critical region just as the density curve was found to he.22 We had intended to have a better dis(22) M.E. Jacox, ,r. T. SIacQueen, and 0. K. ~ iJ. m~y & ~hem., , 64, 972 (1960).
tribution of values of dl’/’dxa in the critical range, but some accidciits prevented this. When more data Of this sort become available, it will be possible to fLu X”-lb2X/bx12 more exactly.
INTERNAL PRESSTTRES OF PERFLUORO-n-HEXANE, n-ITEY-iNE, AKD THEIR MIXTURES1 BY ROBERT D.DUNLAP Department of Chemistry, University of Maine, Ormo, Maine AND
ROBERT L. Scow
Department of Chemistry, University of California, Los ilngeles, California Received October 16. 1961
Values of (dP/dT)v for perfluoro-n-hexane and n-hexane were determined at several tt,mperatures between 10 and 50’. Ratios of the internal pressure, (dE/bT7)~to the cohesive energy drnsity ( - E / V ) at 35’ are 1.30 for thc fluorocarbon and 1.09 for the hydrocarbon. The function V*(d E l d T ’ ) ~ decreased with inerrassing temperature for both liquids; V 3 ( dE/dV) r wtts found to be nearly constant for n-Cd?,,. The values of - [d ln(dE/dV)T/d In T7]rwere found to bc 3.17 for n-CGFlr and 2.35 for n-CBH14. Measurements of (dP/dT)v were obtained for five mixtures a t temperatures ncar 25, 35, and 45’ and were used to derive the thermodynamic functions for mixing at constant volume from those obtained experimentally a t constant ressure. Values of TSVEare negative to the extent of -60 cal., and the function is skewed toward the hydrocarbon. %he discrepancy between the entropy of mixing at constant volume and the statistical value for random mixing is too small to account entirely for the failure of regular solution theory to predict the properties of this system.
Solutions of fluorocarbons and hydrocarbons previously studicd have large positive deviations from Raoult’s law. Large volume and energy changes accompany mixing and the mutual solubilit,ies are much lower than those predicted by the Hildebrandacatchard solubility parameter theory2 of regular solutions. Scott3 in a recent review article has assembled most of the experimental data on these systems, and has critically reviewed the vnrious attempts to explain their anomalous behavior. ‘More recently, Kyle and Reed4 have reported mutual solubilit’iesarid total vapor pressures for several additional fluorocarbon-hydrocarbon systems, and have postulated an empirical correlation of the existing data based on a negative excess entropy of mixing at constant volume. This study was undertaken to supplement the studies of liquid vapor equilibrium6 and heats of mixing for this system,. particularly in order t,o obtain the thermodynamic funct.ions for mixing at constant v o l u m ~ . ~
Experimental The apparatus was a modification of the one used by Benninga and Scotts in their study of carbon tetrachloride and similar to that described by Alder, Haycock, Hildebrand, and Watts.g The constant volume cell was a thermal regu(1) These experiments were carried out in R.L.S.’s laboratory at the University of California at Los Angcles by R.D.D. while on sabbatical leave from the University of Maine. (2) J. H. Hildebrand and R. L. Scott, “Solubility of Nonelectrolytes.” 3rd Edition, Reinhold Publ. Corp., New York, N. Y., 19m. (3) R. L. Scott. J. Phvd. Chem., 61, 136 (1958). (4) G. Kyle and T. M . Reed, 111, J. Am. Chem. Soc., 80,6170 (1958). ( 5 ) R. D. Dunlap, R. G. Bedford, J. C . Woodbrey, and S. D. Furrow, ;bid., 81,2927 (1959). (6 A. G . WillismRon and R . L. Scott, J . Phya. Chem., 66, 275 (1961). (7) R. L.Scott, ibid., 64, 1241 (1960). (8) H. Bennings and R. L. Scott, J . Chem. Phgs., 13, 1911 (1055). (9) B. J. Alder, E. W. Haycock, J. 1%. Rildebrand, and 11. Watts, ibid.. 31, 1060 (1954).
.
lator; a spiral of 7-mm. Pyrex tubing having a volume of approximately 14 In a typical experiment it contained some 10 to 12 cm.Sof the liquid bring studied, and the remaining space filled with mercury t o enclose the liquid and serve as the electrical contact. The regulator was filled in vacuo with degassed liquid and covered with mercury before disconnecting it from the vacuum system. The exact amounts of liquid and nicrcury were determined by weighing the regulator and the container froni which the liquid was removed. The regulator WLUenclosed in a steel bomb to which pressure was applied from a cylinder of nitrogen, the bomb immersed in u, water thermostat, and its tempcraturc regulated by the cell at various pressures from 1 to 65 atmospheres. The heating and cooling cycles were made very nearly equal and temperature was controlled within 0.1’ in the bath and within 0.01’ inside the bomb. The relay operatrd a signal SO that the temperature could be determined a t the times when contact ’ivtts made and broken. The difference between these trmperaturcs was nevcr larger than 0.003’; the average was taken as the value of t a t a given P. Temperature was determined with a calibrated copperconstant thermocouple to 0.001” using a Lcrds and Xorthrup K-2 potentiometer with a high sensitivity galvanometer. The pressure was determined within 0.01 atm. using a Itpfinery Supply Company #e010 dead weight gage. As an additional check, a calibrated Hrise-Bourdon gage, kindly loaned to us by Professor George Kcnnedy, wvas conjoined during several of the experiments. The perfluoro-n-hexane arid n-hexme were the same liquids used for the previous studies.5 G ~ l o , l l The P cs. t functions for the pure liquids and their mixtures were linear within the limits of experimental error. The largest deviation from the linea; equations obtained by lrast squares was 0.05 atm. or 0.01 . The average deviation was 0.02 rttm. \raluts of A P / A t so obtained were corrected for the volume changes of the glass and mercury using the relationship
ROBERT D. DUNLAP AND ROBERTri
632
Vol. 60
SCOTT
TABLE I COEFFICIENTS FOR THE SYSTEM: PERFLUORO-n-HEXANE -/- n-ITEXANE Compositions are expressed in mole fractions of perfluoro-n-hexane. ("/'T)V,P-I etm. (ap/a%,P-l
THERMAL PRESSURE
1, o c .
atm. dcg. - 1
(eq.-obsd.)
t. o c .
-0.010
23.927 27.212 34.903 45.169
n-C& 8.928 8.472 8.148 7.629 7.166 6.749
8.423 16.010 22.030 32.261 41.640 50.333
$1
-
.014 .008 .008
- .008 .007
11.567 19.810 30.300 39.505 48.630
-
6.978 6.463 5.899 5.420 4 * 969
XI =
--
(bP/bT)v.~ I stm. (bP/hT)v.~ 1
= 9.420 = 7.706
6.293 5.736
- 0.06089t - 0.06590t
+ +
0.5409
.008 ,016 .006 .006 .005
6.210 5.784 5.253 21
= 0.7444
27.023 36.651 45.842
5.061 5.442 5.015 XI
7.136 6.687 6.143
n-C& n-CeF14
7.040 6 .790
TI =
0.1478
26.463 34.915 45.890
= 0.2929
27.763 34.920 44.873
n-CsF14
atm
atm. deg. -1
=i
0.8470
22.037 33.138 44.585 1.58 X IO-' t* atm. deg.-l 2.00 x lo-' 19 atm. deg.-I
6,244 5.662 5.081
The goodness of fit is indicated by the deviations in column 3. Plots of the thermal pressure coefficients os. temperature in Fig. 1 for the various compositions in mole fraction of perfluoro-n-hexane show increasing curvature as one approaches the critical solution composition of 0.37. Values of the excess thermal pressure coefficients, viz., Ym - xlyl - z2y2 where ym, y ~ and , y2 are the smoothed values of (bP/bT)v,p atm for the mixtures and pure liquids a t 25, 35, and 4 5 O , respectively, are shown in Fig. 2. Since (bP/bT)v = (bX/i3V)~, these curves show that the increase in entropy per unit volume of the pure liquids is greater than that for their more expanded and less ordered mixtures. The 25' isotherm, a t 2.35' above the critical solution temperature, has a double inflection in the region of the critical solution composition, an indication of higher ordering in the pre-unmixing region. The inflection is a consequence of steeper than average (bP/ bT)y,p 1 us. t curves for the mixtures (shown in Fig. 1) and is associated with the heat capacity and thermal expansion by the relation
-
st-
Fig. l.-Thermd
pressure coefficients for the system: perfluoro-n-hexane n-hexane.
+
to give the thermal pressure coefficient, ( b P / h T ) v at 1 atm. The V's, a's, and 6's are the volumes, thermal coefficients of e ansion, and compressibilities with subscripts Hg, g, s n d T f o r mercury, Pyrex glass, and liquid, respectively. Thermal coefficients of expansion of the liquids and mixtures were calculated from the volumetric data reported earlier The corrections, which depend largely upon the ratio of mercury to liquid, ranged from 2 to 5% and could be determined to better than 1%.
Results and Discussion Thermal Pressure Coefficients.-Experimental data are shown in Table I where the values of (bP/dT)v,p I atm are given for the temperature corresponding to P = 1 atm. for each run. Equaas a function of t for tions of (bP/bT)v,p l each of the pure liquids were obtained using least squares and are shown a t the bottom of Table I.
-
-
-
Such behavior is qualitatively in accord with the large temperature dependence of the heat capacity and thermal coefficient of expansion observed by Hildebrand, et for similar solutions in their supra-cri tical region. Isothermal Compressibilities, Internal Pressured, and Related Functions.-Isothermal compressibilities at 35" calculated from the thermal pressure coefficients and previously reported volumetric (12) €1. Schmidt, G. Jura, and J. H. IIildebrand. J . Fhys. Chsm.,69, 297 (1959). (13) G. Jura, D. Pragi, Q. Maki, and J. 11. IIildebrand, Proc. Nall. Acad. Sei., 99, 19 (1953).
April, 1962
INTERNAL
~"CSSURJCS O F PICRFLUORO-n-HRXANE, n-IIEXANE, ANI)
fifIXTlJRES
633
TABLE I1 VOLUME FUNCTIONS FOR n-CsF14 AND n-CefIl4 INTERNAL PRESSURES A N D I~ELATED EXERW (ax/av)., V. V*(bR/brnT, 'bP/bT)Va?-l nkln. (bE/bV)T. I_
a h . dcg.-'
atrn.
cin.'
atin. 1.'
(-fl/V)
n-CoFlc
5 15 25 35 45 55
7.382 6,763 6.184 5.645 5.146 4.687
2052 1948 1843 1739 1636 1537
1!)5.33 198.67 202.23 205.96 209.95 214.19
78.29 76.89 75.37 73.76 72.11 70.51
1.321 1.314 1.306 1 .2!N 1.292 I . 290
n-CoTIlr
5 15 25 35 45 55
9.120 8.542 7.997 7.482 7,000 6.549
2536 2460 2383 2305 2226 2148
127.96 129.76 131.56 133.43 135.37 137.38
41.52 41.42 41.25 41.03 40.79 40.53
1.084 1.088 1.091 1.095 1.098 1.103
Liquid
T c i i i ~ ~'C. .,
data" are shown in Table 111. The compressibility of perfluoro-n-hexane is 75% larger than that of the corresponding hydrocarbon, and mixtures of these liquids which contain more than 50 mole yofluorocarbon arc even more compressible than perfluoro-nhexane. Internal pressures, ( b E l b V ) ~calculated , from the thermodynamic relation (bE/dv)T = T(dP/dT)v - P (3) and values for two well known functions, V2(bE/ ~ V ) T= a, and ( ~ E / ~ V ) T / ( - E / V=) n are shown in Tablc I1 for each of the pure liquids. The former is van der Waal's a, and the drifts with temperature, -0.25% deg.-l for n-C6F14 and -0.05% deg.-l for n-C6FII4,are larger than ob0 0.2 0.4 0.6 0.8 1.0 served for carbon tetrachloride.s Also where n, Mole fraction, n-C~F14. the ratio of the internal pressure to the cohesive energy density, was found to be reasonably con- Fig. 2.-Exeesa thermal pressure coefficients for the system: perfluoro-n-hexane + n-hexane. stant over a 60' range for CC14, it decreases with temperature for perfluoro-n-hexane and increases determinations of the heats of mixing at 25 and 35' with temperature for n-hexane. Smith and Hildcbrand14 found that V z ( b E / b V ) ~to give a thermodynamically consistent reprealso decreased with increasing temperature sentation of the properties in a single function, for perfluoro-n-hep tane and severa1 chlorofluoro- GpE(T, Po, x). Here Po is practically one atcarbon liquids. They calculated values for the mosphere. function V"+'(bE/bV)T which they found to be Various constant volume processes and related more nearly constant over the temperature range thermodynamic functions have been described.' studied. For perfluoro-n-hexane, we find that V 3 * Two processes of interest to us are: IIA, in which ( b E l b V ) ~is nearly temperature independent. both components are expanded (or compressed) When we plot In ( b E l b V ) us. ~ In V , remarkably isothermally to the same initial pressure a t which straight lines are obtained and the slopes -[d In the volume of the unmixed liquids equals the (bE/bV)T/d In VIP are 3.17 and 2.35 for perfluoro- volume of the mixture at the final pressure and then n-hexane and n-hexane, respectively; these are mixed st constant volume; 1113 in which the somewhat largcr than the corresponding values of liquids arc mixed at constant, pressure and the n 1, to which they should be equal if n were in- mixture compressed (or expanded) isothermally to dependent of V and (b2P/bT2)vwere exactly zero. the volume of the unmixed liquids. The symbols Excess Thermodynamic Properties-Excess correspond to those in the prcvious paper.: The thcrmodynamic functions and related thermody- mcchanical properties of the pure liquids are emnamic properties at 35" are shown in Table 111. ployed to evaluate the thcrmodynamie funcValues of H p " ( T , Po),Gp"(T, PO), and Sp"(T, PO), tions for IIA while those of the mixture are used for the excess enthalpy, Gibbs free energy, and en- IIB. tropy of mixing a t constant pressure, respectively, Values of excess thermodynamic functions for were calculated from equation 14 in the paper by the constant volume processes shown in Table 111 Williamson and Scott.6 These authors have com- were calculated from the relationships bined the liquid-vapor equilibrium data a t 25, 33, and 45" of Dunlap, et U Z . , ~ with their calorimetric AIIA"' (T,VmO) = GpE (T,Po) + ( P ) * / ( 2 (Vpo)) + . , . .
+
(14) E. B. Smith and J. H. Kildebrand, J . Chem. Phya., 31, 145 (1'359).
AIIR" (T,Vuo)=
GpE
(T,Po) - ( P ) 2 / ( 2 Vp,O)
(4) (5)
ROBERTD. DUNJAPAKD ROBERTb. BCOTT
634
Vol. 66
TABLEI 111 THERWODYNAWIC AND MECHANICAL PROPERTIBIS FOR THE SYSTEM fi-CBFl* Mole fraction n-CaF14
0.0000
0.1478
(dP/bT)v,r- 1 atm., atm. deg.-’ 7.482 [a In V / b T ] pX loa,deg.-l 1.427
[ a h V/bP]T x 104,atm.-1 [a(aP/aT)v/dT IP,
6.683 1.665 -2.491 -0.0516
-1.907 -0.0498
0.2929
+ n-CsRl4AT 35‘
0.5409
0.7444
0.8470
6.284 1.828 .2.909 ,O. 0606
5.779 I.963 -3.397 -0.0568
5.525 1.959 -3.546 -0.0514
5.566 1.931 -3.469 -0.0513
159.25 4.57 282 450 168 -36 -63 275 287 239 224
178.03 5.37 312 514 202 -21 -47 305 318 284 271
1.000
5.644 1.876 -3.324 -0.0519
atm.
V, cm.8 mole-’
133.43
mole-l GpE (T, Po), cal. mole-’ H p E (T, PO)), cal. mole-I TSPE ( T , PO),cal. mole-’ T S I I A( ~T , Vmo) cal. mole-’ T S I I B V E ( T , V,o), cal. mole-1 AIIAVE ( T , V,o), cal. mole-’ AIIBVE ( T , Vue), cal. mole-’ E I I A V E ( T , V,O), cal. mole-’ E I I B V E ( T , V,o), cal. mole-’ VE,
#IIAVE
147.14 2.99 187 309 122 23 -35 184 190 161 155
-
( T,Vmo)= S P E ( T,pO) f
~
VTo)
VE
+
( VPO)
-
SIIBVE
(T,V U O )
(VPO) (VTPO) (VTO) (VPpo)( p ) ~ 2 (VPO)* = S P E (T,PO) (aP/aT)V,P=l VE (1/2) (a2s/aVZ)T(VE)’ ( 7 )
-
+
191.89 4.47 233 409 176 -7 18 229 237 222 219
-
198.12 3.26 157 283 126 -7 - 15 155 159 148 144
205.96
certain significance, but it is interesting t o note that the sign is opposite to that which one would expect from the simple “Flory-Huggins” relation sFI*
-R
[XI In 91
+ xz In 921
(10)
where the 4’s are volume fractions, when attemptwhere V T , VP, Vpr, V ~ T are , the derivatives (bV/ ing to correct for the differences in the sizes of the bT)p, ( b v / b P ) ~(,b 2 V / d P 2 )and ~ , bZV/bPbT,re- molecules. This bears out the observation of and Hildebrand15 that the ideal entropy spectively, and symbol ( VT) represents [ x l ( V ~ )Shinoda ~ is better than the “Flory-Huggins” entropy when X ~ ( V T ) ~ ]i.e., , the mole fraction average of the VT coefficients for the pure components. calculating critical solution compositions of similar The superscript O represents the standard state, mixtures. The excess free energy, GpE, is 318 cal./mole a t x vix., one atmosphere, and Vuo and Vmoare the volumes of the unmixed and mixed liquids at Poand T , = 1/2, considerably larger than 85 cal. predicted from solubility parameters. If one adjusts the respectively. Values of ( d 2 S / d V 2 )were ~ calculated from the geometric mean approximation as suggested by temperature derivatives of the thermal pressure Reed16 to account for the differences in size and ionization potentials, the calculated excess free coefficients shown in Table I11 using the relation energy can be increased to 185 cal. Thus it can be ( a z S / a V ZG ) ~ [a(dP/dT)v/dT]~/(bV/aT)p (8) concluded that the discrepancy between the enwhich was derived’ with the aid of the assump- tropy of mixing at constant volume and the statistion that (d2P/dT2)v= 0. Although the P vs. t tical entropy for random mixing is too small to functions were linear within experimental error, account for the failure of solubility parameter this assumption is only moderately supported by theory for this and other mixtures of fluorocarbons this study because the pressure range of 65 at- and hydrocarbons. mospheres is relatively short. Acknowledgments.-Support of the National The excess Gibbs free energy, GpE, is very nearly Science Foundation (R.D.D.) and the U. S. Atomic halfway between the excess Helmholtz free enerEnergy Commission (R.L.S.)is gratefully acknowlgies for the two constant volume processes in the edged. The authors wish to thank Mr. S. D. Furorder row of the University of Maine for helpful discusA I I A ”
