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J. Chem. Thermodynamics1975,7, 839-846

A continuous-dilution device for themeasurement of static vapourpressures ofbinary liquid mixtures

R. S. MURRAY and M. L. MARTIN

Department of Physical and Inorganic Chemistry,University ofAdelaide, Adelaide, South Australia

Received 0 March 2975)

A continuous-dilution evice or the rapid measurement f staticvaponr pressures fbinary liquid mixtures as a function ofcomposition s described. hese measurementstogether with computedxcess ibbs ree energies re reported or benzene n-hexaneat 298.15 Kand compared with the results f Dunlop et al. “)

1. Introduction

In recent years continuous-dilution dilatometry(*) andisothermal-dilution calori-metry(3S4) have yielded highly accurateexcess volumes and excess enthalpies ofbinary liquid mixtures. Thispaper describes the construction and operation ofacontinuous-dilution device for making rapid and accuratedeterminations of staticvapour pressures and excess Gibbs freeenergies of binary liquid mixtures. The entirecomposition range iscovered in two experimental runs. The method has been usedtodetermine the excess Gibbs free energies for benzene + n-hexane at298.15 K.

2. Experimental

A diagram of the vapour-pressure apparatus is shown in figure 1.A Pyrex-glassvacuum line, interposed with Nupro bellows valves andKovar glass-to-metal seals,is mounted in a rigid brass framework towhich is fitted an adjustable three-pointsuspension for levellingpurposes. A calibrated measuring burette MB of volumeabout 18 cm3consists of two sections of Veridia precision-bore (4 mm, 8 mm)glasstubing with three fiducial marks along its length. A bulb B atthe lower end of theburette branches down to a mercury reservoirand out to valve 8 through which theburette is filed with liquidfrom the degassing apparatus. The mercury reservoir isconnected viapulley-operated valve 6 either to a vacuum or to a nitrogensupplyso that the level of the mercury in the burette can belowered or raised. A glass bowlsurrounding the bulb is fYled withice or liquid nitrogen during distillation of liquid

into the burette. A 2 mm bore tube connects the upper part ofthe burette to pulley-operated valve 4 through which additions ofliquid are made to the vapour-pressure

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840 R. S. MURRAY AND M. L. MARTIN

cell C. For very fine control and avoidance of side thrusts onthe valve 4, a brass barof adjustable length is interposed betweenthe valve spindle and the pulley shaft.The cell contains a coiledplatinum stirrer mounted below a small glass-enclosedmagnet whichis activated by a solenoid, and is connected to the manometercon-structed of Veridia precision-bore (20 mm) tubing and mountedover a mercuryreservoir. Mercury levels in the manometer areadjusted as described for the burette

FIGURE 1. Vapour-pressure apparatus. Manometer M constructedfrom 20 mm Veridia precision-bore tubing with fiducial marks F4,F5; cell C, capacity 50 cm3 containing liquid of knownmassintroduced through valve 2; platinum coil stirrer PS connectedto a sealed glass tube containingsoft iron and lifted upwards bysolenoid S; 12.7 mm Nupro stainless-steel bellows valves, 0, 1 to3;and 6.35 mm Nupro stainless-steel bellows valves , 0,4 to 8, withconnexions to the valves throughKovar glass-to-metal seals usingzytel or teflon ferrules and Swagelok fitt ings; pulleys Pl to P3tooperate valves 4 to 6; mercury reservoirs Rl and R2; Dewar D raisedwith rod R to surroundcell, ice water added through Dewar funnelDF; calibrated measuring burette MB constructedof 4 mm and 8 mmVeridia precision-bore tubing with fiducial marks Fl to F3 ; bulb Bsurroundedby glass bowl GB, liquid introduced from degassingapparatus through valve 8.

Calibration (by nitrogen compression) of the volume of the cellbetween fiducialmark F4 and valve 4, about 70 cm3, enablescorrections to be made for vapourspace. When necessary a smallDewar can be raised with a rod to cool the cell anditscontents.

The method for degassing liquids has been described by Dunlop et~1.c~) Usingthe apparatus shown in figure 2, liquid is distilledfrom the storage flask SF intoflask .F which is cooled with liquidnitrogen, With continuous pumping, the frozenliquid is slowlysublimed on to the liquid-nitrogen-cooled cold finger. Althoughonesublimation completely degasses most liquids the procedure isalways repeated.

The measuring burette is filled with liquid as follows : withliquid in the flask belowclosed valve 9 the degassing apparatus isconnected to the vapour pressure apparatusthrough valve 8 and bothsections are pumped down overnight on the bench to a

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CONTINUOUS-DILUTION VAPOUR-PRESSURE APPARATUS 841

pressure of less than 1O-3 Pa. After closing valve 8 about 25cm3 of liquid 1 arethoroughly degassed and then distilled throughre-opened valve 8 into the bulbunder the burette with the mercurylevel slightly below the glass bowl which is filledwith suitablecoolant. Valves 4 and 8 are closed and, after thawing, liquid 1 isforcedinto the burette by raising the mercury level so that it isfinally contained underpositive pressure between valve 4 and themercury meniscus which, ideally, isjust

to valve 8

“=?l

highvacuum

FIGURE 2. Degassing apparatus. Storage flask SF containingliquid and drying agent, sealedwith Nupro valve; 6.35 mm Nuprostainless-steel bellows valves , 0, to 13; cold-fingerCFtoholdliquid nitrogen; flask F to contain liquid distilled from SF:Pirani gauge head P: tran T to removevapour used in flushing theapparatus; glass T-tubing connects valves-10 and 11 to-valve 8 ofthevapour pressure apparatus, replaced by glass U-tubing whendegassing the liquid to be distilled intoa weighed ampoule orflask; weighed break-seal ampoule A with 6.35 mm Kovarglass-to-metalseal for attaching to valve 13. (For connexion tovalve 2 of the vapour-pressure apparatus the 6.35 mmglass-to-metalseal is removed from the reweighed filled ampoule and a 12.7 mmKovar glass-to-metal seal is joined at the break-seal end of theampoule.)

below fiducial mark F2. Any excess liquid is bled off throughvalve 8 before thedegassing apparatus is detached. Thevapour-pressure apparatus is then transferredto a thermostattedbath to test the effectiveness of the degassing procedure.Afterre-connecting the apparatus to the pumps with flexiblestainless-steel tubing andre-evacuating, the mercury is raised tosuitable levels in the manometer arms and asmall volume of liquid 1is admitted to the cell until the mercury meniscus in theburetterises close to the fiducial mark F2. The vapour pressure of liquid1 is measuredas described below. The apparatus is then removed fromthe bath.

The following procedure is used to admit pure liquid 2 of knownmass to the vapour

pressure cell: with valves 10 and 11 connected with glasstubing, about 25 cm3 ofliquid 2 of known mass are degassed and thensublimed into, and finally sealed in,

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842 R. S. MURRAY AND M. L. MARTIN

either a small weighed flask with attached Nupro valve or aweighed break-sealampoule attached to valve 13. The mass of liquid2 is determined from accurateweighings, to +O.OOOl g, corrected tovacua. After attaching the ampoule or flaskto valve 2 of the vapourpressure apparatus and thoroughly evacuating, the liquidisdistilled into the cell cooled with liquid nitrogen. The frozenliquid is pumped onbriefly before raising the mercury level intothe manometer arms and then allowingthawing to proceed.

The loaded vapour-pressure apparatus is placed in avibration-free thermostattedbath, reconnected to the pumps, andlevelled. After temperature equilibration thepositions of Fl and F4and all mercury menisci are measured with a 1 mcathetometer(Precision Tool & Instrument Co.). To make anaddition of liquid 1 the cell is firstcooled by adding ice + waterto the suitably positioned Dewar and then a smallquantity of liquidis admitted from the burette through valve 4. The ice waterremainsin position in the Dewar due to its density and by cooling the cellcontentsobviates large pressure changes if the added liquid has avapour pressure very differentfrom that of the liquid in the cell.(This procedure is also used to bring back into thecell any liquidwhich has condensed on the mercury surface in the manometer,aproblem which occurs with pure liquids and sometimes withmixtures.) After tem-perature equilibration the mercury level inthe burette is recorded and the levels inthe manometer are read offuntil, with periodic stirring, the difference is constant.Thesethree readings together with the known mass of liquid in the cellgive thecomposition of the cell contents to a precision of betterthan +0.0002 in the molefraction and the vapour pressure to within54 Pa. Further additions of liquid aremade to complete theremaining half of the mole-fraction range. At the conclusionof therun the contents of the cell are distilled into a weighed flaskwith attachedNupro valve to test for quantitative transfer ofliquid 2 and accuracy of buretteadditions. The second half of themole-fraction range is covered by a second series ofmeasurementswith the positions of the liquids reversed.

Bath-temperature control to better than + 0.002 K is achieved byuse of a thermistorbridge and the feedback from a sensitive chartrecorder to activate a thyratron relayand a 100 W blackened lightglobe. The absolute bath temperature is measured toabout f 0.003 Kwith a pressure-insensitive bomb-calorimeter thermometercalibratedcarefully and frequently against a Leeds and Northrupplatinum resistancethermometer.

3. Materials

“Univar” A.R. grade benzene and Merck “Uvasol” spectroscopicgrade n-hexanewere purified by methods previously describedc5, @and stored over clean sodiumwire. Impurities of not more than 0.002and 0.02 mole per cent for the respectiveliquids were revealed bygas-chromatographic analyses using 10 m columns packedwith 10 massper cent of didecyl phthalate or squalane on AW-DMCS Chromosorb Wat333 K in an Fl 1 Perkin-Elmer gas chromatograph withflame-ionization detection.

Samples were degassed and stored in flasks SF with attachedNupro valves (figure 2)over B.D.H. type 4A molecular sieves whichhad been previously outgassed and dried

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CONTINUOUS-DILUTION VAPOUR-PRESSURE APPARAT US a43

at high temperature in vacua. These sieves were chosen for theirextreme affinity forwater coupled with their ability to bedegassed, a property not possessed by sodiumwire. Both liquids weredegassed, as described above, just prior to use.

The condition of a liquid to be used for vapour pressuremeasurements was evalu-ated by measuring the equilibrium vapourpressure in the cell, then sweeping awaythe vapour into a cold trapand retesting the remaining liquid. (The manometer levelswerelowered with liquid in the cell by first ballasting the high sideof the manometerwith vapour from the same liquid contained in aflask attached to valve 2.) Thisprocedure produced no observablechanges in benzene but successively reduced thevapour pressure ofn-hexane to a constant value indicating the presence of tracesofeither air or volatile impurity in the sample. Samples of theseliquids of similar purityhave previously been used for related workin this laboratory at which time theirdensities were determinedaccurately and are in accord with those in reference 1 towithin&2x low5 g cme3. The masses of benzene and n-hexane injectedfrom theburette during a run were computed from thesedensities.

The vapour pressures of benzene (12.683 kPa) and n-hexane(20.153 kPa) at298.15 K are in good agreement with literaturevalues corrected to IPTS-68.‘l’

4. Results and discussion

Excess Gibbs free energies GE(~l) were calculated from measuredvapour pressuresusing the method of Barker. (‘) A vapour phasecorrection was applied in order toobtain the true composition ofthe liquid phase. A computer program was usedto calculate GE&)and yl, the vapour phase composition, from an initial estimateof x1which ignored the vapour phase entirely. This value of y1 was thenused tocompute a new x1 and the iterative cycle continued untilconvergence was obtainedin both modes, i.e. until successive valuesof x1 showed negligible changes while thesum of the squares of thepressure residuals was minimized to give a least-squaredfunction ofthe form:

GE(xl)/RT =~1x2 I;i Ui(Xl-~z)i. (1)

Addition of extra terms ai and the introduction of a skewingparameter K in equa-tion (2) due to Myers and Scott,(*)

GE(xl)/RT = ~1 x2 Z, Ui(Xl -~z)i/{ 1-K(X, -x2)}, (2)

produced no further significant reduction in the sum of thesquares of the pressureresiduals.

Table 1 lists the experimental vapour pressures for two seriesof experiments atcalculated mole fractions x1 and y1 of n-hexanefor the liquid and the vapour phases,as well as the activitycoefficients of n-hexane and benzene in the liquid phase andexcessGibbs free energies at each mole fraction. The second virialcoefficients of thevapours used in calculating GE are thosecontained in reference 1.

In table 2 a comparison of the values of GE computed from thevalues of ni for bothruns in this work is made both against theoriginally reported values of Harris andDunlop(‘) and, moredirectly, against the values calculated from their data fittedto

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844 R. S. MURRAY AND M. L. MARTIN

TAB LE 1. Experimental results for n-hexane (1) + benzene (2) at298.15 K

Sp = p(expt) - p(ca lc.)

Xl Yl plkpa Sp/kPa fi h P/J mol-1

Run 1

00.00390.01070.02120.03120.03980.06290.10790.14020.16430.19530.22470.25990.28530.31010.3320

*0.407s0.43240.45990.49470.53320.56670.6076

0.65020.70460.75930.82810.89780.93470.95910.98351

-0.01320.03520.06630.09360.11520.16700.24730.29360.32380.35850.38830.42060.44220.46240.47900.53510.55220.57150.59490.62110.64410.6721

0.70180.74110.78240.83790.89830.93350.95770.9827

-

12.68312.80713.01813.31113.58413.80714.34815.24415.78016.13716.55916.90417.28817.53717.76117.96318.50918.67818.83419.04619.24419.40019.576

19.73719.90620.04120.15620.22420.12020.19420.17320.153

- -0.003 2.16810.008 2.13270.002 2.08090.004 2.03370.0061.99520.001 1.8992

-0.003 1.7407-0.007 1.6459-0.006 1.5838

0.000 1.51250.005 1.45340.005 1.39130.003 1.35180.0011.31680.017 1.2885

-0.003 1.20700.004 1.1851

-0.009 1.16280.004 1.13760.001 1.1132

-0.003 1.0946-0.001 1.0749

0.000 1.0575-0.003 1.0392-0.004 1.0249-0.005 1.0120

0.013 1.00400.002 1.0016

-0.001 1.00060.000 1.0001-

a, = 0.61990 al = -0.11672, az = 0.03304, a3 = -0.01375

E(SP,)~ = 0.050 kPa2

Run 2

0 - 12.683 -0.0133 0.0430 13.079 -0.0030.0287 0.0866 13.5070.0000.0463 0.1304 13.958 0.0030.0872 0.2128 14.849 0.0010.14040.2940 15.784 - 0.0020.1966 0.3603 16.571 -0.0030.2590 0.420117.283 0.0030.3243 0.4739 17.880 -0.0030.3736 0.5106 18.2740.0030.4094 0.5362 18.530 0.0060.4562 0.5688 18.825 0.002

*0.4569 0.5695 18.821 -0.0050.5271 0.6172 19.212 -0.0030.62770.6867 19.650 -0.009

-

l.1.00011.00051.00121.00191SW451.01271.02081.02781.03821.04931.06411.07561.08761.09881.14171.15701.17471.19851.22621.25171.2845

1.32061.36981.42261.49361.56991.61151.63931.6674

-

2.10512.03451.95931.80711.64591.51131.39421.29901.24141.20571.16591.16531.11731.0672

-1.00021.00091.00241.00821.02031.03811.06301.09441.12121.14241.17211.17261.22131.2999

-7.5

20.539.857.772.5

110.6176.2217.0244.1275.2300.8326.7342.3355.2364.7384.,387.1387.6384.9377.8368.2352.3

331.2297.6256.6195.4123.0

80.951.621.1-

-25.152.882.9

146+216.3275.7325.6361.3377.9384.9387.6387.6379.3343.3

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CONTINUOUS-DILUTION VAFOUR-PRESSUR E APPA RAT US

TABLE l-c*ntinued

845

Xl

0.69110.74400.81350.86440.92240.97050.98961

Yl PI@ Gp/kPa A A2 GE/J mol-l

0.7314 19.885 0.007 1.0445 1.3552 307.30.7708 20.028 0.0061.0297 1.4050 269.80.8260 20.152 -0.003 1.0153 1.4763 210.*0.869020.206 -0.003 1.0080 1.5333 160.10.9217 20.221 -0.003 1.0026 1.603896.70.9685 20.202 0.009 1.0004 1.6674 38.30.9888 20.169 O.OOG1.oooo 1.6941 13.8

- 20.153 - - - -

a, = 0.61993, al =-0.11567, a2 = 0.03563, a3 =-0.00392

Z @ = 0.025 kFa2

TAB LE 2. Comparison of excess Gibbs free energies GE forn-hexane (1) + benzene (2)with the results of Harris andDunlop(l)

Run 1 Run2 Harris and Dunlop”)

observed cake., equa tion (1)

Xl GE/J mol-1

0.09787 e 162.5 161.5 162.2 162.00.17675 257.1 256.3 257.6257.9

0.29029 345.1 344.7 346.6 347.20.36452 375.7 375.5 377.a377.80.37531 378.5 378.4 380.3 380.60.48754 385.7 385.7 387.0386.50.59742 356.7 357.0 356.8 355.90.69838 301.8 302.6 300.8300.60.79959 222.0 223.5 220.6 221.60.90882 110.7 112.4 109.8111.7

a Misprinted in the original paper.(l)

a four-parameter equation (1) at their mole fractions. Theagreement is within experi-mental error which, from an analysis ofthe equations : ( ’ )

GE = x&+x,& (3)

P? = RTln(~~i/~ix,)+(Vi-Bii)(Pi-~)+~6ijYj”, (4)

is approximately +2 J mol-l taking into account theapproximation 6,, = 0 whichis widely used and is discussed inreference 1. The external consistency is shown bythe measurementsaround the overlap region (marked by asterisks in table 1).

It is believed that this apparatus offers some advantages overcontinuous-dilutionmethods previously described. ~‘,~r) Therelative simplicity of the cell ensures speedyequilibration afteran addition is made and, because of its extremely small leakrate(less than 2 x 10V4 Pa mm-l), the vapour pressure of anenclosed liquid remainsstatic within experimental error for longperiods. The “mercury piston” type buretteallows the introductionof rigorously degassed liquids and their subsequent storage inthatcondition for indefinite periods.

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846 R. S. MURRAY AND M. L. MARTIN

As transfer and testing of degassed liquids in the apparatusrequire 1 to 2 d, whilemeasurements of vapour pressures for eachhalf of the composition range take afurther day, a complete mixturecan normally be studied in 5 to 6 d.

We are grateful to Mr J. Netting and Mr G. Duthie for theconstruction of theapparatus and to Mr M. A. Yabsley for assistancewith the computing program.This work was supported by a grant fromthe Australian Research Grants Committee.

REFERENCES1. Harris, K. R.; Dunlop, P. J. J. Chem.Thermodynamics 1970,2, 805.2. Stokes, R. H.; Levien, B. J.; Marsh,K. N. J. Chem. Thermodynamics1970,2, 43.3. Stokes, R. H.; Marsh, K.N.; Tomlins, R. P. J. Chem. Thermodynamics1969, 1, 211.4. Ewing, M.B.; Marsh, K. N.; Stokes, R. H.; Tuxford, C. W. J. Chem.Thermodynamics1970,

2, 751.5. Bell, T. N.; Cussler, E. L.; Harris, K. R.; Pepela, C.N.; Dunlop, P. J. J. Phys. Chem.1968,72,4693.

6. Shepard, A. F. ; Henne, A. L.; Midgely, Jr., T. J. Amer.Chem. Sot.1931, 3, 1948.7. Barker, J. A. Aust. J. Chem.1953, 6,207.8. Myers, D. B.; Scott, R. L. Ind. Eng. Chem.1963, 5,43.9.Scatchard, G.; Raymond, C. L. J. Amer. Chem. Sot. 1938, 60,1278.

10. Tomlins, R. P. Paper presented at the Fifth NationalConvention of the Royal Australian

11.Chemical Institute, Canberra, 1974.

Gibbs, R. E.; Van Ness, H. C. Ind. Eng. Chem.1972, 1, 410.