CRITICAL COMPOSITION IN LIQUID MIXTURES
Oct., 1961
1885
CRITICAL COMYOSITIOX IS LIQUID MIXTVRES OF COMPOXESTS 01: VERY DIFFERENT MOLAR VOLURSES B Y K626
SHINODi4’ AKD
JOELH. HILDEBRAKD
Department of Chemistry, University of California, Berkeley 4, California Received M a y d.0, l g S l
Solubility-temperature curves have been determined for mixtures of pentaerythritol tetraperfluorohutyratc, (CpF;COOCH2),C, with 5 other liquids. The criticd temperatures, in “C., and critical composit>ionsexpressed as mole-per cent. 78.80’, 17; n-CsHls, 119.4”, of the above compound arc: C€12C12,38.5”,5.7; n-CJ!12, 52.lo, 13; c7CsHlo,80.8’, 1.0; z:(;~RH!~, 16. These critical compositions ale very unsynimetr.ical in accord with the large disparities in molal volume. They agvee well with values calculated on the basis of the equation for regular solutions using ideal entropy instead of “Flory-Huggins” entropy.
Introduction The extraordinarily large molal volume of peiitaerythritol tetraperfluorobutyrate, “PETB,” 541.5 cc. a t 2 5 O , mztkes this liquid exceptionally well suited for testing the relation between disparity of molal volumes rand the asymmetry of liquid-liquid solubility-composition curves. We reported recently that the critical composition of solutions of chloroform and carbon tetrachloride with PETR show good agreement with theoretical values derived from the regular solution equation using ideal entropy of mixing rather than “Flory-Huggins” type entropy.2 We also have shown that iodine solutions in both PETB and octamethylcyclotetrasiloxane3b show no additional entropy of solution attributable to disparity in molal volume compared with solutions in other solvents with much smaller molal volumes. The present investigation was undertaken in order to test this conclusion ill additional cases.
temperatures, given in Table 11, were obtained by aid of the rectilinear diameter r e l a t i ~ n . ~Thc curves for all liquid mixtures are SO unsymmetrical that they offer a good test of the equations we have used for calculating the critical composition RT In a1
=
RT In
5,
+ vl@ ( & - 6,)*
(1)
where a1 denotes the activity of component 1, x1 its mole fraction, v1 its molal volume, 42 the volume fraction of component 2, and the 6’s are the respective solubility parameter^.^ The term, ZZ In xl, assumes that the partial molal entropy is 120
100
Experimental Materials.-Tiie PETB was obtained from the hliiincisota Mining and Manufacturing Company through t h kindness of Dr. N. W. Taylor. Its purification and physiral properties were describcld in the paper referred to.’ The dichloromethane, of “Spectro Grade,” a product of Eastman Organic Chernicals, was used without further purification. The n-pcntane, cyclopentane, n-octane (synthetic) were obtained from hlatheson Company. The “isooctane” (2,2,2trimethylpentane) waa a Phillips “pure” product. These were dried over activated silica eel and fractionated in a vacuum-jacketed, 15-plate columnYat3a reflux-ratio of 1 5 : l . The boiling points corrected to 760 mm. wcre: nCsH12, 34.5-34.7’; c-CsHlo, 49.3’; n-CRH18,125.8’; iCsHis, 99.2”. Procedure.-Various amounts of deeapsed PETR were weighed into tubes 6 mm. io diamete; and 12 cm. long. The second liquid then was added, the contents frozen, evacuated, sealed and reweighed. Consolute temperatures were observed by repeated gradual heating and cooling, 0 01” per minute, while shaking the tubes. Successive ohservations agree within 0.02” near the top of the liquidliquid curves, and within 0.1-4.2’ on the sides. The ther monieters uscd W~XB calibrated against N.R.S. Standard thermometers. Corrections were made for the emerged stem.
so
F u
40
20
Results The results are shown in Table I and are plotted together with our earlier figures for CHCll and CCla in Fig. 1. The critical compositions and (1) Department of Chemistry, Yokahama National University. MinarnikB, Yokabama, Japan. (2) Kbzb Shinoda md J. If. IIildebrand, J . I’hye. Chem., 62, 481 ( 1 958).
(3) (a) Kazb Shinoda and J. 11. Iiddebrand, rbzd., 62, 292 (1058); (b) 61, 789 (1957).
0
0.2 0.4 Mole fraction of (CaF&OOCI&)&. Fig. 1.
0.6
(4) J . H. IIildebrand and R. L. Scott, “Solubility of Non-clcctrolytes,” Reinhold Publ. Corp.. New York, N. Y., 1850.
K6z6 SHINODA AND JOEL H. HILDEBRAND
Vol. 65
TABLE I Mom % OF (W&OOCH&C IN LIQUIDMIXTURES --CHzC+ lOOtl
0.51 1.04 1.77 2.54 3.38 5.22 6.94 9.26 13.99 25.01
t,
-n-C~Hu--1OOZl
oc.
16.7 22.2 34.8 37.1 38.09 38.47 38.22 37.33 31.9 16.5
1.58 2.97 4.55 7.10 8.19 10.09 13.88 21.65 30.04 52.99
t, oc.
YC-CIHIO l On
52.0 56.8 59.26 61.47 61.89 62.04 62.06 60.98 56.95 35.4
1.21 2.34 3.51 5.74 7.07 9.22 12.95 17.72 25.93 47.07
ideal. There has been, till recently, a question whether the non-ideal entropy of athermal solution of high polymers is to be attributed entirely to configurationti of the polymer chain, or whether disparity in molal volumes of the component alone is accompanied by non-ideal entropy as formulated by Flory and by Huggins. R[hdl
- 44vz - Vl)/VZI
(2)
Equations for the critical composition are derived by setting b In al/b In x1 = 0 and d2 in al/b In x12 = 0. In this way we obtain for the critical composition Xl?C = [Vl + (v2 - VlV*)’/.I/(V2 VI) (3) from ey. 1 and
-
iXllZz),
= (V2/Vl)’/X
(4)
from eq. 2. Table I1 gives (1) the critical temperatures; (2) the mole yo of PETB a t the critical point, zl, ( 3 ) the molal volumes of the pure liquids at the critical temperature; (4) the values of the experimental composition at the critical point; (5) the same calculated from eq. 3 ; (6) ibid. from eq. 4. The data for solutions with CHCL and CCL are added from th.e earlier paper.2 One sees that in every case eq. 3, based upon ideal entropy, gives much better agreement with the experimental value than does eq. 4, based upon “F-Hff entropy. There is one system,j however, for which, significantly, t h e reverse is true, Le., stannic iodide and dicetyl, m-CaHss. The critical temperature is 193.5’ and t,he critical composition close to 10 mole 5j of diicetyl. The molal volumes a t this ( 5 ) J . 11. Hildebrand, J. Am. Chem. Sac., 67, 866 (1935).
t, oc.
64.4 73.6 77.66 80.17 80.66 80.76 80.65 79.65 74.9 50.8
,-.-CaHilO0zx
t,
2.06 2.99 5.05 7.27 9.87 13.36 18.47 23.69 30.94 41.49 62.02
58.5 64.3 73.26 76.43 78.16 78.77 78.84 78.56 77.14 72.52 53.0
-----n-GHls----.
oc.
1 oom
t, “C.
1.89 4.42 6.72 9.40 12.43 16.10 20.11 28.48 37.10 54.04
95 109.5 115.6 118.1 119.3 119.4 119.3 118.3 115.6 103.6
TABLEI1 EXPERIMENTAL CRITICAL OMP POSITIONS WITH THOSE CALCULATED BY EQUATIONS 3 A N D 4
COMPARISON OF
to,
“C.
38.5 43.5 62.1 72.1 78.8 80.8 119.4
VI
65.7 82.6 123.8 103 178 101 185
72
Expt.
-‘.*
Eq. 3
Eq. 4
549.5 0 057 0 061 0.040 ,055 553 ,073 077 13 115 .093 564 079 57 1 .09 094 ,147 573 .17 164 ,069 575 .10 092 145 603 I6 ,162
temperature are 174 and 615 (T., respectively. The critical mole fraction of dicetyl is 15, according to eq. 3, and 13 according‘ to eq 4. One may infer that the long, flexible chain of dicetyl slightly favors the “F-H” expression for entropy of mixing. The foregoing calculations have neglected, as does eq. 1, the contribution of the unknown expansion to the entropy of mixing, therefor(. thr evidence is not a s complete as that afforded by the iodine solutions. The critical temperatures are not consistent with the solubility parameters of the components, which is not strange, in view of the departures of these substances from spherical force-fields. Wc have here again6 evidence of exceptionally weak attraction between fluorocarbons and aliphatic hydrocarbons. This work ha5 been supported by the Atomic Energy Commission, under a contract administered by J. H. Hildebrand. We thank Dr. Nelson W. Taylor for the PETB and Dr. Berni *J.Alder for criticism. ( 6 ) Cf. J. H. IIildebrtrnd. J . Chem. I’hys , 18, 1337 (1950).
