 M D 1 / 1 / p Σν Σν (a) t 01 x 10 5 Pa and 98 and 7K (b) t.065 x 10 5 Pa and 98K. 8. The solute HCl () is diffusing through a thin film of water ().0 mm thick at 8 K. The concentration of HCl at point 1 at one boundary of the film is 1.0 wt% HCl (density, ρ 1 = kg/m ), and at the other boundary at point it is 6.0 wt% HCl (ρ = 100. kg/m ). The diffusion coefficient of HCl in water is.5 x 10-9 m /s. ssuming steady-state and one boundary impermeable to water, calculate the flux of HCl in kg mol/s. m. 9. It is desired to predict the diffusion coefficient of dilute acetic acid (CH COOH) in water at 8.9K and at 98K using the Wilke-Chang method (see equation below).compare the predicted values with the experimental value (7.69 x10-10 m /s at 8.9K; 6 x m /s at 98K). 16 T D 1. 17x10 φm 0. 6 μ V 10. The diffusivity of dilute methanol in water has been determined experimentally to be 6 x 10-9 m/s at 98K. (a) Estimate the diffusivity at 9K using the Wilke-Chang equation. (b) Estimate the diffusivity at 9K by correcting the experimental value at 88K to 9K. 1 Predict the diffusivity of the enzyme urease in a dilute solution in water at 98 K using the modified Polson equation (see below) and compare the result with the experimental value (4.01x10-11 m /s) x10 T D μm

3 ERT 16 HET & MSS TRNSFER SEM, 01/ layer of gelatin in water 5 mm thick containing 5.1 wt% gelatin at 9K separates two solutions of sucrose. The concentration of sucrose in the solution at one surface of the gelatin is constant at.0g sucrose / 100 ml solution, and 0.g/100ml at the other surface. Calculate the flux of sucrose in kg sucrose/s.m through the gel at steady state. 1. Oxygen is diffusing through a solution of bovine serum albumin (S) at 98K. Oxygen has been shown not to bind to S. Predict the diffusivity D P of oxygen in a protein solution containing 11g protein / 100ml solution. Diffusivity of O in water =.41 x 10-9 m /s. Tutorial: Principles of Mass Transfer (Part ) flat plug 0mm thick having an area of 4.0 x 10-4 m and made of vulcanized rubber is used for closing an opening in a container. The gas CO at 5 0 C and.0 atm pressure is inside the container. ssume that the partial pressure of CO outside is zero. The solubility of the CO gas is 0.90 m gas (at STP of 0 0 C and 1atm) per m rubber per atm pressure of CO. Calculate the total leakage or diffusion of CO through the plug to the outside in kg mol CO /s at steady state.. The gas hydrogen is diffusing through a sheet of vulcanized rubber 0 mm thick at 5 0 C. The partial pressure of H is 5 atm inside and 0 outside. Calculate: (a) The diffusivity D from the permeability P M and solubility S, and compare with the experimental value (0.85 x 10-9 m /s). (b) The flux N of H at steady state.. Hydrogen gas at.0 atm and 7 0 C is flowing in a neoprene tube.0 mm inside diameter and 11mm outside diameter. Calculate the leakage of H through a tube 0 mm long in kg mol H /s at steady state. 4. Nitrogen gas at.0 atm and 0 0 C is diffusing through a membrane of nylon 0mm thick and polyethyelene 8.0 mm thick in series. The partial pressure at the other side of the two films is 0 atm. ssuming no other resistances, calculate flux N at steady state. 5. It is desired to calculate the rate of diffusion of CO gas in air at steady state through a loosely packed bed of sand at 76 K and a total pressure of 01 x 10 5 Pa. The bed depth is 5m and the void fraction ε is 0.0. The partial pressure of CO is.06 x 10 Pa at the top of the bed and 0 Pa at the bottom. Use a τ of Cellophane is being used to keep food moist at 8 0 C. Calculate the loss of water vapour in g/day at steady state for a wrapping 0.10 mm thick and an area of 0.00 m 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. Permeability of water in cellophane is 8 x m H O (STP)/s.m.atm/m.

4 ERT 16 HET & MSS TRNSFER SEM, 01/ window of SiO.0 mm thick and 0 x 10-4 m in area is used to view the contents of a metal vessel at 0 0 C. Helium gas at 0.6 kpa is contained in the vessel. Use D = 5.5 x m /s, (a) Calculate the loss of He in kg mol/h at steady state. (b) Calculate the permeability P M. 8. very thick slad has a uniform concentration of solute of c 0 =0x10 - kg mol /m. Suddenly, the front face of the slab is exposed to a flowing fluid having a concentration c 1 =0.10 kg mol /m and a convection coefficient k c = x 10-7 m/s. The equilibrium distribution coefficient K = c Li /c i = The diffusivity in the solid is D = 4x10-9 m /s. (a) ssuming that the slab is a semi-infinite solid, calculate the concentration in the solid at the surface (x=0) and x=0.01m from the surface after t = x10 4 s. (b) Plot the data. 9. solid rectangular solid block of 5.15 wt% agar gel at 78K is mm thick and contains a uniform concentration of urea of 0.1 kg mol/m. The block is mm thick in the x direction, 7.6 mm thick in y direction and mm thick in z direction. Diffusion occurs at all six faces. The slab is suddenly immersed in pure turbulent water, so the surface resistance can be assumed to be negligible; that is, the convective coefficient k c is very large. The diffusivity of urea in the agar is 4.7x10-10 m /s. Calculate the concentration at the midpoint of the block after 10h. 10. flat slab of Douglas fir wood 50.8 mm thick containing 0 wt% moisture is being dried from both sides (neglecting ends and edges). The equilibrium moisture content at the surfaces of the wood due to the drying air blown over it is held at 5 wt% moisture. The drying can be assumed to be represented by a diffusivity of.7 x 10-8 m /h. Calculate the time for the center to reach 10 % moisture. Tutorial: Principles of Mass Transfer (Part ) In a wetted-wall tower an air-h S mixture is flowing by a film of water that is flowing as a thin film down a vertical plate. The H S is being absorbed from the air to the water at a total pressure of 50 atm abs and 0 0 C. value for k c of 9.567x10-4 m/s has been predicted for the gas-phase mass transfer coefficient. t a given point the mole fraction of H S in the liquid at the liquid-gas interface is.0 x 10-5 and p of H S in the gas is 0.05 atm. The Henry s law equilibrium relation is p (atm) = 609 x (mole fraction in liquid). Calculate the rate of absorption of H S. 4

5 ERT 16 HET & MSS TRNSFER SEM, 01/014. Toluene is evaporating from a wetted porous slab by having inert pure air at 1 atm flowing parallel to the flat surface. t a certain point the mass-transfer coefficient k x for very low fluxes has been estimated as 0.0 Ib mol/hr.ft. Calculate the flux ratios k x 0 /k x for x 1 = 0.65, 0.0, and 0.01 to correct for high flux and plot the ratio versus x 1.. large volume of pure water at C is flowing parallel to a flat plate of solid benzoic acid, where L = 0.17 m in the direction of flow. The solubility of benzoic acid in water is kg mol/m. The diffusivity of benzoic acid is 45 x 10-9 m /s. The physical properties of water at C: µ = 8.71 x 10-4 Pa.s, ρ = 996 kg/m, D = 45 x 10-9 m /s. (a) Calculate x M (b) Calculate the flux for a water velocity of 0.15 m/s. 4. pure water at C is flowing at a velocity of m/s in a tube having an inside diameter of 6.5 mm. The tube is 89 m long with the last m having the walls coated with benzoic acid. The physical properties of water at C: µ = 8.71 x 10-4 Pa.s, ρ = 996 kg/m, D = 45 x 10-9 m /s. ssuming that the velocity profile is fully developed, calculate the average concentration of benzoic acid at the outlet. 5. It is desired to estimate the mass-transfer coefficient k G in kg mol/s.m.pa for water vapour in air at 8.6K and 10 kpa flowing in a large duct past solids of different geometries as stated below. The velocity in the duct is.66 m/s. The water vapour concentration in the air is small, so the physical properties of air can be used. Water vapour is being transferred to the solids. (a) single 5.4 mm diameter sphere (b) packed bed of 5.4 mm spheres with ε =

Mass Transfer Operations

Mass Transfer Operations College of Engineering Tutorial # 1 Chemical Engineering Dept. 14/9/1428 1. Methane and helium gas mixture is contained in a tube at 101.32 k Pa pressure and 298 K. At one point the partial pressure methane