Postal Correspondence GATE & PSUs -MT To Buy Postal Correspondence Packages call at 0-9990657855 1
TABLE OF CONTENT S. No. Ttle Page no. 1. Introducton 3 2. Dffuson 10 3. Dryng and Humdfcaton 24 4. Absorpton and Strppng 34 5. Dstllaton 40 6. Extracton and Leachng 57 7. Adsorpton 64 Annexure - A Important Formulae used n Mass Transfer 66 Annexure - B Practce Set 72 Annexure - C Gate Based Questons 86 2
Chapter-1 Introducton The process of mass transfer occurs due to concentraton dfference of mxture components. It occurs from a regon of hgher concentraton to a regon of lower concentraton. Concentraton dfference s the pllar of mass transfer. Varous separaton technques such as dstllaton, gas adsorpton, lqud extracton, dryng, crystallzaton, etc. are studed n Mass transfer, where operaton may occur sothermally or non-sothermally. Mass transfer operaton may occur smultaneously wth heat transfer, for example; Dryng, Humdfcaton, Dstllaton, crystallzaton etc. Mass transfer operaton may occur n one drecton example, gas absorpton. The contactng can be done n sx ways namely, Gas-Gas, GasLqud, Gas-sold, Lqud-Lqud and Lqud-Sold and Sold-Sold. (a) Lqud-Vapour Dstllaton. (b) Lqud-gas Gas absorpton, strppng, Humdfcaton and Dehumdfcaton. (c) Lqud-Sold Crystallzaton, Leachng, Adsorpton. (d) Lqud- Lqud Extracton. (e) Sold-Gas Adsorpton, Dryng. The equllbrum between phases s attaned after suffcently long tme. Snce Mass transfer occurs due to both molecular dffuson and turbulence, the detaled study of factors affectng mass transfer s studed. At the phase nterface there s no resstance due to thermodynamc equllbrum (T, P, ) at nterface. Rate of mass transfer s measured by devaton from equllbrum.e. hgher the devaton, hgher s the drvng force. 1.1. Some Important Defntons: 1) Dstllaton: Dstllaton s a vapour-lqud operaton n whch the mxture components are separated by use of thermal energy. When lqud mxture s heated, dfferent components exert dfferent vapour pressure, expressed n terms of relatve volatlty. Ths pressure dfference results n separaton of components n such a way that the top product contans hgher amount of lght component and bottom products contans hgher amounts of heaver component, as shown n fgure 1.1. A dstllaton example s separaton of crude petroleum nto gasolne, kerosene, etc. Fg. 1.1. Schematc dagram of a dstllaton column 3
2) Absorpton and Strppng: Gas absorpton s a gas-lqud operaton n whch one or more consttuents of a gas mxture are separated by usng a sutable lqud solvent.e. component moves from gas phase to lqud phase as shown n fgure 1.2. Example of gas absorpton methods s ammona washng from ammona-ar mxture by means of water. Strppng s opposte of absorpton.e. a component moves from lqud phase to gas phase. 3) Fg. 1.3. Schematc dagram of a Lqud-Lqud Extractor Crystallzaton: It s lqud-sold operaton n whch we obtan unform crystals of good purty. The saturated lqud s subjected to changes n temperature and pressure n such a way that crystals get separated from the feed lquor as shown n the fgure 1.4. 5) Fg. 1.2. Schematc dagram of an absorpton column Lqud-Lqud Extracton: It s a lqud-lqud operaton, also called as solvent extracton, n whch components of a lqud mxture are separated by treatng t wth sutable solvent whch dssolves one or more consttuents of mxture more preferably. It s an effcent separaton process n cases where separaton s ether not possble or not economcal by usng dstllaton eg. Separaton of components of an azeotropc mxture. 4) Fg. 1.4. Schematc dagram of a crystallzer Dryng: Dryng s gas-sold operaton n whch a relatvely small amount of water s removed from sold materal, by contactng t wth a contnuous stream of gas (ar) as shown n fgure 1.5. Fg. 1.5. Schematc dagram of a dryer 1.2. Important concepts to remember: 1) Ideal gas law : PV nrt Where, P Pressure (kpa), V Volume (m3) 4
n number of moles (kmol), T Temperature (K) m2 kpa R 8.31451 Unversal gas constant kmol K v or psa ) and partal pressure (p A, pb ) : The vapour pressure of a lqud 2) Vapour Pressure (p A s defned as the absolute pressure at whch the lqud and ts vapour are n equllbrum at gven temperature n a closed vessel. The partal pressure of a gas component that s present n a gaseous mxture, s a pressure that would be exerted by that component f t alone were present n the same volume and at the same temperature. p A x A p Av 3) Dalton s law : Dalton s law mathematcally s gven by: P pa + p B, Where P s the total pressure exerted by gaseous mxture. pa and pb are the partal pressures of component gases A and B respectvely. 4) More Volatle Component: More volatle component s lower bolng pont component or the component wth hgher vapour pressure at a gven temperature. It s also called as the lghter component. 5) Less Volatle Component: In a bnary system, t s the component wth hgher bolng pont or lower vapour pressure at a gven temperature. It s also called as the heaver component. 6) Concentraton: 6.1. Mass Concentraton (Also known as mascon): It s defned as the mass of consttuent dvded by the volume of mxture. It s denoted by or. m where, m mass of consttuent, V volume of mxture. V For a pure chemcal the mass concentraton equals ts densty. For Bnary system havng components A and B, mass densty ( ρ ) of soluton s gven byρ A + ρ B ρ, where ρ A and ρ B are mass concentraton s of A and B respectvely. 6.2. Molar concentraton (Molarty): Molar concentraton s defned as the number of moles of speces A per unt volume of the soluton. 3 Mathematcally, It s gven as c A (kmol/m ) na ρ A V MA where, n A moles of speces A, MA molecular weght of component A For a bnary system of A and B, the total molar concentraton of the soluton s gven by C ca +cb 6.3. Mass Fracton (x A') : 5
WA, where WA and WB are gven weghts of A and B respectvely x A' WA + WB 6.4. Mole Fracton (x A ) : The mole fracton (xa) of speces A can be defned as the rato of number of moles of component to the total no. of moles. Mathematcally, for a bnary system, x A na na + nb Note: x A + x B 1 and x' A + x' B 1 In gas phase the concentratons are expressed n terms of partal pressures. In case of an deal gas p A V n A RT or ca na pa V RT Where, p A partal pressure of speces A n the mxture n A number of moles of A V molar volume of mxture T absolute temperature (K) R unversal gas constant xa n terms of p A s gven as: xa ca pa /RT pa C P/RT P Where P s the total pressure exerted by the gas mxture. C ca + cb pa pb P + RT RT RT 7) Velocty of Speces: Dfferent chemcal speces are movng at dfferent velocty n a dffusng mxture. The bulk velocty of the mxture would be some sort of an average velocty. For a mxture of n speces local mass average velocty u s defned as n ρ u u 1 n ρ Where u s velocty of th speces. 1 In case of bnary system, u ρ A u A +ρ B u B ρ n c U Local molar average velocty U of mxture s gven by U 1n c 1 6
c U +c U In a bnary system, U A A B B C 8) Flux: Flux s a vector quantty. The amount of speces (mass or molar unts) that crosses a unt area per unt tme s called flux (mass transfer flux or molar flux respectvely) of a speces. 8.1. Mass Flux: The mass flux of speces s defned as the mass of speces that passes through a unt area per unt tme. It s also defned as mass flow rate per unt area. () Mass flux relatve to fxed coordnate s gven by, ρ u For a bnary system, the mass flux of A and B relatve to statonary coordnate are A A u A and B ρ Bu B respectvely () Mass flux relatve to the mass average velocty u s gven by, j (u u ) For a bnary system, the mass flux of A and B relatve to mass average velocty are- ja ρ A (u A u) and jb ρ B(u B u) respectvely 8.2. Molar Flux: Molar flux s defned as moles of speces that passes through a unt area per unt tme. It s also defned as molar flow rate per unt area. () Molar flux relatve to the statonary coordnate s gven by, N c U For a bnary system, the molar fluxes of A and B wth respect to statonary coordnates are- N A ca U A and N B c c BU B respectvely () Molar flux relatve to molar average velocty U (also known as bulk velocty) s gven by, J c (U U) For a bnary system, the molar fluxes of A and B wth respect to an observer movng wth bulk velocty, J A c A (U A U) and J B c B (U B U) respectvely 1.3. Dmensonless numbers used n mass transfer: (1) Sherwood number (Sh) k'l convectve mass transport Sh, k' Mass transfer coeffcent DAB molecular mass transport Where L s the characterstcs length (2) Schmdt Number (Sc) Sc 1 Momentum dffusvty ν D AB DAB Mass dffusvty (3) Prandtl Number (Pr) 7
Pr C p Momentum dffusvty α K Thermal dffusvty (4) Lews Number (Le) Le K 1 Momentum dffusvty α Sc Mass dffusvty Pr DAB ρcp DAB (5) Reynolds Number (Re) ρvd Inertal force Re μ Vscous force (6) Stanton number (St) k' Sh St υ ReSc (7) Peclet number (Pe) Pe ReSc 1. Calculate the equllbrum composton of the lqud and vapour phase for a mxture of methyl alcohol and water at a temperature of 400 K and under a pressure of 45 kpa. Assume that both lqud and vapour behave deally Data : Vapour pressure of water at 400 K 15 kpa Vapour pressure of methanol at 400 K 60 kpa Soluton: Let x1 and y1 be mole fracton of methyl alcohol n lqud and vapour respectvely. p1 partal pressure of methyl alcohol p1 p1v x1 60x1 p2 water partal pressure p2 p2v x 2 15 1 x1 and we know total pressure P p1 p2 45 60x1 +15(1 x1) 45 15 60x1 15x1 30 45x1 x1 0.67 y1 p1 p1x1 60 0.67 0.89 P P 45 Hence at equllbrum: Lqud phase 0.67 mole fracton of methyl alcohol 8
Vapour phase 0.89 mole fracton of methyl alcohol. 2. A mxture of benzene and toluene bols at 380 K under a pressure of 101.325 kpa. Determne the composton of bolng lqud assumng that mxture obeys Raoult s law. At 380 K the vapour pressure of benzene s 160 kpa and the toluene s 70 kpa. Soluton: Let mole fracton of benzene n lqud xa P 100.325 kpa (gven data) pa 160 kpa p B 70 kpa xa P p vb p va p vb xa 101.325 70 0.348 0.348 160 70 Mole fracton of benzene n bolng lqud 0.348 100 34.8 Hence composton of the bolng lqud 34.8 mole% 9
10