Chap. 6 Multiphase Systems

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1 Cha. 6 Multhase Systems All chemcal rocesses nvolve multhase oeratons: - Phase-change oeratons: freezng, meltng, evaoraton, condensaton - Searaton and urfcaton rocesses: leachng, absorton, dstllaton, extracton, adsorton, crystallzaton, (Examles) 1. Brewng a cu of coffee - leachng( 침출 ) 2. Removal of sulfur doxde from a gas stream - absorton( 흡수 ) S SO2 n the ar SO3 H2SO4(acd ran) 3. Recovery of methanol from an aqueous soluton - dstllaton 4. Searaton of araffnc and aromatc hydrocarbons - lqud extracton( 추출 ) 5. Searaton of an somerc mxture - adsorton( 흡착 ), crystallzaton -Molecular seve 6. Concentrate O2 for breathng mared atents - adsorton 7. Obtan fresh water from seawater-evaoraton, reverse osmoss Drvng force n the searaton rocesses concentraton dfference hase equlbrum 6.1 SINGLE COMPONENT PHASE EQUILIBRIUM 6.1a Phase Dagram A hase dagram of a ure substance s a lot of one system varable aganst another ( mostly PT dagram ) that shows the condtons at whch the substance exsts as a sold, a lqud, and a gas. 1

equlbrum: sublmaton ont trle ont crtcal ont: crtcal

2 PT dagram vaor-lqud equlbrum: bolng ont/vaor ressure sold-lqud equlbrum: meltng ont(freezng ont) sold-vaor equlbrum: sublmaton ont trle ont crtcal ont: crtcal temerature/crtcal ressure Freezng ont of water decreases wth ncreasng ressure: 2

3 CO2 Crystal H2O Lqud ce Molecular crystals: many small, dscrete, covalently bonded molecules by van der Vaals or hydrogen bondng Methane(below -183C): FCC H2O(I h at atmosherc ressure): HCP Many organc comounds: energetc materals,.. 3

4 6.1b Estmaton of Vaor Pressure -The volatlty of a seces: the degree to whch the seces tends to transfer from the lqud (or sold) state to the vaor state -The vaor ressure of a seces: a measure of ts volatlty -Often vaor ressure data are not avalable at temeratures of nterest. - Measure the vaor ressure at the desred temerature - Estmate the vaor ressure usng an emrcal correlaton Claeyron equaton: relatonsh between the vaor ressure of a ure substance ( ) and the absolute temerature (T ) d dt Hˆ T Vˆ Vˆ v (6.1-1) g l Where V ˆ ˆ : vaor와 lqud의 secfc molar volume g, V l Ĥ v : Latent heat of vaorzaton When ressure s not extremely hgh: Vˆ Vˆ g l, Vˆ g Vˆ l Vˆ g d dt The vaor s assumed to be deal gas: ˆ RT V g Hˆ v RT T d Hˆ v Hv 1 dln d R dt 2 T ˆ R T d ln Hˆ v (6.1-2) used to determne heats of vaorzaton. 1 R d( ) T Clausus-Claeyron equaton: Suose that the heat of vaorzaton of a substance ( Ĥv ) s ndeendent of temerature, Hˆ ln v B (6.1-3) Plot of RT 1 ln vs. T should be straght lne. Antone equaton: an emrcal equaton B log 10 A ( : mmhg, T : C T C, constants A,B,C: Table B.4 ) 4

6.2 THE GIBBS PHASE RULE Extensve varable( 크기변수 ): deend on the system sze(mass, volume, ) Intensve varable( 세기변수 ): temerature, ressure, densty, degree of freedom( 자유도, DF) : the number of ntensve

5 6.2 THE GIBBS PHASE RULE Extensve varable( 크기변수 ): deend on the system sze(mass, volume, ) Intensve varable( 세기변수 ): temerature, ressure, densty, degree of freedom( 자유도, DF) : the number of ntensve varables that can be secfed for a system at equlbrum. Gbbs hase rule DF 2 c, where : number of hase c : number of seces Ex The Gbbs Phase Rule Josah Wllard Gbbs (February 11, 1839 Arl 28, 1903): an Amercan theoretcal hyscst, chemst, and mathematcan. He devsed much of the theoretcal foundaton for chemcal thermodynamcs as well as hyscal chemstry. As a mathematcan, he nvented vector analyss (ndeendently of Olver Heavsde). Yale Unversty awarded Gbbs the frst Amercan Ph.D. n engneerng n 1863, and he sent hs entre career at Yale. 5

6 6.3 GAS-LIQUID SYSTEMS: ONE CONDENSABLE COMPONENT Saturaton: the gas hase contans all the vaor of a condensable seces t can hold at the system temerature and ressure. In an ar-water system: humdty Raoult s law, sngle condensable seces: y P ( T) Suerheated vaor: a vaor resent n a gas n less than ts saturaton amount: y P ( T) Dew ont: f a gas contanng a sngle suerheated vaor s cooled at constant ressure, the temerature at whch the vaor becomes saturated: y P T d Degree of suerheat of the gas: the dfference between the temerature and the dew ont of a gas Bolng ont of the lqud at the gven temerature: the temerature at whch P Relatve saturaton (relatve humdty) : ( ) s r hr 100% Molal saturaton (molal humdty): s m ( hm ) P moles of vaor moles of vaorfree( dry) gas Absolute saturaton (absolute humdty): s a ( h Percentage saturaton (ercentage humdty): s h s s / P 100 % / P m m 100% a ) M massof vaor P M massof dry gas dry Ex ) comoston of a saturated gas-vaor system Ex) 6.3-2) Materal Balances around a Condenser 6

7 6.4 MULTICOMPONENT GAS-LIQUID SYSTEMS 6.4a Vaor-Lqud Equlbrum data 6.4b Raoult s law and Henry s law Raoult s law: A yap xa A( T) : Generally vald when xa s close to 1. Henry s law: y P x H (T ) : (T ) s the Henry s constant. Generally A A A A H A vald when x A s close to 0 rovde that A does not dssocate, onze, or react n the lqud hase. Ideal soluton: Ex.6.4-2) Raoult s Law and Henry s Law 6.4c Vaor-Lqud Equlbrum Calculatons for Ideal Solutons bubble ont: the temerature at whch frst bubble forms when a lqud s heated slowly at constant ressure. dew ont: the temerature at whch the frst lqud drolet forms when a vaor s cooled slowly at constant ressure. Suose an Ideal soluton follows Raoult s law and contans seces A, B, C, If the mxture s heated at constant ressure P to ts bubble-ont tem., T b, the further addton of a slght amount of heat wll lead to the formaton of a vaor hase. The artal ressures of the comonents are gven by Raoult s law. x T, A, B, C, b P x T b T may be calculated by tral and error. T can be obtaned by Antone b equaton or tables. Bubble ont ressure: the ressure at whch the frst vaor forms when a lqud s decomressed at a constant temerature. The mole fracton n the vaor n equlbrum wth the lqud (deal lqud) s y P b x ( T) P b 7

8 Suose a gas hase contans the condensable comonents A, B, C, and a noncondensable comonent G at a fxed ressure P. If the gas mxture s cooled slowly to ts dew ont, t wll be n equlbrum wth the frst lqud that forms. Assumng that Raoult s law ales, the lqud hase mole fractons are: x y P ( T d), A, B, C, excludngg x y P ( ) Td 1 Dew ont ressure: the ressure at whch the frst lqud drolet forms when a vaor s comressed at a constant temerature P d 1 y ( T ) Ex ) Bubble and dew-ont calculatons 6.4d Grahcal Reresentaton of Vaor-Lqud Equlbrum Fgure Bolng: a secfc tye of vaorzaton rocess n whch vaor bubbles form at a heated surface and escae from the lqud. Vaorzaton: molecular evaoraton of lqud from a gas-lqud nterface, whch may occur at temeratures below the bolng ont. Ex ) Bubble and Dew-ont Calculatons usng Txy Dagrams 8

a secfed amount of the lqud at equlbrum. In general, g solute dssolved/100g solvent.

9 6.5 SOLUTIONS OF SOLIDS IN LIQUIDS 6.5a Solublty and Saturaton Solublty of a sold n a lqud: the maxmum amount of that substance whch can be dssolved n a secfed amount of the lqud at equlbrum. In general, g solute dssolved/100g solvent. Saturated soluton: A soluton that contans as much of a dssolved seces as t can at equlbrum Suersaturaton: dfference between actual and equlbrum concentratons. Fgure Solubltes of norganc solutes Metastable zone wdth 9

6.5b Sold Solubltes and Hydrate Salts Polymorhsm ( 다형 ( 多形 ), 동질이형 ( 同質異形 ), 동질다상 ( 同質多像 ) ) - Ablty of any element or comound to crystallze nto at least two dfferent crystallne structures, but they

- Dfferences n morhologcal aearance do not necessary reflect olymorhsm.

10 6.5b Sold Solubltes and Hydrate Salts Polymorhsm ( 다형 ( 多形 ), 동질이형 ( 同質異形 ), 동질다상 ( 同質多像 ) ) - Ablty of any element or comound to crystallze nto at least two dfferent crystallne structures, but they should be dentcal n the lqud or gaseous state. - The dfferent structures are called olymorhs, olymorhc modfcatons. - If the materal s an element, olymorhs are called allotroes. - Dfferences n morhologcal aearance do not necessary reflect olymorhsm. -Molecular conformaton and ackng caused by varous ntermolecular forces, hydrogen bondng, van der Waals forces, nteractons wth solvents and addtves, etc.. -Whch olymorhc form of a comound s formed deends on the rearaton and crystallzaton condtons: method of synthess, temerature, ressure, solvent, coolng and heatng rate, seed crystals, etc. Ex 1) C(fullerene) 10

11 Examle 2) Ammonum Ntrate ( NH 4 NO 3 ) Ind. Eng. Chem. Res. 49, , olymorhs between and 125 C I: Cubc, II: Tetragonal, III: Orthorhombc, IV: Orthorhombc, V: Tetragonal 11

Pseudoolymorhsm Solvates (Hydrates) whch form

adductve crystallzaton, ncluson comound (the

Nonstochometrc Examle ) Ind. Eng. Chem. Res.

C6H5CH2CH(NH2)CO2H ) One of the essental amno

12 Pseudoolymorhsm Solvates (Hydrates) whch form as the result of comound formaton wth the solvent (water). Stochometrc Clathrate 내포화합물 포접 ( 包接 ) 화합물 : adductve crystallzaton, ncluson comound (the host and the guest). Nonstochometrc Examle ) Ind. Eng. Chem. Res., 40, , 2001 L-henylalanne ( C6H5CH2CH(NH2)CO2H ) One of the essental amno acd Pharmaceutcal ntermedate Food ntermedate-asartame (l-asartylhenylalanne methyl ester) (L-asartc acd) Monohydrate Anhydrate 12

13 6.5c Collgatve Soluton Proertes Collgatve roertes( 결합특성, 총괄성 ): roertes of a soluton that deend on the number of solute artcles resent but not on the chemcal roertes of the solute: vaor ressure, freezng ont, bolng ont, osmotc ressure Consder a soluton n whch the solute mole fracton s x and assume that the solute s nonvolatle, nonreactve, and nondssocatve and Raoult s law holds. By Raoult s law, effectve solvent vaor ressure: s e s ( 1 x) s Vaor ressure lowerng: s s ( s ) e s (1 x) s xs The lowng of solvent vaor ressure has two mortant consequences. The solvent n a soluton at a gven ressure bols at a hgher temerature and freezes at a lower temerature than does the ure solvent at the same ressure. Relatonsh between concentraton and both bolng ont elevaton and freezng ont deresson (Proof: rob. 6.87) Bolng ont elevaton: T b T bs T b0 RTb Hˆ 2 0 v x Freezng ont deresson: T m T m0 T ms RT Hˆ 2 m0 m x ex)

14 6.6 EQUILIBRIUM BETWEEN TWO LIQUID PHASES 6.6a Mscblty and Dstrbuton Coeffcents Ex.6.6-1) extracton of acetone from water Water/Chloroform-mmscble, Water/Acetone-mscble, Chloroform/Acetone-mscble Water/acetone soluton + chloroform acetone/water + acetone/chloroform dstrbuton coeffcent (artton rato): K 6.6b Phase Dagram for Ternary Systems x x A A C hase W hase 1.72 Fgure Trangular hase dagram for water-acetone-mibk (methyl sobutyl ketone) at 25C (1941) Regon A: a sngle lqud, Regon B: two hases/te lne Pont K: 15wt% water, 65%acetone, 20%MIBK Pont M: 55wt% water, 15% acetone, 30% MIBK two hases: ont L(85% water, 12%acetone, 3%MIBK) ont N (4%water, 20%acetone, 76%MIBK) 14

15 6.7 ADSORPTION ON SOLID SURFACES ADSORPTION: The surface of a sold reresents a dscontnuty of ts structure. The forces actng at the surface are unsaturated. Hence, when the sold s exosed to a gas, the gas molecules wll form bonds wth t and become attached. ADSORBENT /ADSORBATE Industral sorbents Actvated carbon: 320m 2 /g Molecular Seve Carbon (carbon molecular seve) 15

16 Actvated Alumna Slca Gel Zeolte 16

17 Macroores: d > 500 Å (50nm) Mesoores: 20 Å < d < 500 Å Mcroores: d < 20 Å 17

18 ADSORPTION ISOTHERM: adsorbate equlbrum data on a secfc adsorbent are often taken at a secfc temerature. 18

19 DETERMINATION OF AN ISOTHERM: CCl 4 /actvated carbon (.234) Langmur sotherm: X ak L 1 K L 19

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CHE-201. I n t r o d u c t i o n t o Chemical E n g i n e e r i n g. C h a p t e r 6. Multiphase Systems

CHE-201. I n t r o d u c t i o n t o Chemical E n g i n e e r i n g. C h a p t e r 6. Multiphase Systems I n t r o d u c t o n t o Chemcal E n g n e e r n g CHE-201 I N S T R U C T O R : D r. N a b e e l S a l m b o - G h a n d e r C h a t e r 6 Multhase Systems Introductory Statement: Phase s a state of