PRESSURE-VOLUXIE-TEMPERATURE RELATIONS I S SOLUTIOXS. IL OBSERVATIONS ON THE BEHAVIOR OF SOLUTIONS OF BENZENE AND SOME OF ITS DERIVATIVES R. E. GIBSON
AND
0. H. LOEFFLER
Geophysical Laboratory, Carnegie Institution of Washington, Washington, D. C . Received October 1.2. 1958 INTRODUCTION
In common with other properties of liquids and liquid solutions, the pressure-volume-temperature relations depend on the nature of the constituent molecules and the forces between them. The connection between molecular mechanics and thermodynamics is, however, still so obscure in this field that an experimental attack with a view to obtaining empirical generalizations seems not only justifiable but even desirable a t the present time. The changes in volume which occur when two components are mixed a t different temperatures and pressures to form solutions of various concentrations have been assumed to be closely connected with the intermolecular forces between the components and, moreover, they are quantities of considerable thermodynamic interest because the changes of activity coefficients with pressure may be computed directly from them. In the course of a systematic study of the volume changes on mixing of aqueous solutions at different pressures and temperatures, it became evident that the complex behavior there encountered could be better understood if more were known about the behavior of simple solutions. Binary mixtures of benzene and some of its monosubstituted derivatives appeared to be suitable for such an investigation. Many of their properties have been investigated, the densities, vapor pressures, and dielectric constants, quite recently, in fact (11, 12); it is highly unlikely that structural effects complicate the behavior of these solutions. This paper presents a few questions of more general interest which have arisen during a systematic study of the densities, compressions, and thermal expansions of mixtures including benzene, aniline, chlorobenzene, Presented a t the Symposium on Intermolecular Action, held a t Brown University, Providence, Rhode Island, December 27-29, 1938, under the auspices of the Division of Physical and Inorganic Chemistry of the American Chemical Society. 207
208
K. E. GIBSON AND 0. H. LOEFFLER
bromobenzent~,: i n d nitrobenzene. clsrwhrre. CoiwnEssIoNs
The complete results will be published
OB THE PURE COMPONENTS
The compressions of the liquid components (suitably purified) to 500 and 1000 bars (metric atmospheres) were measured a t 25O, 45O, 65O, and 85OC. in our latest pressure apparatus (4). We had already found (6) that the bulk compressions of benzene were represented within experimental error by the Tait equation: k =
c log [ ( B+ P ) / B ]
where k is the bulk compression and P the pressure; B and C are constants, the latter being independent of the temperature. TABLE 1 Constants in the T a i t equation for benzene and some of i t s derivatives at diferent temperatures For all the liquids a t all temperatures C = 0.21591 B UUBBTANCB
0
___Benzene. . . . . . . . . . . . . . . . . . . . 1.14461 Chlorobenzene. . . . . . . . . . . . . . Bromobenzene . . . . . . . . . . . . . . Xitrobenzene . . . . . . . . . . . . . . . Aniline. ....................
IN XICOBARB
AT 26°C.
0.90817 0.67177 0.83451 0.98291
25°C.
0.970 1.248 1,4044 1.8652 2.009
41'C.
____-
0.829 1.0978 1.2473 1 ,6794 1 ,7983
ffi".
wc.
0.701 0.9609 1.1033 1 ,5035 1 ,6056
1.4304 ~-
Using the same value of C as we had employed for benzene, we were able to calculate B for the other liquids from the compressions at 1000 bars. These values of C and B , when used in equation 1, reproduced our determinations at 500 bars within experimental error, and we have found by repeated checks at intermediate pressures that this agreement at 500 bars means that the equation reproduces the compressions to any pressure between 1 and 1250 bars. I n table 1 we give the value of the constant C and the values of B (in kilobars) at different temperatures, the figures for benzene being taken from the previous paper. The fact that C is independent of temperature and the same for all these liquids supports the suggestion made by Dr. Teller (private communication) that i t depends on the repulsive forces between the molecules themselves. It follows from the constancy of C that the compressibility of any of the monosubstituted derivatives of benzene mentioned in table 1 is the same as that of benzene itself under a hydrostatic pressure equal to the difference between the net internal pressure ( B )of the compound and that of benzene.
PRESSVHE - VOLCYE-TEMPERATURE
RELATIONS
209
In other words, the introduction of a polar group acts on the compressibility of benzene in the same way as the application of an external pressure,-it changes the attractive potential but leaves the form of the repulsive potential unaltered. From an analysis of the results for benzene it has been shown (6) that B may be interpreted as the difference between the cohesive pressurp set up by the attractive forces between the molecules and the expansive pressure due to the thermal energy of the molecules, (R!l'/(V - b) in van der Waals' equation). In other words, B represents the net internal pressure of the liquid. Increase in the attractive potential between the molecules, decrease of temperature, and increase in the free volume (V - b ) all cause B to increase in value. There is a rough parallelism between B and the electric moments of the molecules in the dif-
5-LINILINE
FIG.1. The surface tensions of benzene and some derivatives a t different temperatures plotted against the average force between the molecules (in IO8 dynes per mole) computed on the assumption that B is the net internal pressure.
ferent liquids, but the parallelism is so rough that we must conclude that the dipole forces do not play a predominating rBle in determining B. The surface tensions of these liquids at different temperatures are closely related to their net internal pressures. In figure 1 we have plotted the surface tensions (interpolated from the data given in the Landolt-Bornstein Tables) of the various liquids a t 25", 45", and 65°C. against BV:, a quantity which represents the sverage force acting on one mole of a liquid whose net internal pressure is given by B. The points for all five compounds a t 25°C. lie on a straight line, and the points for the higher temperatures scatter very closely around this line. As the surfaces of all these liquids are presumably the same as that of benzene, we should expect the surface tension to be determined almost completely by the intermolecular forces and the size of the molecules. Figure 1 may be taken as contributory evidence in favor of our interpretation of B. By means of the Tait equation me may compute the molal volumes of
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R. E . GIBSOX AND 0. H. LOEFFLER
benzene under hydrostatic pressures a t which its Compressibility is equal to that of its derivatives. On comparing molal volumes under such conditions (constant B ) we obtain very reasonable estimates of the volumes of the substituent groups. It will be seen from the foregoing that this is equivalent to a comparison of parachors (15). Relations between surface energy, compressibility, internal pressure, etc. have been studied extensively for many years (2, 8). We seek to avoid confusion by emphasizing that the net internal pressure B is not equal to the internal pressure defined in any of the usual ways (8) such as @E/bV)T. APPARENT VOLUMES, EXPANSIONS AND COMPRESSIONS O F A N I L I N E I N SOME SOLUTIONS
The specific volumes of solutions of aniline in benzene, chlorobenzene, and nitrobenzene were measured a t 10°C. intervals between 25" and 75°C. in a new weight-dilatometer made of fused silica. The compressions to 500 and 1000 bars of the same solutions were also determined over this temperature range. From these data the apparent volumes of aniline in the different solutions were computed at various pressures and temperatures. It will be recalled that the apparent volume (per gram) of a component in a binary mixture is defined by the equation:? 2,
= z1v;
+ z24.2
and it may be noted that the volume change taking place when the requisite amounts of components are mixed to form 1 g. of solution is given by z2(+2
- 4 or zl(+l - 2,;)
In figure 2 we have plotted (& - v;) in milliliterb per gram for aniline in different solvents a t various concentrations, pressures, and temperatures against the mole fraction of aniline. It will be noted that a wide variety of behavior is represented on this diagram. Benzene and aniline contract on mixing; this contraction increases with temperature and diminishes with pressure. Aniline and chlorobenzene expand slightly on mixing; the expansion is almost independent of temperature and is increased by rise of pressure. A greater expansion is observed on mixing aniline and nitrobenzene, but this expansion diminishes with pressure. Our compressibility results are given in more detail in table 2, where observed values of B are 2 The symbols used in this paper are as follows: The subscripts 1 and 2 refer respectively to each component in the solution; generally aniline is taken a s component 2. The weight fraction is represented by x, the mole fraction by X,the specific volume of the solution by v , the molal volume by I-, the apparent volume by +, and the relative volume change with pressure (bulk compression) by k. The superscript 0 denotes the pure liquid component. A p indicates the finite change with pressure of the quantity to which i t is prefixed. P i s the pressure; T i s the absolute trmperature.
21 1
PRESSURE-VOLUME-TEMPERATURE RELATIONS
recorded, and in figure 3, where the differences between the apparent compressions to 1000 bars of aniline in solution and of pure aniline are plotted against the moIe fractions of aniline in different solutions. Compressions of the solutions to 500 bars confirmed the presumption that the constant C was the same for the solutions as for the pure liquids. It will
I
-omo
l&HoNHr-C,& 01
02
n6y
1 I I I I 1
03 04 05 06 MOLE FRACTION OF ANILINE
07
5‘
00
09
I O
FIG.2. The difference between the specific volume of aniline and its apparent volume in different solvents at various temperatures, pressures, and concentrations. The black dots represent results computed from the data of Martin and Collie. TABLE 2 Constants in the T a i t equations for the’compressions of solutions at 86°C. In all cases C = 0.21591 SOLUTION
WEIQKT FRACTION OF ANILINE
I
B’
VOLUME FRACTION OF ANILINE
I N XILOBAR8
-
Aniline-benzene
0 8507 0 7560 0 5050
0 8303 0 7268
1.7887 1,6693 1.3838
0 7923
0 8050 0 5192 0 2632
1.8210 1.5857 1.4080
0 7410
0 7712 0 5360
1.9506 1.9132 1.8832
Anlllne-chlorobenzene
Aniline-nitrobenzene
be seen from figure 3 that the compressions of aniline-benzene and anilinechlorobenzene mixtures are less than those computed from the simple law of mixtures, whereas in aniline-nitrobenzene solutions the opposite holds. N E T INTERNAL PRESSURES AND VOLUME CHANGES ON MIXING
In dealing with solutions whose components differ widely in compressibility, such as aqueous salt solutions, we have applied Tammann’s
212
R. E. GIBSON AND 0. H. LOEFFLER
hypothesis that the solvent (component of the greater compressibility) in the solution behaves as if it were under an external hydrostatic pressure, and we have shown that the volume changes on mixing may be computed with useful accuracy from the observed compressions or net internal pressures (3,5). The method involves one assumption concerning the compression of the solute, however, which makes it inadequate for solutions whose components do not differ widely in compressibility, such as those we are now discussing, but it can readily be modified. In view of the fact that the constant C in the Tait equation is the same for all the liquids and solutions mentioned here, we may apply the following argument: Let B1,Bz, and B' be the net internal pressures of the pure components and of the solutions, respectively. When the net internal pressure of a component is
-.006
1 1 BENZENE
I
v
I / /
changed from B1 to B', the corresponding volume change according to the Tait equation is given by equation 2:
B' - A P V ~= vo ~ log C -
(2) B1 If we assume that, on forming the solution, the components first expand until their net internal pressures come to the common value B' and then mix without further change, we arrive a t the following formula:
-AV - (& + Z& -C
log B' - ( z ~ vlog : Bi
+
log B,)
Z~V;
(3)
In this equation -Av is the decrease in volume when 1 g. of solution is made from the appropriate quantities of the pure components. It should be noted that C is independent of temperature etc. only when the com-
PRESSURE-VOLUME-TEMPERATURE
RELATIONS
213
pression is expressed as the volume change per unit volume. and this constancy of C leads to a relation involving log B‘ and the volumefractioiis of the components. In view of the increasing importance that is being attached to the volume fraction by theoretical workers (7, 14), we regard this observation as significant. I n figure 4 we have plotted log B’ against the volume fractions of aniline,
,a>
z*d (z,v;
+
in the three series of solutions (open circles). Qualitatively the formula holds; where log B’ falls below the straight lines joining log B1 and log BI the volume change on mixing is positive, and where the points for log R’
FIG. 4. Illustration of the relation between the logarithm of the net internal pressure of solutions of aniline a t 25°C. and the volume fraction of the components. The open circles indicate the observed values of log B’, and the dots, the values computed from the volume change on mixing.
fall above this line, the volume change on mixing is negative. Quantitatively equation 3 leaves something to be desired. The black dots in figure 4 represent values of log B‘ computed from the observed volume changes on mixing. The agreement gets progressively worse as the solutions become more dilute in aniline, except in the rase of nitrobenzene. This may be due in part to our overstraining the Tait equation by using it to extrapolate to negative pressures exceeding 500 bars. The volume changes on mixing computed from the observed values of B agree with those actually measured within a factor of 2, and, as these volume changes are very small as compared with the specific volumes of the components, we may say that the agreement is not despicable. Solutions of aniline and nitrobenzene were chosen for examination
214
R , E. GIBSON AND 0.
E. LOEFFLER
because the net internal pressures of the pure liquids were nearly the same and hence less extrapolation with the Tait equation was necessary. The agreement between the observed and calculated values of log B‘ is, however, particularly poor for these solutions, a fact for which another phenomenon to be discussed later must be held partly responsible. Summing up, we may say that equation 3 gives a means of calculating approximately the compressibilities of a solution from the volume changes on mixing, or vice versa, provided that the volumes and the net internal pressures of the components are known. It gives a means of connecting the volume change on mixing with the net internal pressure of the solution. Figure 5, giving the results of computations from Bramley’s data (l), shows that the volume changes occurring when phenol is dissolved in various solvents parallel those we have observed with aniline. We are,
a’pl
I
I
I
I
I
I
I
I
I
I
008
001
c$
0
f P
-001
1-008
- 011 -
010
-020
0 WElOHl FRICTION OF
PHENOL-
FIG.5. The difference between the specific volume of phenol and its apparent volume in different series of solutions, as computed from Bramley’s data.
therefore, not dealing with any isolated case. An essential feature of figures 2, 4, and 5 is that, as the ratio of the net internal pressures of the pure components approaches unity, the volume change on mixing per unit of aniline or phenol becomes more positive, and accordingly the departures of log B’ from the straight lines become more negative. This statement covers not only the volume changes a t 25°C. but also the results a t different pressures and temperatures, From table 1 i t will be seen that the ratio of the net internal pressures for aniline and benzene approaches unity as the temperature falls; for aniline-chlorobenzene solutions this ratio changes in the same direction but to a much less extent. At higher pressures the quantity ( B + P ) must be used instead of B, and it is obvious that the higher P is, the closer will the ratios of ( B + P ) for pairs of the liquids approach unity. Figure 6 shows that a t 1000 bars (1 kilobar) the depar-
PRESaURE-VOLUME-TEMPERATURE
RELATIONS
215
tures of log (B’ + P) from the straight lines are more negative than at atmospheric pressure. Our investigations of aqueous and non-aqueous solutions of electrolytes have led us to similar conclusions about the relations between the volume changes on mixing and the ratio of the compressibilities of the components in those cases where structural effects do not predominate ( 5 ) . The activity coefficients of aniline, phenol, nitrobenzene, chlorobenzene, etc. in benzene solutions all increase as the solutions become more dilute, and the activity coefficients have been adequately correlated with the change in electrostatic energy of the solutions arising from changing concentrations of the polar molecules (11). Negative values of (& - v i ) mean that the activity coefficients decrease with pressure and that the chemical potential of the solute becomes closer to what it would be in the
FIG.6. The logarithms of the net internal pressures of aniline solutions at 25°C. and loo0 bars plotted against the volume fraction of aniline.
ideal solution of the same chemical nature as the pure solute. I n other words, the electrostatic energy due to the polar molecules becomes relatively less important as the volumes of the solutions are diminished, shortrange forces becoming quite significant. NITROBENZENE-ANILINE
MIXTURES
What has been said in the preceding discussion is applicable to nitrobenzene-aniline solutions except that rise of pressure appears to decrease rather than increase the change in volume on mixing. These solutions present a rather interesting phenomenon. It has been known for a long time that when reasonably pure nitrobenzene and aniline are mixed, the solution instantly develops a deep orange color (10, 13). Investigation of the thermodynamic properties and viscosities of these solutions (IO, 16)
216
R. E. GIBSON AND 0 . H. LOEFFLER
has revealed no trace of compound formation in the usual sense of the term. It occurred to us that a grouping of the aniline molecules around the highly polarizable nitro group, the energy of association being quite low, might account for this color, and, if so, the absorption of light should be pushed even farther towards the red by application of hydrostatic pressure. Such was found to be the case. With a suitable blue lightfilter, a reversible color change from green to yellow could readily be seen as the pressure over the solution was raised. This phenomenon is now being systematically studied, and further details will be published later. It is mentioned here to show that nitrobenzene-aniline solutions exhibit a curious type of intermolecular phenomenon, but further speculations about the effect of pressure on tliese solutions must wait till the phenomenon is more carefully investigated. We must state in conclusion that we still regard the theoretical implications of the Tait equation as very obscure. Similar equations on a much sounder theoretical basis have been developed (9), but they lack the simplicity of the Tait equation. It is our purpose to apply this equation empirically until it breaks down completely; in so doing we hope to uncover what is most needed a t present in the study of liquids, some valid simplifying assumptions. SUMMARY
New measurements of the compressions and expansions of some derivatives of benzene and of the specific volumes, compressions, and expansions of mixtures of benzene and these derivatives have confirmed and extended the empirical use of the Tait equation. The exponential constant C in this equation has been found to be the same for all the liquids and solutions examined, and the internal pressure constants, B , for the pure liquids and the solutions have been correlated with volume changes which take place when the liquids are mixed. The conclusions based on studies of electrolytic solutions concerning the volume changes on mixing and the internal pressures of the components are found to hold qualitatively in benzene solutions. A new phenomenon in aniline-nitrobenzene solutions is described. REFERENCES (1) BRAMLEY, A.: J. Chem. SOC.109, 10 (1916). (2) EDSER,E.:Brit. Assoc. Colloid Repts. 4,40 (1922). (3) GIBSON,R. E.: J. Am. Chem. SOC.67,284 (1935). (4) GIBSON,R. E.: J. Am. Chem. SOC.69,1521 (1937). (5) GIBSON,R. E.: Am. J. Sci., in press. ( 6 ) GIBSON,R. E., AND KINCAID, JOHNF.: J. Am. Chem. SOC.80,511 (1938). (7) GIJGGENHEIM, E. A,: Trans. Faraday SOC. 33,151 (1937).
PRESSURE-VOLUME-TEMPERATURE
RELATIONS
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(8) HILDEBRAND, J. H . : Solubility, Chap. 9. The Chemical Catalog Co., Inc., New York (1924). (9) KINCAID,JOAN F., AND EYRING,H.: J. Chem. Phys. 6, 593 (1937). (10) KREMANN, R.: Monatsh. 26, 1271 (1904). (11) MARTIN,A. R . : Trans. Faraday SOC.33, 191 (1937). (12) MARTIN,A. R., AND COLLIE,B . : J. Chem. SOC.1932, 2658. I.: Ber. 44, 268 (1911). (13) OSTROMISSLENSKY, (14) SCATCHARD, G . : Chem. Rev. 8,321 (1931). (15) SUGDEN,S.: J. Chem. SOC.126, 1177 (1924). (16) TBAKALATOB, D. E.: Bull. 6 0 0 . chim. [4] lf,284 (1912).
