J . Phys. Chem. 1986, 90, 4860-4865
4860
Apparatus To Measure Vapor Pressure, Differential Vapor Pressure, Liquid Molar Volume, and Compressibility of Liquids and Solutions to the Critical Point. Vapor Pressures, Molar Volumes, and Compresslbillties of Protiobenzene and Deuteriobenzene at Elevated Temperaturest Zorawar S. Kooner and W. Alexander Van Hook* Chemistry Department, University of Tennessee, Knoxville, Tennessee 37996 (Received: February 26, 1986;
In Final Form: May 8, 1986)
An apparatus designed to measure vapor pressure differences between two similar liquids, such as isotopic isomers, or between a solution and its reference solvent at temperatures and pressures extending to the critical point is described. Vapor-phase volume is minimized and pressure is transmitted to the transducer through the liquid, thereby avoiding several experimental difficulties. Liquid can be injected into the heated part of the system by volumetrically calibrated screw injectors, thus permitting measurement of liquid molar volume, compressibility, and expansivity. The addition of a high-pressure circulating pump and injection valve allows the apparatus to be employed as a continuous dilution differential vapor pressure apparatus for determining partial molar free energies of solution. In the second part of the paper data on the vapor pressure, molar volume, compressibility, and expansivity and their isotope effects for C6H6and C6D6from room temperature to near the critical temperature are reported.
Introduction We are honored to be invited to present a paper in memory of Professor Paul H. Emmett. Professor Emmett’s scientific example has had an important and positive effect on the senior author of this paper (A.V.H.) which has persisted since his tenure as a graduate student with Emmett. Van Hook’ has recently reemphasized the importance of a detailed knowledge of isotope effects on volumetric properties, including the volumes themselves, the compressibilities, and the expansivities, in formulating a proper theoretical understanding of condensed-phase isotope effects. The treatment of condensed-phase isotope effects originally due to Bigeleisen,* and reviewed by Jancso and Van Hook,3 calculates reduced partition function ratios of isotopic isomers and thus deduces isotope effects on the various thermodynamic properties. Under conditions where the comparison is proper’ the potential energy surface of the isotopic isomers are identical, at least to the precision of the Born-Oppeheimer a p p r ~ x i m a t i o n . ~From this it follows that isotope effect data can be employed to extract information on the potential energy surface (PES) used to describe the condensed phase. It is important to recall that the energy and the free energy of the liquid (and therefore the position and shape of the potential surface)’ are sensitive functions of condensed-phase molar volume or pressure. For the energy
(dE/d v) T = 31/ ~ v ) ( d E / d P )T (dE/dP)T = -TVa
+ PVK
V’and Vrepresent volumes in the condensed phase and Vk and Vg are volumes in the vapor phase. The second term on the right-hand side is the PVdifference term between the Gibbs and Helmholtz free energies, and the third term expresses the nonideality correction in the vapor phase. The last term in eq 3 calculates the free energy change that results when one isotope isomer, say the unprimed one, is compressed or expanded from its equilibrium PVcondition to a new condition, P * P , where its PES is in a corresponding state with the PES of the other isotopic isomer. In the general case an J(d In Q/dv) dVcorrection might be needed because RPFR is volume dependent and because there exists a significant isotope effect on the molar volume, compressibility, and expansivity of the condensed phase.5 It is not obvious whether the separated samples of isotopic isomers will be in corresponding state when they display identical volumes, when each is at the volume it displays under its equilibrium vapor pressure, or under some other set of conditions. Interest in this particular question has led to the experimental program described in this paper. Because the correction terms in eq 3 increase rapidly in relative importance as the temperature rises, we decided to design and build an apparatus to make measurements at elevated temperatures and pressures, even approaching critical conditions. In view of the extensive thermodynamic and spectroscopic information available on the C6H6/C6D6system, it was chosen as the initial material for study.
(1)
(2)
Here the coefficient of thermal expansion cy = (d In V/dT), and K is the compressibility, K = -(d In V/dP)T. The isotope effect on the free energy of transfer, liquid to vapor, is equal to R T times the logarithm of the reduced partition function ratio, RPFR = In CfJf,). RPFR is closely related to the vapor pressure isotope effect expressed as In (P’IP). The prime designates the lighter isotope.
‘Presented in memory of Paul H. Emmett at the symposium honoring him at the 190th ACS National Meeting, Chicago, IL, September 8-13, 1985.
0022-3654/86/2090-4860$01.50/0
Experimental Section
Apparatus. The differential PV apparatus is shown schematically in Figure 1. Two matched stainless steel sample vessels of nominal volume 25 cm3 are mounted in a massive copper block hung in a Hart 5005 thermostatic bath filled with Dow Corning 210H silicone fluid. Both bath and block are fitted with platinum resistance thermometers read with either a Keithley 705 scanner and 195A multimeter feeding an Apple 11+ microcomputer or with a Guildline 9576A Datastore digital voltmeter that can also be interfaced to the computer. The thermal stability of the bath is z t 1 mK or better over the entire range from room temperature (1) Van Hook, W. A. J . Chem. Phys. 1985, 83, 4107. (2) Bigeleisen, J. J. Chem. Phys. 1961, 34, 1485. (3) Jancso, G.;Van Hook, W. A. Chem. Rev. 1974, 74, 689. (4) Kleinman, L.; Wolfsberg, M. J . Chem. Phys. 1974, 60, 4740, 4749; 1973,59, 2043. (5) Matsuo, S.; Van Hook, W. A. J. Phys. Chem. 1984, 88, 1032.
0 1986 American Chemical Society
-
The Journal of Physical Chemistry, Vol. 90, No, 20, 1986 4861
Liquid Phase Properties of C6H6 and C6D6
rtl' CID
1
'
m
. ..... .. ... ...... _. ..._ ..... .
G
TABLE I: Vapor Pressure of CnHnand CAD6 C6H6
I
323.68 333.74 343.58 353.25 362.92 372.67 384.38 393.61 404.7 1 414.52 424.46 434.79 443.47 452.44 463.40 474.59 484.29 494.03 504.03 514.27 524.30 534.87 539.22 543.68 548.12 552.60 559.36
-
Figure 1. Schematic diagram of differential P V apparatus. A, A', sample cells; B, copper block; C, thermostated oil bath; D, Pt resistance thermometer; E, quartz oscillator transducer measuring absolute pressure; F, quartz oscillator transducer for differential pressure; G, G', screw injectors; H , HPLC solute injection valve; I, pump; X, valves.
to 300 "C. Working thermometer calibrations are traceable to NBS. We estimate temperature differences between the samples while taking a point to be +0.1 mK or less. Samples are introduced by the 1.6-mm stainless capillary lines, and pressure is transmitted to the transducers through those same lines. In a vapor pressure run the cells are kept almost full of liquid. This minimizes the amount of material in the vapor phase, and that is important for experiments studying solutions. Another advantage of using the liquid as the pressure-transmitting fluid is that the transducers can be conveniently thermostated near r w m temperature. In our design a correction for the head of liquid suspended between the transducer and cell liquid level is required. This is small at vapor pressures of interest to us. The screw injectors are precision machined from stainless steel (HIP Engineering). They permit the amount of material in the cells and pressure measuring network to be obtained to --f0.001 cm3. The absolute pressure of one cell and the differential pressure between cells are measured by quartz oscillator "zero" displacement transducers (Paroscientific, Redmond, WA, rated precision 0.01% of full scale, 60 and 1.4 bars, respectively). In the present configuration of the apparatus one cell is employed as reference, and the other is used for isotopically substituted material or for solutions. In the solution mode the material in the cell is mixed with a low-volume-high-pressure liquid pump of the kind used for liquid chromatography. An injection valve is included in the loop so that an aliquot portion of solute can be added to the solution following the method of Hutchings and Van ~ o o k . ~The , ~experiments on C6H6 and C6D6 were carried out in separate runs using the absolute gage by itself. This was necessary because the differential gage was damaged during calibration and is currently under repair. Future experiments on solutions, especially solutions of isotopic isomers one in the other, will require additional sensitivity, but the absolute gage by itself is sufficiently precise for the present purpose. For molar volume and compressibility studies the degassed samples are fed from the screw injector into the measuring cells while the valves to the pressure transducer are kept open. It is essential that the apparatus and the liquid sample be very carefully degassed. As the cell completely fills, the pressure jumps abruptly from the equilibrium vapor pressure to some other value. Continued injection of liquid allows the compressibility to be determined. The intersection of the steep and flat parts of the curve defines the liquid volume required to just fill the cell and permits calculation of the liquid molar volume. Results
Vapor Pressure Measurements. Vapor pressures for C6H6 and C6D6 at various temperatures, each run on virgin samples (Le., never previously heated above 353 K), are reported in Table I. We have fit the data for each isotopic isomer with one of the (6) Hutchings, R. S.; Van Hook, W. A. J. Solution Chem. 1985, 14, 13. (7) Hutchings, R. S.; Van Hook, W. A. J . Chem. Thermodyn. 1985, 17, 531.
C6D6
Wd 0.368 86 0.533 03 0.745 25 1.01449 1.353 30 1.779 18 2.41922 3.03485 3.927 66 4.868 72 5.985 25 7.335 31 8.637 39 10.1534 12.255 4 14.7199 17.1365 19.847 2 22.951 2 26.469 0 30.309 0 34.804 1 36.802 7 38.937 1 41.1639 43.526 1 47.610 1"
323.39 333.44 343.28 352.97 362.64 372.39 384.72 393.96 405.05 414.88 424.83 435.16 443.86 454.65 463.80 474.99 484.67 494.44 504.48 514.69 525.24 533.76 540.13 544.55 548.97 555.74 560.29
0.373 83 0.54047 0.756 49 1.030 35 1.375 36 1.808 35 2.497 13 3.130 76 4.048 11 5.015 92 6.16362 7.548 84 8.885 46 10.775 5 12.5964 15.122 1 17.590 1 20.373 6 23.5532 27.1559 31.2986 34.969 5 37.939 8 40.1469 42.435 3 46.1468 49.798 6"
Not included in least squaring.
-'t Figure 2. Deviations of measured vapor pressures of C6H6 from predictions of eq 4 as a function of temperature: ( 0 )present measurements, A = In (Pcalcd,4) -In (Pexpt),(-) comparison with ref 8, A = In - In (pref8),
standard forms suggested by Ambrose, Broderick, and Townsends (ABT) In P (Pa) = A ( 1 ) / ( T
+ A ( 2 ) ) + A ( 3 ) + A(4)T + A(5)T2 (323 C T / K C 555) (4)
A ( i ) parameters and variances of fit are reported in Table I1 for each isotopic isomer. Figure 2 is a deviation plot that compares the present C6H6 data with the smoothing relation, eq 4,and with the seven-parameter fit of ABT-their eq 8. The ABT fit included then-new data from the National Physical Laboratory as well as earlier literature values.g-" The deviations 6 ( h P ) = In Pcalcd.4 - In Pexpt= 6P/P, are small. Here In Pcalcd,4refers to the value (8) Ambrose, D.; Broderick, B. E.; Townsend, R. J. Chem. SOC.A 1967, 633. (9) Selected Values of Properlies of Hydrocarbons and Related Compounds; American Petroleum Institute Research; College Station, TX, 1972; Project 44. (10) Bender, P.; Furakawa, G. T.; Hyndman, J. R. Ind. Eng. Chem. 1952, 44, 387. (11) Connolly, J. F.; Kandalic, G. A. J. Chem. Eng. Data 1962, 7, 137.
4862 The Journal of Physical Chemistry, Vol. 90, No. 20, 1986 TABLE 11: Parameters of 4 4 41) K C6H6 C6D6
-4417.727 f 189 -4324.653 f 291
Kooner and Van Hook
42) K
43)
103A(4)/K-’
-15.883 f 4.3 -18.717 f 6.7
28.975 28 f 0.72 28.78636 f 1.1
-16.6609 f 1.2 -16.5502 f 1.8
10’A(5)/K-*
10-2a2
1.227 40 f 0.07 1.23289 f 0.11
11
21
Figure 3. Vapor pressure isotope effects for C6H6/&&, In(P’/P) = In(PH/PD),as a function of temperature. The points marked ( 0 )represent the present data and those marked (X) are from ref 12. The solid line is a plot of eq 5, the dashed line is a plot of eq 5 from Jakli, Tzias, and Van Hook,I2 and the dotted line represents the data of Kiss, Jakli, and Illy.” I03/T,(C6H6)= 1.78. The error bars at the bottom of the figure show the result of a 2% uncertainty in the head correction.
obtained from eq 4 and In Pcxptto the measured pressure. We (0.03%). For the and u = 3.3 X find 6(ln P),,, = 7 X C,D6 tit u = 5.2 X IO4. The present data for C6H6 are in excellent agreement with eq 8 of ABT; the average magnitude of the difference is 6 X lo4 and the maximum difference is 11.8 X lo4. ABT shows a deviation plot with maximum deviations near 0.1% and standard deviations about 0.06%. We conclude that the present results for C6H6are in satisfactory agreement with the literature between 323 and 553 K. To report vapor pressure isotope effects (VPIEs) to the maximum precision allowed by the experiment, we constructed large-scale deviation plots of the C6H6 and C6D6 data against the ABT reference and then calculated h(P’/P)T = (In P’- In P ~ B T ) T - (In P - In P2BT)p In this fashion any systematic ripple introduced by a mismatch of the assumed empirical form is minimized because both the P’and the P data are equally spaced over the same temperature range. The isotope effects are plotted in Figure 3 where they are compared with VPIEs reported earlier by Jakli, Tzias, and Van HookI2 (JTVH) and Kiss, Jakli and IllyI3 (KJI). Earlier measurement^'^^'^ have been discussed by JTVH. JTVH and KJI are in excellent agreement over the entire range of the JTVH experiment (278 < T/K < 353), and the earlier worker^'^^'^ are in satisfactory agreement with both over the range (313 < T/k < 353). It is clear the present p i n t s at the two lowest temperatures (323 and 333 K) are too low. They have not been included in the least-squares analysis reported below. We have ascribed the systematic error in these points to imprecision in the head correction, which becomes untenably large as the pressure drops below 1 bar. The present data joins the JTVH/KJI (278 (12) (13) 59. (14) ( 1 5)
Jakti, G.; Tzias, P.; Van Hook, W. A. J . Chem. Phys. 1978,68, 3177. Kiss, I.: Jakli, G.; Illy, H. Acta Chem. Acad. Sci. Hung. 1972, 71,
Davis, R. T., Jr.; Schiessler, R. W. J . Phys. Chem. 1953, 57, 966. Rabinovich, I. B. Influence of Isotropy on the Physicochemical Properties of Liquids; Consultants Bureau: New York, 1970, p 37.
< T / K < 353) results
smoothly and with good precision. To represent the VPIE over the entire liquid range from triple to critical point we solved eq 5 of JTVH at 278 K and at IO-deg intervals (283 < T/K < 353), added these points (marked “ X ” in Figure 3) to the 26 generated from Table I (marked “O”), and least squared to the standard obtaining
In (P’/P) = In ( P H / P D )= (1434.8 u2 = 16.8 X
+ 50.9)/T2- (12.819 + 0.142)/T (278
< T / K < TJK)
(5)
The standard deviation is us = 4 X (0.04%). A simpler analysis would have taken the ratio of the two fits to eq 4 (Table 11) and obtained a similar result but with u4,4= 6 X It is interesting that the parameters of eq 5 are near those reported by JTVH, In (P’/P) = 1226.5/71- 12.178/T(278 < T/K < 353). That extrapolated fit is plotted as the dashed line in Figure 3; the close agreement between the present data and the predictions of the earlier experiment at low temperature is reassuring. The present results establish that the results of Kiss, Jakli, and Illyi3 (plotted as the dotted line in Figure 3) are systematically low in the temperature range, (353 < T/K < 433). No other workers have reported benzene VPIEs above the normal boiling point. As in the case of methane,l6 the only other hydrocarbon studied far above its normal boiling point, the VPIE remains large all the way to the critical temperature. The present data extend to T,. = T/T,‘ > 0.98. Volume and Compressibility Measurements. Condensed-phase molar volumes were determined by measuring the system pressure as a function of the number of moles injected. To analyze the experiment we recognize that a valve separates the screw injectors and connecting line from the sample vessel and dead line. The screw injector, transducers, connecting line, and dead line are all (16) Grigor, A. F.; Steele, W. A. J . Chem. Phys. 1968, 48, 1032.
Liquid Phase Properties of C6H6and C6D6
The Journal of Physical Chemistry, Vol. 90, No. 20, 1986 4863
TABLE 111: Experimental Molar Volumes and Compressibilities of C&
and C6Ds
C6H6
C6D6
TIK
1061/,po/m3.rnol-'
1O1OK,"/Pa-'
288.15 298.15 313.15 323.40 343.27 362.55 384.92 405.65 425.46 445.11 464.05 484.16 506.43 524.38 543.77
88.332" 89.411" 91.106' 92.316 94.756 97.329 100.573 103.970 107.61 1 11 1.747 1 16.446 122.421 129.763 141.05 lb 1 60.969b
8.98" 9.67" 10.88" 11.6 13.4 18.4b 19.3 26.6 33.6 41.5 57.5 80.2 127 281b 1077b
TI K 288.15 298.15 313.15 323.56 343.41 362.76 384.41 405.00 425.15 444.18 463.41 484.30 504.08 524.83 544.24
106v,po/m3-mo1-'
io3 In V,$/V,p
10'°K,o/Pa-' 8.83" 9.52" 10.78' 15.1b 15.1 16.8 20.8 25.0 31.0 41.4 57.5 85.7 137 275b 1087b
88.1 36" 89.234" 90.945" 92.038 94.464 97.079 100.203 103.578 107.230 111.241 1 15.996 122.271 129.953 141.375b 162.542b
3.2 3.3 2.9 3.0 4.3 4.0 2.0 2.2 1.7
-1 1 -0.> -79
"Reference 5 . bNot included in least squaring. thermostated at t' = 28 "C. The terms "connecting line" and "dead line" are used to distinguish the volume of the connecting lines before and after the valve. They include any dead space in the valve. The number of moles on the measuring side of the system, n(s), is the difference between the number of moles on the screw injector side at the beginning of the experiment (Le., when the valve is closed and no material has yet been injected into the sample side), n(i,O), and the number on that side under measurement conditions, n(i,f) n(s) = n(i,O) - n(i,f) (6) Here we use s to symbolize system side, i for injector side, 0 for initial, and f for final. The initial measurements are made at negligible pressure; each final measurement is at some pressure, P, so n(s) = (n(i,O) - n(i,f)) = (u*(O) + uc)/V,(,o - (u*(f) + 0, + 4 P ) / V P , P (7) where u*(O) and u*(Q are the initial and final readings of the screw injector, u, is the volume in the connecting lines (Le., between screw injector and valve), and V,,,oand Vt,,pare the molar volumes at negligible and final pressure, both at 2'. The term A,P = (ho,/AP)P accounts for the deformation of the membrane in the 'almost zero displacement" tranducer under applied pressure. Recall k'f,,p= V,,,oexp(-.fiK,, dP) (Q is the compressibility) so 4 s ) Vf,O= (u*(O)
- u*(f)
- A,P) - (u*(f)
+ u, + A,P)(
x
+ ud
K,,
dP) (8)
(9)
where assis the coefficient of thermal expansion of the cell. The average molar volume in the measuring system is (V) = u(s)/n(s). Most of the sample is at the experimental temperature, t , but a small fraction is in the lines at t'. We write
(v)= (ndVt',P + n'V(:,p)/n(s)
(10)
nd and nt are the number of moles in the dead line and cell, respective1 With nd/nt = ( u d / u t ( t ' ) ) exp(];(cu - ass)dt) and In (u'(t)/u'(t') = J:aSs dt. V,, = ( u ( s ) / n ( s ) ) x
+
+
n(s)V,,, = (u*(O)
- (a
+ bP + cP2) - A,P) (u*(f) + u,
-
+ 4 P ) ( J P K f , dP) (12)
The last term is small with a systematic uncertainty always less than 0.04% and a random uncertainty less than 0.01%. The later uncertainty is of interest for the isotope effect on V,,oand its derivatives. The molar volume at the temperature and pressure of the experiment is calculated by substituting eq 12 into eq 11. For the system in its present configuration, u d / u t = 0.0016 and assover the range of experiment is 5.2 X K-l. The parameter A , was fixed by demanding agreement between the calculated compressibility and the literature valueSat the lowest experimental temperature, 50.524 "C. The transducer is very nearly of "zero displacement" and A, is small. To obtain the compressibility, note V,,p c(s)/n(s) and d In V,,,/dP = -K,,, = - d In (n(s))/dP = d In ( ~ ( S ) V , , , ~ ) -/ ~dPIn V,,,,/dP (13)
=
P
On the high-temperature side the volume is u ( s ) = u t ( t ) + cd, where u t ( t ) is the volume of the measuring cell thermostated at the temperature of the measurement, t , and ud is the dead volume in the lines (t'in "C). The volumes of the injectors, connecting lines, and measuring cells all depend on temperature but are independent of pressure. The high-temperature volume is u(s) = u+(t') exp( l,'aSsdt)
For highest precision it would be necessary to take account of the pressure dependence of CY. The experiment measures P as a function of screw injector setting ( u * ( f ) , eq 8). At any given temperature such data can be fit with the empirical form, u * ( f ) = a bP 4- cP2, but in the present case they only extend over a narrow pressure range and c can be set equal to zero with no loss in precision. The integral d P = K,,,,P over the compressibility in eq 8 is expressed .f{~,, Kr,,lP2/2, So
so K
~
=,
-~ d In (n(s)V,,,,)/dP
-
K,,,,
(14)
because d In (u(s))/dP = 0. K , , , ~ is the compressibility at the reference temperature t ' and negligible pressure. Volumes and compressibilitiesof C6H6 and C,D6 were measured by determining n(s) as a function of P from just above the equilibrium vapor pressure to that pressure plus 3.5 bars, at 20-deg intervals between 323 and 555 K. Normally five to seven points were obtained over the pressure range and the data were leastsquares fit with the relation u*(f) = a + bP, typically with a variance of 6 X lod cm6. Since the injected volume is on the order of 25 cm3, the standard deviation accounts for an uncertainty in V(fn of 0.01%. Trial fits to three-parameter equations, u * ( f ) = a + bP + cP2, did not improve the statistical reliability and are not further considered. Volumes under condition of equilibrium vapor pressure, V f p ,and zero pressure compressibilities, K , , ~ , calculated from these fits and eq 11, 12, 13, and 14, are reported at the experimental temperatures in Table 111. Figures 4 and 5 are graphical representations of the temperature dependence of In Vf,pand In K , , ~ . As expected, curvature increases as temperatures rise close to the critical point, and we have been unable to reproduce the high-temperature curvature with the simple empirical forms of eq 15 and 16. Least-squares analysis has
The Journal of Physical Chemistry, Vol. 90, No. 20, 1986
4864
f i
Kooner and Van Hook
TABLE I V Least-Squares Fits to Molar Volumes and Cornpressibilities
Equation 15
c(o)
103c(1) / K-1
C6H6 3.7782 f 0.04 C6D6 3.5291 f 0.10
A
A
+
NO) P
I
6
P
C6D6
B
~ - 2
-1.1275 f 0.08 -1.7048 f
0.77
0.20 Equation 16 1 1~ K - I
om
1o*c(3) I K - ~ 1072
1.2520 f 0.07 1.7767 f 0.17 105~(2)/~-2
C6H6 -8.0337 f 0.35 -13.556 f 1.8 3.1964 f 0.23 C,D, -7.7170 f 0.73 -15.390 f 3.8 3.4616 f 0.48
8 + M
losc(2)/
4.6474 f 0.3 1 6.7300 f
3 19
1042 11
49
Equation 18 E(O) 1 0 3 ~ ( 1 ) / ~ - 1 1 0 5 ~ ( 2 ) / ~ - 21 0 3 ~ 2 -26.427 k 0.77 59.449 f 3.7 -2.795 f 0.44 6 -26.077 f 0.77 57.604 f 3.7 -2.531 f 0.44 6
The parameters and variances of fit for least-squares analysis to eq 15 and 16 are presented in Table IV.
d A'
In V,p = C(0) + C(1)T
0
+ C ( 2 ) p + C(3)T3
(288
< T/K < 508) (15)
600
400
T/K Figure 4. The orthobaric molar volume of C6H6, ( 106V,,o/m3mol-'), as a function of temperature: present results ( 0 ) ;Matsuo and Van HookS (0);Connolly and Kandalic" (+); Campbell and Chatterjee" (A). -4
,
-€
-. 0
i-.
/
y' C -I
I
xx
X
E 3
400
T/K
Figure 5. Logarithmic limiting (zero pressure) compressibilities, ( K , , ~ / ( Pa-')) of C6H6 as a function of temperature. Present results ( 0 ) ; Matsuo and Van HookS (0);Connolly and Kandalic" (X); Dymond, Glen, Robertson, and Isdalel' (A).
therefore been restricted to the temperature range (288 < T/K < 508). We have included points at 288.15, 298.15, and 313.15 K from Matsuo and Van Hook5 in order to gain a more accurate representation of the low-temperature behavior. Again, it is important to recognize that the high-temperature data were not included in the fits because of an inadequate empirical formula not because of experimental uncertainty. An alternative representation in powers of ( 1 - T / T,) was not warranted because of the small number of data points near the critical temperature.
In K ~ =, ~ D ( 0 ) D(1)T
+
+ D ( 2 ) p + D(3)T3
(288
< T/K < 508) (16)
Here Vf@is in units of lo6 m3.mol-' = cm3.mol-', and K ! , ~is in lo5 Pa-I = bar-'. The fits to the molar volume of C6H6 show a standard deviation of 6 X (0.06%) for compressibility 3 X (3%). For C6D6 the figures are somewhat larger, 0.1% and 7%, respectively. For Vf,p(C6H6)the present data can be compared with Campbell and Chatterjee," whose orthobaric molar volumes are within 0.4% of ours over the range (378 < T/K < 500), and with Connolly and Kandalic" (CK), where the agreement is better, within 0.1%. The present values for K ~ are , ~2% lower than calculated from the data of Dymond, Glen, Robertson, and Isdale'* at 323 K, and this difference increases to 6% at 373 K. The difference between the present results and those of CK increases steadily from -4% (present data lower) to +lo% between 403 and 443 K. Above that temperature the differences rapidly increase as can be deduced from Figure 5. In comparing our data with CK remember that the CK measurements were over a pressure range extending from to (Polbars + 180); the present measurments only extend to (Polbars + 3.5). Therefore the CK results, which show significant curvature in V, P plots, will be much more susceptible to errors occurring in the extrapolation to zero pressure. This is borne out by the observation of a physically unrealistic maximum in their q 0 vs. T plot, Figure 5. We conclude that the present values are likely the more reliable, at least above 440 K, but it is clear that large uncertainties in-limiting compressibilitiesat high temperature remain. It is convenient to be able to calculate the volumetric properties of the liquids as functions of temperature and pressure using a simple formalism. The experimental measurements determine the properties at with highest precision. To recover the properties at P = 0 we write
The correction term involving the integral is small and it is convenient to expand its logarithm
(17) Campbell, A. N.; Chatterjee, R. M. Can. J . Chem. 1968, 46, 5 7 5 . (18) Dymond, J. H.; Glen, N.; Robertson, J.; Isdale, J. D. J . Chem. Thermodyn. 1982, 14, 1149.
The Journal of Physical Chemistry, Vol. 90, No. 20, 1986 4865
Liquid Phase Properties of C6H6 and C6D6
TABLE V: Two of the Terms in Ekl 1 at Different Temperatures
4
T/K 273.15 323.15 373.15 423.15 473.15 523.15 548.15
2 h
> '3 v
c
Gc
-lo4 In (P'/P) 277 259 24 1 223 207 193 186
- ~ O ~ ( P Y ' / ( R Tx )) (1 - P V / ( P Y ? )
1 4 8 21 39
c
373 K the present results lie 0.05-0.1% higher than the general average. The difference is realistic in light of the experimental errors presented in Table IV. In the high-temperature region both ' ~ off markedly the present results and those of R a b i n ~ v i t c hdrop as the temperature increases, eventually becoming negative and relatively large (as much as -1% or more around 543 K. Again, the present results lie above those reported by Rabinovich, but the pattern is consistent. We have also examined the data in Tables I11 and IV to determine the isotope effect on K , , ~but find they are not precise enough to come to any conclusion beyond limiting the effect, if any, to less than about 5%.
t
-L
4
-4
+
-6
+. *
I~*.T/K
5
Figure 6. Molar volume isotope effects, In (V'/V) = In (V(H)/V(D)), for C6H6/C6D6 as a function of temperature. Present results (e); Matsuo and Van Hook5 (X); Rabinovit~h'~ (+); Kiss, Kovacs, and Jakli20 (0);Dixon and Schliessler22 (A); Bartell and Roskos2' ($); DuttaChoudhury, Dessauges, and Van Hook23 ( 0 ) .
Therefore the volume at a general temperature and a pressure that is not too high is
+
+
+
h(Vl,p) = C(O) C ( I ) T C ( 2 ) P C(3)T3 + exp(E(O) + E(1)T E(2)TZ) - (exp(D(O) D ( 1 ) T D(2)TZ))P (19)
+
+
+
C(i), D ( i ) , and E(i) parameters for C6H6 and C6D6are reported in Table IV. We have employed the information in Tables I11 and IV to calculate the isotope effect on the molar volume a t each experimental C6D6 temperature and have reported the result in the last column of Table 111. These are plotted in Figure 6, where the present results are compared with literature v a l u e ~ . ~ JBelow ~-~~ (19) See ref 15, pp 124-125. (20) Kiss, I.; Kovacs, Zs.; Jakli, G. Acra Chim. Acud. Sci. Huna. 1979, 100, 383.
Discussion and Conclusions The objective of the experimental program described in this paper is to critically test eq 3 for molecular fluids up to the critical region. An apparatus for that purpose has been described and measurements of the vapor pressure and molar volume ratios of C6H6 and C6D6 have been established from the triple point to near the critical point. Smoothed values of the first two terms on the left-hand side of eq 1 are shown in Table V. The table shows that the relative contribution of the ( P V - P V ) / R T term remains small until the temperature rises above 500 K. At 548 K it amounts to more than 20% of In (P'/P) and is increasing rapidly in relative importance. To complete the experimental information needed to test eq 1 measurements of vapor-phase nonideality will be required, especially in the high-temperature and -pressure region. This information should be supplemented with further volumetric data above 550 K with improved precision. We are currently engaged in such measurements.
Acknowledgment. This research was supported by the National Science Foundation under Grant CHE-84-13566. Registry NO. C6H6, 71-43-2; C6D6, 1076-43-3. (21) Bartell, L. S.; Roskos, R. R. J . Chem. Phys. 1966, 44, 457. (22) Dixon, J. A.; Schiessler, R. W. J . A m . Chem. SOC.1954, 76, 2197. (23) Dutta-Choudhury, M. K.; Dessauges, G.; Van Hook, W. A. J . Phys. Chem. 1982, 86, 4068.
