4392
U. BIANCHI, G. AGABIO,AND A. TURTURRO
Internal Pressure of Simple Liquids
by Umberto Bianchi, Giuseppe Agabio, and Antonio Turturro Istituto d i Chimica Industriale, Sezione V del Centro Nazwnale d i Chimica delle Macromolecole, Universiti d i Genova, Qenova, Italy (Received August 81, 1966)
Internal pressures [ (bU/bV)T]have been measured for carbon tetrachloride, benzene, and cyclohexane over a range of temperature, both at constant pressure and at constant volume. (bU/bV)Tis shown t o decrease slightly by increasing the temperature at constant volume, thus showing the liquid intermolecular energy not to be, strictly speaking, a function of volume alone.
Introduction
i-J=
Our previous on the internal pressuretemperature behavior of various polymers has often demanded a more extensive knowledge of some properties of simple liquids. I n particular, we are interested in the comparison between energy-volume-temperature relationships for both simple and polymeric liquids (like an amorphous polymer well above its glass transition temperature T,) . The internal pressure Pi,defined by Pi =
(g)T =
T(%)
The Journal of Physical Chemistry
where a is a constant (independent of T ) and n is equal to or near unity.g From (1)it follows
b In Pi
(T), = -(n + O
b In V
( F )P
= -(n
+ l), (3)
-P V
can be determined by direct measurement of the thermal pressure coefficient y v = (bP/bT)v, and its fundamental correlation with intermolecular energy makes this quantity particularly suited for our purpose~.~!~ This paper deals with a first group of measurements on the Pi change with temperature both at constant pressure and at constant volume, for three liquids: carbon tetrachloride, benzene, and cyclohexane. A number of papers has recently been published on the equation of st,ate (that is, an equation relating P I V , and 7‘) for simple liquids and on their thermodynamic proper tie^.^ ,* The general assumption is to consider the intermolecular energy U to depend only on the volume, while the temperature influences the intermolecular energy only through the alteration of the average distance of interaction between molecules. This assumption is equivalent to writing
--a V”
(3‘> where a in eq. 3 is the cubical thermal expansion coefficient of the liquid. Equations 3 and 3’ show how the measurement of Pi over a temperature interval at constant pressure (eq. 3) and at constant volume (eq. 3’) can provide a simple, direct way to test the assumption connected with eq. 1. .
(1) U. Bianchi, Ric. Sci., IIA, 32, 651 (1962). (2) U. Bianohi and C. Rossi, Chim. I n d . (Milan), 45, 33 (1963). (3) U. Bianchi and E. Bianohi, ibid., 4 5 , 657 (1963). (4) C. Rossi, U. Bianchi, and E. Bianohi, J . Polymer Sci., C4, 699 (1963). (5) J. H.Hildebrand and R. L. Scott, “The Solubility of Nonelectrolytes,” Reinhold Publishing Corp., New York, N. Y., 1950. (6) G. Allen, G. Gee, and G. J. Wilson, Polymer, 1, 456 (1960). (7) E. B. Smith, J . Chem. Phys., 3 6 , 1404 (1962). (8) P. J. Flory, R. A. Orwoll, and A. Vrij, J . Am. Chem. Soc., 8 6 , 3507 (1964).
(9) E. B. Smith and J. H. Hildebrand, J . Chem. Phys., 31, 145 (1959).
4393
INTERNAL PRESSURE OF SIMPLELIQUIDS
P
Figure 1. Pyrex glass cell used for PI measurements on liquid samples.
Experimental Section Materials. The solvents used were of high purity (RS according to the Carlo Erba reagents classification) and were distilled immediately before Pi measurements. Pi Measurements. The experimental technique has been already described in detail2; we show in Figure 1 the cell used in these experiments. C is a Pyrex glass cell, of about a 30-cc. capacity, which is first filled with the liquid to be studied and connected through the capillary end E to a vacuum line. By repeated freezing with liquid nitrogen and melting under vacuum, the gas dissolved is eliminated. After disconnecting from the vacuum line, E is rapidly immersed in the Hg contained in A; by a suitable change in temperature, the liquid Hg meniscus is formed in h, i e . , near the end of the platinum wire Pt. The Hg in A is in electric contact, through the holes 0, with some Hg contained at the bottom of the pressure vessel in which the cell is sealed.2 I n this way, a lamp connected with a transformer through the platinum wire Pt and the Hg in A will reveal the position of the liquid Hg meniscus in the capillary tube E.2
Results To measure the change of Pi by varying the temperature at constant pressure, we started with the measure-
ment of Pi at the lowest temperature, under an average pressure of 5 atm. Our practical experience has shown that the application of a small pressure increases the reproducibility of the results. After performing three or four runs at the lowest temperature, the temperature is raised while the pressure is released; this results in some solvent coming out of the cell. At this point, a pressure of -5 atm. is applied, and, by suitably changing the temperature, a new temperature is obtained, at which the liquid Hg meniscus in the cell is just in contact with the P t wire. This makes possible the determination of Pi at this new temperature; by repetition of this procedure, we have studied the Pi behavior over some temperature intervals, as it is shown in Table I. Measurements of the function Pi = Pi(T) at constant volume is simpler, as in going from the lowest to a higher temperature (at which Pi has to be measured) it is necessary simply to increase the pressure proportionally so that the liquid Hg meniscus is always kept in the same, initial, position. Results are shown in Table 11. All Pi values in Tables I and I1 are averages over at least two independent measurements, the reproducibility being within 1%of the total value. As has been pointed out previously,10 the experimental value of y = (bP/dT)Vhas to be corrected for Table I: Pi Values a t Constant Pressure (at a n Average Pressure of 5 atm.)
yccht,
"C.
21.5 22.4 26.7 36.8 45.1 53.8 60.0
7-----CeHPi, aal./cc.
82.7 82.5 81.3 79.2 77.4 76.2 75.0
7 c 6 H I Pit
t , "C.
26.3 32.2 36.7 43.8 48.4 54.1 54.4 60.3
cal./cc.
90.7 89.2 88.4 86.6 85.9 83.9 83.6 82.7
t , 'C.
22.3 28.9 35.2 37.2 45.0 52.8 60.3
Pi, cal./cc.
78.6 76.9 75.9 76.1 73.8 72.6 70.6
Table 11: Pi Values a t Constant Volume
-cch-
-CeHu-----
t , "C.
pi, oal./oc.
21.5 22.4 28.7 34.9 41.7 48.0 55.3
82.7 82.5 82.5 81.7 81.6 81.6 81.3
-CeHipi,
t, OC.
26.3 32.0
37.7 43.9 50.0 55.5
cal./oc.
90.7 90.7 90.4 89.5 89.0 89.4
Pi,
t,
O C .
29.4 36.9 44.8 52.2 59.9 66.5
aal./co.
77.3 77.3 76.3 76.6 76.3 76.2
4394
U. BIANCHI,G. ACABIO,AND A. TURTURRO
thermal expansion and compressibility of the Pyrex cell, using the equation
Table 111: Comparison among Pi Values a t 20°, Taken from Different Sources'
(4) where ag = Pyrex thermal expansion coefficient (9.9 X deg. - I ) , pg = Pyrex isothermal compressibility (3.0 X atm.-l), and = liquid isothermal compressibility. It is t o be noted that our experimental data in Table I1 (V = constant) are not strictly values at constant volume because to keep the liquid Hg meniscus just in contact with the P t wire does not mean a true constancy of the liquid volume. This nonconstancy is obviously due to the change in temperature and pressure which affect the Pyrex cell volume. This effect can be estimated by calculating the change in glass cell volume (ie., the volume of the liquid) by changing P and T . The glass cell volume is a function of T and P as
V , = V2(1
+ a,AT
- PgAP)
(5)
I n our case we have an average of 1" for AT and a corresponding change of 10 atm. for AP; from eq. 5 we get
This means that the Pi values of Table I1 at different temperatures are not exactly at constant volume but refer to a liquid which is slightly contracting by increasing the temperature. The contraction is, however, very small. Discussion of the Results It is interesting, first of all, t o compare our P i values at 20' and about 1 atm. with equivalent values taken from l i t e r a t ~ r e . 6 > 1 ~(See - ~ ~ Table 111.) As these data have not been obtained by the same method, the agreement is satisfactory and shows the accuracy with which Pi can be measured. From Tables I and I1 we can calculate the slopes (a In P i / d T ) p and ( b In P i / b T ) v which are collected in Table IV. I t can be seen that ( 3 In Pi/S)T)pvalues are in fairly good agreement with -2a values, thus confirming the value n = 1 in eq. 2 and 3. This also confirms Gee's conclusion6 about the possibility of using eq. 3 (with n = 1) t o calculate the change of Pi over small temperature intervals . The most important point, however, is to note that ( b In Pi/bT)V values are significantly different from zero (see eq. 3), their uncertainty being =t10%. The Journal of Physical Chemistry
Liquid
6
Ref. 11
ccl4
82.4 90.5 77.8
83.0 92.8 74.7
Ref.
CsHa CeHu
Pi, cal./oo. Ref. 12
82.2
... ...
Ref. 13
82.3 89.4
...
This work
82.7 92.0 79.2
Pi values from ref. 6 are determined through sound velocity measurements; ref. 11 gave values of isothermal compressibility which, together with expansion coefficient data, have been used to calculate Pi values.
Table IV : Temperature Coefficients of Ln Pi a t Constant Pressure and at Constant Volume
Liquid
ccl4 CEHE CsRi2
OK. -1
OK. -1
OK. -1
-2.6 -2.7 -2.7
-0.46 -0.52 -0.40
-2.5 -2.6 -2.4
Moreover, we expect these values to be more negative than those quoted because they refer to an experiment in which, as previously noted, the volume of the liquid is slightly decreasing by increasing the temper% ture; the observed Pi values are thus a little higher than those referring to a liquid truly kept at constant volume, and consequently the absolute values of the slope ( bIn P i / b T ) V are decreased. We can conclude that the intermolecular interaction energy of a liquid is not strictly a function of the volume alone and that, even keeping the volume constant, the temperature itself is capable of introducing an alteration, perhaps through a change in the average arrangement of each molecule and its neighbors. Previous experimental results on CCld and some fluorocarbons have been taken as evidence that yv ( ~ P / ? I T )was ~ constant over some Z O O temperature interval (at constant v o l ~ r n e ) . ~ The evidence was based on the linearity of the pressure-temperature plot in these temperature intervals. The change of yv with temperature (at constant volume) is however too minute, and the temperature interval of 20' too small 5
(10) W.Westwater, H. W. Frantz, and J. H. Hildebrand, Phys. Rev., 31, 35 (1928). (11) G.A. Holder and E. Whalley, Trans. Faraday Soc., 58, 2095 (1962). (12) H. Bonninga and R. L. Scott, J. Chem. Phys., 23, 1911 (1955). (13) J. S. Rowlinson, "Liquids and Liquid Mixtures," Butterworths Scientific Publications, London, 1959.
4395
NOTES
to be able to discover the slight curvature in a plot of P against T . Work is in hand to extend these measurements to other simple liquids, including polar compounds,
and to high molecular weight polymers, on which some preliminary results have been already published. Acknowledgment. It is a pleasure to acknowledge the continuous interest of Prof. C. Rossi in this work.
NOTES
Barium-Iron-Oxygen Compounds with Varying Oxygen Content and Iron Valence
by Anna Clyde Fraker Department of Engineering Research, North Carolina State University at Raleigh, Raleigh, North Carolina (Received M a y $4, 1966)
The hypothesis of Erchak and Wardl that bariumiron-oxide can accommodate different amounts of oxygen and that the Eitructure maintains stability by varying iron. valencies is supported by this paper, and a correlation between oxidation state and interatomic spacing is shown. Mossbauer measurements'Z of the perovs:kite BaFe03compound reported by Derbyshire, Fraker, and Staclelmaier3 show that 76% of the iron is in the f4 valence state and 24% is in the +S state. Thus the empirical formula for this compound is probably Ba(Fe3+4.Fe.+3)02.9 instead of the stoichiometric BaFe03. Two +3 iron ions are formed for every oxygen ion which is lost. The X-ray pattern of BeFe02.9is shown in Figure 1A along with charts of two other materials which were equilibrated as described in Table I. The Mossbauer absorption spectrum of preparation A, Table I, as well as a mixture of preparation B and C is shown in Figure 2. I n Figure 2A, the principal absorption peak corresponds to F'e+4, the minor peak to Fe+a, It is characteristic of these structures that their principal diffraction lines coincide and have comparable intensities. The :X-ray patterns of materials E and C show a remarka'ble shift of the diffraction lines due to changes in the experimental conditions. This shift is associated with variations in ionic distances in the basic structure and must be attributed to the ionic radius of the iron. It i s the size of the iron ion inside the octahedron which d.etermines the lattice parameter
shift in the close-packed arrangement of barium and oxygen ions. The Fe-0 distance which is listed in Table I was determined by dividing the interplanar spacing for the strongest diffraction peak by fi. This peak corresponds to { l l O ) planes for the cubic structure of Figure 1A. It may be concluded from Table I that materials B and C are oxygen deficient, and Mossbauer measurements (Figure 2) of a mixture
WK-
C
I (1) M. Erchak, Jr., and R. Ward, J. Am. Chem. Sac., 68, 2093 (1946). (2) Dr. Uri Shimony of the Massachusetts Institute of Technology,
Cambridge, Mass., did the Mijssbauer work. (3) S. W. Derbyshire, A. C. Fraker, and H. H. Stadelmaier, Acta Cryst., 14, 1293 (1961).
Yalume 69, Number 18 December 1966
