Understanding Mass Transfer: Mechanisms and Applications

School

Batangas State University - Alangilan**We aren't endorsed by this school

Course

CHE 432

Subject

Chemistry

Date

Dec 10, 2024

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Uploaded by UltraCaribouPerson605

CHE 409MASS TRANSFERCHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.INTRODUCTION TO MASS TRANSFER

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.MASS TRANSFERMass transfer is of concern in many areas of engineering and science, but it is probably more important in conjunction with chemical reactions than in any other single area

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.MASS TRANSFERMigration of a component in a mixture either within the same phase or from phase to phase because of a displacement from equilibrium.

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.DRIVING FORCE FOR MASS TRANSFER1.Concentration difference2.Pressure Difference3.Electrical Difference

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.MECHANISMSMOLECULAR DIFFUSION•Transfer of individual molecules through a fluid by a random movement from higher concentration to low concentration

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.MECHANISMSCONVECTIVE MASS TRANSFER•Using mechanical force or action to increase the rate of molecular diffusion

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.MASS TRANSPORT•The transfer of mass within a fluid mixture or across a phase boundary is a process that plays a major role in many industrial processes.1.Dispersion of gases from stacks 2.Removal of pollutants from plant discharge streams by absorption 3.Stripping of gases from waste water 4.Neutron diffusion within nuclear reactors 5.Air conditioning

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.PROPERTIES OF MIXTURES •Mass transfer always involves mixtures. Consequently, we must account for the variation of physical properties which normally exist in a given system. The conventional engineering approach to problems of multicomponent system is to attempt to reduce them to representative binary (i.e., two components) systems.

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.COMPONENT •To delve deeper into mass transfer within mixtures, it's crucial to understand the definitions and relationships between the components. This includes concepts like:a.Concentrationb.Mole Fractionc.Mass Fraction

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.CONCENTRATION OF SPECIES •Concentration of species in multicomponent mixture can be expressed in many ways. For species A, mass concentration denoted by ρA is defined as the mass of A, mA per unit volume of the mixture.

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.VELOCITIESIn a multicomponent system the various species will normally move at different velocities; and evaluation of velocity of mixture requires the averaging of the velocities of each species present.

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.VELOCITIESBy similar way, molar-average velocity of the mixture ν*The velocity of a particular species relative to the mass-average or molar average velocity is termed as diffusion velocity

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.VELOCITIESThe mole fraction for liquid and solid mixture, xA ,and for gaseous mixtures, yA, are the molar concentration of species A divided by the molar density of the mixtures.

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.VELOCITIESExample 1.1: The molar composition of a gas mixture at 273.15 K and 1.5 x 10^5 Pa is: Determine: a) the composition in weight percent b) average molecular weight of the gas mixture c) density of gas mixture d) partial pressure of O2

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.VELOCITIESDetermine: a) the composition in weight percent?2= 0.07 ??? × 32 = 2.24 ??? = 0.10 ??? × 28 = 2.80 ???2= 0.15 ??? × 44 = 6.60 ??2= 0.68 ??? × 28 = 19.04 ?????? ???? = 30.68?2=2.24𝑔30.68 𝑔× 100 = 7.30%?? =2.80𝑔30.68 𝑔× 100 = 9.13%??2=6.60 𝑔30.68 𝑔× 100 = 21.51%?2=19.04 𝑔30.68 𝑔× 100 = 62.06%

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.VELOCITIESb) average molecular weight of the gas mixture ? =??𝑖?ℎ? ?? ??? ?𝑖???????????? ?? ?????? =30.681????

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.VELOCITIESc) density of gas mixture ?? = ?????=???? × ??=????=1.5 × 10530.68(8314 × 273.15) ???= 2.026???3

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.DIFFUSION FLUXJust as momentum and energy (heat) transfers have two mechanisms for transport molecular and convective, so does mass transfer. However, there are convective fluxes in mass transfer, even on a molecular level.

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.DIFFUSION FLUXThe mass (or molar) flux of a given species is a vector quantity denoting the amount of the particular species, in either mass or molar units, that passes per given increment of time through a unit area normal to the vector.

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.DIFFUSION FLUXThe mass (or molar) flux of a given species is a vector quantity denoting the amount of the particular species, in either mass or molar units, that passes per given increment of time through a unit area normal to the vector.??= ????−𝑉+ ?????= ????−𝑉+ ???

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.FICK’S LAWAn empirical relation for the diffusional molar flux, first postulated by Fick and, accordingly, often referred to as Fick’sfirst law, defines the diffusion of component A in an isothermal, isobaric system.𝐽?= −???(?????)

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.FICK’S LAWA more general flux relation which is not restricted to isothermal, isobaric system could be written as:

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.EQUIMOLAR COUNTER DIFFUSIONThe total pressure is constant all through the mixture. Hence the difference in partial pressures will be equal. The Fick’sEquation when integrated for a larger plane volume of thickness L will give.???= 𝐽 = ??[?1− ?2]????= 𝐽??= ???[?1− ?2]????= (???)(?1− ?2?1− ?2)Assumptions for the working equations:1. Diffusion occurs in steady state2. The gas mixture behaves ideally3. The temperature is constant throughout4. Diffusion occurs through constant area.

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.EQUIMOLAR COUNTER DIFFUSIONThe total pressure is constant all through the mixture. Hence the difference in partial pressures will be equal. The Fick’sEquation when integrated for a larger plane volume of thickness L will give.

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.STATIONARY MEDIAThe total pressure is constant all through the mixture. Hence the difference in partial pressures will be equal. The Fick’sEquation when integrated for a larger plane volume of thickness L will give.??=?1− ?2?????? ?????𝑃=??????????? ????𝑖?????𝑖????𝑦𝑙=?? (?2?1)2??????????? ??ℎ??????=14????1?1−1?2

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.EXAMPLEOxygen gas is flowing through a 10 m long circular pipe with a radius of 16 cm. The concentrations of Oxygen at the ends of the pipe e 30 kg per cubic meters and 10 kg per cubic meters. The diffusion constant for Oxygen gas at 20 degrees C is 1.8 ×10^-5 sq.m per seconds.a.Calculate the diffusion flow rateb.How many Oxygen will flow through this pipe in 5 minutes?c.Calculate the concentration gradientd.What is the concentration of Oxygen 2m away from the end of the pipe at high concentrations?e.How long will take 100 kg of Oxygen to travel through this pipe?

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.EXAMPLEa.Calculate the diffusion flow rate𝐽 = ??[?1− ?2]?𝐽 = (1.8 × 10−5)(??2)[?1− ?2]?𝐽 = (1.8 × 10−5?2?)(?)(16100?)230 − 10???310𝑱 = ?. ???? × ??−????

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.EXAMPLEb.How many Oxygen will flow through this pipe in 5 minutes?2.8953 × 10−6???600 ?= 1.7372 × 10−3??c. Calculate the concentration gradient????𝑖??? =∆??????𝑖??? =(30 − 10)10????𝑖??? =2 ???

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.EXAMPLEd. What is the concentration of Oxygen 2 m away from the end of the pipe at high concentrations?30???3−2???3?2?= 26???3How long will take 100 kg of Oxygen to travel through this pipe?100 ??1 ?2.8953 × 10−6??= 34 538 735. 19 ?

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.DIFFUSIVITY•Fick’slaw proportionality, DAB, is known as mass diffusivity (simply as diffusivity) or as the diffusion coefficient. •Diffusivities of gases at low density are almost composition independent, increase with the temperature and vary inversely with pressure. Liquid and solid diffusivities are strongly concentration dependent and increase with temperature.

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.DIFFUSIVITY in GASESPressure dependence of diffusivity is given by and temperature dependency is according to:Wilke Equation

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.DIFFUSIVITY in LIQUIDS?????? − ?𝑖????𝑖? ?????𝑖?????=??6???𝜇?Or in another form:(???𝜇?) ?= ??(?)

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.EXAMPLE 1To avoid the pressure-build up of ammonia has 1 atmospheric pressure, it is vented to atmosphere through a 3mm ID, 20 m length. Determine the mass of ammonia diffusing out and mass of air diffusing in per hour. Assuming D = 0.28 × 10^ -4 m^2/s, M = 17kg/kg-kmol.NH3P1=1 atmP2 = 0 atm?𝑁𝐻3=??(?)???1− ?2??𝑁𝐻3=0.28× 10−4(?4× 0.0032)(17)8315101325 − 020?𝑁𝐻3= 2.0500 × 10−9

CHE409: Heat and Mass Transfer. Copyright 2024 Leonel C. Tingson. All rights reserved. All trademarks, images and symbols belongs to it’srespective owners. Usage of any image requires prior notification and consent.EXAMPLE 1To avoid the pressure-build up of ammonia has at atmospheric pressure, it is vented to atmosphere through a 3mm ID, 20 m length. Determine the mass of ammonia diffusing out and mass of air diffusing in per hour. Assuming D = 0.28 × 10^ -4 m^2/s, M = 17kg/kg-kmol.NH3P1=1 atmP2 = 0 atm??𝑖?, ??= −??=2.0500 × 10−9???28.9717??𝑖?= 3.4935 × 10−9??/?