Liquid-Vapor Equilibria in Binary Systems 1

Transcription

1 Lqud-Vapor Equlbra n Bnary Systems 1 Purpose The purpose of ths experment s to study a bnary lqud-vapor equlbrum of chloroform and acetone. Measurements of lqud and vapor compostons wll be made by refractometry. The data wll be treated accordng to equlbrum thermodynamc consderatons, whch are developed n the theory secton. Theory Consder a lqud-gas equlbrum nvolvng more than one speces. By defnton, an deal soluton s one n whch the vapor pressure of a partcular component s proportonal to the mole fracton of that component n the lqud phase over the entre range of mole fractons. Note that no dstncton s made between solute and solvent. The proportonalty constant s the vapor pressure of the pure materal. Emprcally t has been found that n very dlute solutons the vapor pressure of solvent (major component) s proportonal to the mole fracton X of the solvent. The proportonalty constant s the vapor pressure, p o, of the pure solvent. Ths rule s called Raoult's law: psolvent = p o solvent Xsolvent for Xsolvent = 1 (1) For a truly deal soluton, ths law should apply over the entre range of compostons. However, as X solvent decreases, a pont wll generally be reached where the vapor pressure no longer follows the deal relatonshp. Smlarly, f we consder the solute n an deal soluton, then Eq.(1) should be vald. Expermentally, t s generally found that for dlute real solutons the followng relatonshp s obeyed: p solute =K X solute for X solute << 1 (2) where K s a constant but not equal to the vapor pressure of pure solute. Equaton (2) s called Henry's law. The mplcaton of the foregong dscusson s that deal solutons are not lkely to be found. Only very dlute solutons could be consdered deal. Furthermore, there s no theory avalable whch places lmts on just how concentrated a soluton must be f devatons from dealty are to be observed. Such lmts are set by expermentaton and vary, of course, from system to system. A useful way of treatng data relatng the vapor pressure of any component to ts mole fracton n soluton s to plot p /X versus X. Varatons of the rato wth X ndcate devatons from dealty. From the dscusson of the prevous paragraphs a plot such as that shown n Fg. 1 mght be expected for a bnary soluton. At hgh concentratons of component, Raoult's law should be vald and the ordnate should be constant and equal to the vapor pressure of pure component. At some lower mole fracton of (more concentrated n solute) devatons from dealty may be observed and p/x may ncrease or decrease. At very low concentratons, the solvent becomes the solute and Henry's law becomes vald. Thus, p/x becomes constant agan and takes on the value of Henry's law constant. Idealty and devatons from t may be qualtatvely understood by consderng molecular nteractons. For the purposes of ths dscusson, we vew the gas-lqud nterface at the

2 molecular level. A crude representaton of a dlute bnary system s shown n Fg. 2. Component s the more concentrated (solvent). Ideal Soluton p X Henry's law regon Raoult's law regon Mole fracton, X Fgure 1. Varaton of p /X j Vapor j j j j j Lqud Fgure 2. Molecular representaton of a bnary gas-lqud system. If the system were pure, then all the molecules n the surface layer would be molecules and the observed vapor pressure would be that of the pure lqud. Addton of j molecules to the lqud so that the mole fracton of s less than unty reduces the concentraton of molecules n the surface layer just as t does n the body of the lqud. Energy s requred to transfer a molecule from the lqud to the gas phase, mplyng that ntermolecular potentals are mportant n determnng partal vapor pressures. If molecule "looks about" and "sees" the same potental feld as molecule j regardless of what ts neghbors are, then molecule wll requre the same energy as molecule j to transfer from the lqud phase to the gas phase. The partal vapor pressures wll then be drectly proportonal to the concentraton of each component n the soluton and wll extrapolate to the vapor pressure of each component when pure or pure j s used. Thus, a suffcent condton for an deal soluton s to requre the nteracton potental between (, j) pars to be dentcal to that between (, ) pars and (j, j) pars. Expermentally observed devatons from dealty are then attrbuted to dfferences n nteracton potentals between dfferent pars of molecules. From ths pont of vew devatons

3 from dealty become very ntutve snce there s no a pror reason to expect molecules of wdely dfferng propertes to have the same nteractons. At very hgh or very low concentratons of one component the constancy of p /X s easly understood snce the partners n these extremes are mostly of a sngle knd. From an expermental pont of vew, a bnary, two-phase equlbrum system at constant pressure can be characterzed by plottng the equlbrum bolng pont as a functon of the lqudand vapor-phase compostons (usually mole fractons). These two compostons are dfferent because of varatons n the escapng tendency of the molecules nvolved. Fgure 3 shows temperature versus composton dagrams for hypothetcal deal and nondeal mxtures. At the left s a typcal deal (or nearly deal) system. The center fgure shows the case of a strong negatve devaton from dealty n whch the bolng pont of some mxtures rses above that of the hghest bolng pure component. At the molecular level there are stronger forces between solvent and solute than between solvent and solvent. Azeotrope T T T 0 1 Mole fracton 0 1 Mole fracton Azeotrope 0 1 Mole fracton Fgure 3. Temperature versus composton for a bnary two component system. At some ntermedate composton the lqud- and vapor-phase compostons come together at the so-called azeotropc composton. Separaton of one component from another by fractonal dstllaton s mpossble at ths composton because the vapor and lqud phase have the same composton. The fgure at the rght n Fg. 3 s also a nondeal mxture n whch a postve devaton from dealty s found. As usual, the equlbrum propertes of these solutons are developed by consderng the Gbbs free energy or the chemcal potental. For the present case of a bnary two-phase system at equlbrum, we requre the chemcal potental, µ, of each component to have the same value n every phase: µ (l) = µ (g) (3) The chemcal potental s related to molar volume V and pressure p by the relaton du (g) = V dp (4)

4 If the gas s deal, substtutng for V of the gas n terms of the deal gas law furnshes dµ (g) = RT p d p (5) whch upon ntegraton, from a standard state pressure of p o =1 bar to a pressure for component of p,leads to µ (g) = µ o(g) + RT ln p o p (6) where µ o(g) s the standard-state chemcal potental. Substtutng Raoult's law for deal solutons nto Eq. (6) and notng that at equlbrum µ (l) = µ (g) leads to µ (l) = µ (l) + RT ln X (7) where µ (l) =/ µ o(g), whch serves to emphasze an mportant pont. If you are makng calculatons nvolvng standard states, make certan the standard state used s consstent wth the concentraton unts beng used (.e., just as p =/ X, so µ (l) =/ µ o(g) ). Equaton (7) depends for ts development on both the deal gas law and the deal soluton law. Use of these laws permtted the connecton between V and p and then X. Devatons from both these laws do occur. To examne how devaton from deal soluton behavor s formally treated, we return to Eq. (6) whch s vald as long as the vapor phase s deal for any soluton. To make progress toward nondeal soluton condtons, the vapor pressure of a component above the real soluton must be known. Generally speakng, vald equatons are not readly avalable n analytcal form. Rather, the expermental data have smply been tabulated for those systems that have been studed. Wth these data, Eq. (6) can then, n prncple, be used to furnsh the chemcal potental of the soluton. An alternatve, ntroduced by G. N. Lews, preserves the form of Eq. (6) or (7) but does not requre dealty. In ths formulaton the mole fracton s replaced by a quantty a, called the actvty of component, and Eq. (7) becomes µ (l) = µ (l) + RT ln a (8) In ths formulaton all devatons from dealty are contaned n the actvtes. Generally they are not amenable to quanttatve theoretcal nterpretaton and, as such, are smply emprcal expermental quanttes. The form of Eq. (8) however, s qute convenent because t preserves the form of all equlbrum constant expressons. The actvty of component s gven by

5 p a = (9) p where p s the partal vapor pressure of component and p s the vapor pressure of pure at the same temperature. Concluson: We have exchanged one dffculty for another. The form of thermodynamc relatons has been preserved through the ntroducton of the actvty. However, the problem of understandng nondealty has not been advanced at all. From one pont of vew, the actvty s smply a fudge factor whch brngs expermental data nto the form of an deal equaton. From a dfferent pont of vew, the use of Eq. (8) requres a method of obtanng actvtes from expermental measurements of concentratons. The actvty a appearng n Eq.(8) s related to a concentraton varable through the use of an actvty coeffcent γ. Ths coeffcent depends on both the speces and the concentraton scale. For the present experment the actvty coeffcent of nterest s that of a speces present n a soluton at mole fracton X and a= γx. Substtutng nto Eq.(9) and rearrangng gves γ = p (10) X p The vapor pressure of the pure lqud, p, s a functon of temperature and can be predcted usng the relatonshp B log p = A - t + C (11) wth t the temperature n degrees Centgrade and tabular values for A, B, and C (see Lange s Handbook). Expermental A refractometer s used n ths experment to measure mole fractons. To obtan mole fracton nformaton from refractve ndex measurements, the refractometer must be calbrated (.e., construct a graph of refractve ndex versus composton) usng solutons of known composton. Ths calbraton curve can then be used "n reverse" to fnd the composton of unknown mxtures from an expermental measurement of the refractve ndex. The calbraton chart for chloroformacetone mxtures s gven n Table 1. The bolng apparatus s shown n Fg. 4. An ntegral part s a reservor heated by a resstve flament,. Wth a soluton n the reservor and bolng, the vapor phase s condensed and trapped n the tube below the condenser. Under equlbrum condtons n the bolng soluton-vaporphase system, the trapped condensate represents the vapor phase, whle the lqud remanng n the reservor represents the soluton phase. In what follows chloroform-acetone mxtures are assumed. The same procedure of sample treatment and analyss works very well for toluene-ethanol mxtures.

6 Condenser Heater connectons to power supply Thermometer Stopper Trap for dstllate sample Heater Fgure 4. Apparatus for determnng lqud and vapor compostons as a functon of temperature. The system studed wll be chloroform-acetone. Samples of the followng solutons should be run startng set A wth 12 ml of acetone and set B wth 12 ml of chloroform: A B Increments added to (ml of acetone added to (ml of chloroform added exstng solutons 12 ml of chloroform) to 12 ml of acetone) Frst Second Thrd Fourth Ffth Sxth Chloroform s a suspected carcnogen-use gloves and keep solutons n the hood Notce that you wll begn set A wth pure chloroform and add sx consecutve portons of acetone to the bolng lqud. If n the course of the run the flask becomes too full, pour out about 10 mlmake certan the heater s off-and contnue the addton of acetone. Set B begns wth pure acetone. To empty the reservor, tlt the flask and rng stand together; don t loosen the clamps holdng the flask. The followng should be followed:

7 1. Place 12 ml of pure chloroform n the flask through the sde arm. Stopper the flask and start water flowng through the condenser. Record the barometrc pressure. 2. Close the swtch to the heater to start the lqud bolng. Cauton: Never operate the heater unless lqud covers t. If the heater s operated dry, the flament wll burn out. 3. After the dstllate trap s flled, empty by usng the strrer so that the dstllate wll flow back nto the body of the lqud. The dstllate trap should be empted at least three tmes before the sample of any soluton s wthdrawn. Contnue to empty the trap untl the temperature remans constant. 4. After the dstllate trap has been flled a thrd tme, allow 2 mn for overflow to establsh steady-state condtons and then stop heatng. Remove the dstllate sample wth a ppet and mmedately place nto one of the sample holders. Several small test tubes wll be needed for samples. Place the sample holders nto an ce water bath. The dstllate sample represents the vapor-phase composton. 5. Take a sample from the flask as representng the lqud phase at the same tme the dstllate sample s taken. 6. Record the equlbrum temperature correspondng to these two equlbrum compostons. 7. Measure the refractve ndex of both samples shortly after takng the sample to avod sample loss va evaporaton. Repeat the refractve ndex measurements to check for evaporatve losses and reproducblty. 8. Record the barometrc pressure. Calculatons 1. Use the ndex of refracton of pure chloroform and pure acetone to calbrate the refractometer. If there s an error, use the average error from the two measurements to correct all your readngs. From the calbraton curve, Table 1, determne the composton of the samples taken from the vapor and lqud phases n each experment. 2. Construct a phase dagram usng temperature versus mole percent composton. In the present case, there wll be two compostons plotted at each equlbrum bolng temperatureone for the lqud phase and one for the vapor phase. Construct ths one, sngle phase dagram by combnng the results from both set of runs on one dagram. Make sure to nclude the pure lquds. Draw smooth curves for the lqud and vapor composton lnes. You can draw these curves by hand usng a rubber ruler or French curve f Excel curve fttng proves problematc. 3. In lqud-vapor equlbrum systems, there sometmes exsts a partcular composton at whch the lqud phase and the vapor phase both have the same composton. Ths s called an azeotropc mxture. What s the azeotropc composton n the chloroform-acetone system and what s ts bolng pont? 4. Calculate the vapor pressure of acetone from Dalton's law, P =Yacetone Ptot for each measurement. Calculate the vapor pressure of pure acetone at the temperature of each measurement usng Eq. 11. Calculate the actvty coeffcent for acetone for each measurement usng Eq. 10. Use sgnfcant fgure rules to estmate the uncertanty n the actvty coeffcents.

8 5. Construct a plot of p/x versus X and comment on the dealty or nondealty of chloroform-acetone mxtures. Dscuss any observatons from a molecular vew-pont. 6. Plot the actvty coeffcent γa for acetone as a functon of the mole fracton of acetone. What nferences may be made from ths plot? Dscusson 1. Consder an azeotropc mxture of two components. Would fractonal dstllaton be an approprate way to separate the two components? Why? 2. Accordng to the phase dagram, what can be sad about the attracton between acetone molecules as compared to the attracton between chloroform and acetone molecules? What mght be the orgn of ths attracton? 3. Does ths system show postve or negtve devatons from dealty? 4. Is the vapor pressure at the azeotropc composton more or less than that predcted by Raoult's law? Explan. Table 1. Refractve-ndex vs. Composton for Acetone-Chloroform Mxtures M% M% M% M% nd 25 CHCl 3 nd 25 CHCl3 nd 25 CHCl3 nd 25 CHCl

9 Or f you prefer, you can use the followng polynomal ft to the tabular data, wth somewhat larger uncertanty: mol % = x x10 5 n D x10 4 n D x10 4 n D 3 If you use ths ft equaton, t s best to use the Table for the few compostons closest to 0% or 100%. References 1. John M. Whte, Physcal Chemstry Laboratory Experments, Prentce-Hall, Englewood Clffs, NJ, 1975, Experment 5.5. Appendx: Index of Refracton The ndex of refracton s the rato of the speed of lght n vacuum to the speed of lght n the sample medum, n=c v /c m. Index of refracton s a fundamental property of matter that s easly measured. Index of refracton s mportant n determnng fundamental molecular propertes such as polarzablty, as an analytcal tool, and as a practcal matter n optcal wavegude technology. Refractometers are used as analytcal tools, for example n the determnaton of sugar n beverages (wne) and the water content of hydraulc fluds used n automobles, among many uses. Most refractometers determne the crtcal angle of a substance as a measure of the ndex of refracton. The crtcal angle s also the parameter necessary to understand optcal fbers. Optcal fbers play a crtcal role n communcatons technology, ncludng the Internet and satellte technology, and also n analytcal nstrumentaton. The Crtcal Angle: When lght passes from a medum wth a hgher ndex of refracton to a medum wth a lower ndex of refracton, the angle wth respect to the perpendcular to the nterface ncreases, Fgure 1. θ v low n θ m hgh n Fgure 1. Refracton of lght passng from a medum, m, wth hgh ndex of refracton to one of lower ndex of refracton, such as n passng from glass nto vacuum or ar. The wave crests are shown wth sold lnes. The propagaton drecton s normal to the wave crests. The speed of lght n the medum wth lower ndex of refracton s faster causng the wave to bend and then θ v > θ m.

10 As the angle of ncdence s ncreased, the refracted beam angle also ncreases untl the refracted beam les along the surface of the sample, Fgure 2. Ths angle s called the crtcal angle. If the ncdence angle s greater than the crtcal angle, the lght s totally reflected from the nterface. θ v θ v θ v θ v θ m θ m θ m crtcal angle θ m total nternal reflecton Fgure 2. Crtcal angle. The angle of ncdence s ncreased untl the refracted beam makes a 90 angle wth the surface normal. Total nternal reflecton results f the ncdence angle s greater than the crtcal angle. Total nternal reflecton explans how optcal fbers can transmt lght wth lttle loss over large dstances through a flexble core. The requrement s that the outsde layer of the fber, whch s called the claddng, must have a lower ndex of refracton than the glass core. The angles n Fgure 2 can be related to the ndex of refracton: 1 n = c v c m = sn θ v sn θ m Measurng the crtcal angle s relatvely easy. The relatonshp between the crtcal angle and the ndex of refracton s gven by settng θ v = 90 : n = c v c m = 1 sn θ crt Normally the measurement s made n ar rather than vacuum, and then n (vacuum) = n (ar). Index of refracton s both wavelength and temperature dependent. The glass prsm n a refractometer s usually kept at constant temperature by crculaton of water from a constant temperature bath at 25 C. The ndex of refracton s normally determned usng a sodum arc emsson lamp as a monochromatc lght source. These lamps are also used for hgh ntensty street lghtng. The brght yellow color of a sodum arc lamp s due to the sodum D lne, therefore the ndex of refracton measured at ths wavelength s denoted n D. The most common type of refractometer s called an Abbe refractometer, Fgure 3. The lght from an ncandescent bulb s passed through a thn flm of the sample, whch s placed on a refractng prsm. The lght from the refractng prsm s reflected from a rotatng mrror to an eye pece. When the rotatng mrror s set properly, the user sees a feld of vew that s half-dark and half-brght. The nterface between the dark and lght regon corresponds to the crtcal angle.

11 Feld of vew Lenses Illumnatng prsm Amc prsms Sample Refractng prsm Rotatng mrror and scale Fgure 3. Abbe refractometer. The optcal measurement s complcated by the refracton of the refractng prsm whch s n addton to the sample. 1 However, the nstrument s calbrated verses a sample of known ndex of refracton. The measurement s taken by llumnatng a prnted scale on the rotatng mrror that s read drectly n ndex of refracton unts. You mght wonder how a property that s wavelength dependent can be measured usng a whte lght source. A cleaver optcal trck s used to cause all wavelengths to refract at the angle that would be obtaned usng a monochromatc arc lamp. Two Amc prsms are placed n the refracted beam. Each Amc prsm s actually three prsms that are cut at the proper angle from glass wth the approprate ndexes of refracton. The Amc prsms must be set properly for each measurement to focus all the dfferent wavelengths at the eye pece of the nstrument. Procedure: The refractng prsm of most refractometers s made from relatvely soft glass. To avod scratchng, clean the prsm wth clean cotton swabs. Never touch the prsm surface wth a glass ppette or other hard object. Turn on the constant temperature bath several hours n advance. Have avalable a pure lqud wth known ndex of refracton to check the calbraton of the nstrument. Use spectrophotometrc grade solvents for calbraton. Use the followng procedure for each measurement. 1. Open the prsm cell by lftng the top prsm usng the stanless steel handle. The llumnatng prsm wll rotate to the left. 2. Usng a Pastuer ppette add a few drops of the sample to the prsm surface. Take care not to touch the surface wth the ppette to avod scratchng the refractng prsm. 3. Quckly close the llumnatng prsm. Lft the lght so that t almost touches the llumnatng prsm. Turn on the lght by lftng the swtch on the left-hand sde of the nstrument.

12 4. Lookng through the eye-pece, turn the large metal knob on the rght-sde of the nstrument untl the vsual feld has the dark-lght nterface algned at the cross-hars. You can adjust the focus by pullng or pushng on the barrel of the eye pece. 5. Adjust the Amc prsms by rotatng the dal on the front of the nstrument. When set properly the dark-lght nterface under the cross-hars wll be colorless. The nterface wll be red on one sde and blue on the other, but colorless n the center under the cross-hars. Carefully realgn the the dark-lght nterface to the center of the cross-hars, Fgure Depress the swtch on the left-hand sde of the nstrument to llumnate the scale. Lookng n the eye-pece, record the ndex of refracton to fve sgnfcant fgures. 7. Open the prsm cell. For volatle samples, smply let the sample evaporate. No addtonal cleanng s necessary. For hgh bolng lquds, wash the prsms usng a cotton swab and methanol. If the sample sn t soluble n methanol, try acetone or methylene chlorde. 8. When you have fnshed all your samples, turn off the constant temperature bath and make sure the lamps are turned off. Leave the prsm cell clean, dry, and closed to avod scratches. Reference: 1. D. P. Shoemaker, C. W. Garland, J. I. Stenfeld, J. W. Nbler, Experments n Physcal Chemstry, McGraw-Hll, New York, NY, 1989.