is a properly averaged mass. Hence A.So,/R
VOl. 70:
LEONSLUTSKY AND S. H. BAUER
constant
-
6
In ,T k , r=l
+
It follows that when AS: is plotted against log p , a straight line with slope 13.7 would result, provided (a) ki did not vary from one molecule to the next; (b) the simple reduced masses were equal to the properly averaged masses; and (c) the magnitudes of the remaining terms in the expansion are negligible. I n Fig. 1, group 2 has roughly a slope of 14, while group 1 has roughly a slope 5.5. Analyses of other bimolecular association reactions in this manner will be of interest, particularly where the vibrational spectra are unknown, or have not been worked out. We are currently investigating the tri-aryl methyl radical dimers. ITHACA,K. Y.
[COSTRIBCTIOS FROM
THE
DEPARTMEST O F CHEMISTRY, CORSELL
UNVERSITY
]
Computations of Entropy Increments in Gaseous Bimolecular Associations. 11. The Dimerization of Carboxylic Acids, and the Addition of Fluorine to Halogen Fluorides BY LEONSLUTSKY A N D S. H. BAUER RECEIVED JUNE 18, 1953 The procedures described in the preceding paper (I)6 have been extended t o two groups of reactions, the dimerization of carboxylic acids and the addition of fluorine to three halogen fluorides. For the first group, the magnitude of A s o v i b has been cited as a n argument for describing the dimers as consisting of weakly coupled monomers, according t o the principle discussed in paper I. A highly simplified model for the structure of the dimers permitted a normal coordinate treatment which led to the six new fundamental frequencies ascribed t o each dimeric species (formic, acetic, trifluoroacetic acids), as a consequence of the association process. The fact that the computed entropy increments check the reported values t o better than one entropy unit lends strong quantitative support to the model proposed. Since the addition of fluorine t o the three halogen fluorides involves the rupture of one bond, the formation of two new bonds, and extensive rearrangements of the original structures, the magnitudes of the entropy increments d o n o t have a simple interpretation. They are useful in the making of estimates of average bond energies. Interesting differences between the several central halogen atoms appear when their fluorine ligancies go up by two. Arguments are presented for selecting the "higher" of the two possible values for the heats of dissociation of CIF. B r F and I F .
The Carboxylic Acids.-That the equilibrium constants for the dimerization of carboxylic acids differ appreciably, depending on the group substituted into the carboxyl carbon atom has been known for some time. Recently' speculations have appeared as to whether such differences are due primarily to enthalpy or entropy factors. The literature is replete with reports of experimental results regarding these systems, from which one may select values to prove either conclusion. Where available we prefer the data by Taylor and BrutonZs3since these investigators worked in the low pressure region where corrections for higher degrees of polymerization and deviation from ideal behavior are unnecessary. In the case of trifluoroacetic acid, Nashl computed equilibrium constants after he had extrapolated isothermal density curves to zero pressure. Reference to Table I shows that small differences appear both in the enthalpy and entropy terms, and that due to the rather close balance between them, appreciable variations in the magnitudes of the equilibrium constants result. Indeed, closer inspection of the reported entropy increments raises the question why these should be so nearly alike, since the masses and moments of inertia of the molecular species vary over a considerable range. The computations (1) R. H, I,undin, F. l i . Harris arid L. K.Nash. T H r s J O U R N A L , 74, 4tiX (1952). ( 2 ) hl. L). Taylor and J. Bruton, i b i J . 74, -1131 (ll152). (3) h1. I>. Taylor, ibid., 73, 315 (1951).
described below permitted the unscrambling of the effects due to mass, moments of inertia, internal rotations and molecular vibrations. TABLE I
HCOOH H3CCOOH I:~CCOOH CHsH2CCOOH
AHoarr kcal./ mole
AS"a0s, e.u.
KP(432i. atrn.
Rei.
-14.1
-35.98 -3fi.84
0.299 ,474
2
-1.5.8 -14.0
-15.2
-3i,30 -2ti.29
,185
,503
3 1 2
The structures for which the moments of inertia were computed are those given by Karlc and Brockway,4 cf. Table 11. From these and the known molecular weights, one may readily compute ASot,.+,. (rigid molecules). These are summarized in Table 111. The deduced values for .lS"(rigid) first must be corrected for contributions due to restricted internal rotation. For simplicity we have assumed that the heights of the barriers hindering free rotation about c-C bonds remain unaltered due to the association process, and that both in acetic and trifluoroacetic acids the magnitude is 2500 cal./ mole, with three equal minima in the angular potential function. Although these are not valid assumptions, the errors introduced thereby are of the order of one entropy unit, which is within other limitations to be introduced later. For acetic acid ( 4 ) J . K d ~ l ca u d 1.. U. h u c k u d y , i b ~ d . ,66, 2 7 1 ( 1 ! # 4 4 ) .
Jan. 5 , 1954 DIMERIZATION OF CARBOXYLIC ACIDS AND ADDITIONOF F2 TO HALOGEN FLUORIDES271 TABLE I1 I s J b I e X 10114(g. cm.2)3
Formic Acetic Tri-F-acetic Propionic
Monomer
Dimer
0.0776 1.209 28.88 5.327
30.02 177.7 4999 808.5
TABLE 111 Ideal gas, a t one atm. e.u. monomer ( u = 1)
SQua (tr. r.), e.u. dimer ( 0 = 2)
61.19 64.79 69.84 67.35
67.85 70.39 75.66 73.03
SO433
(tr.
Formic Acetic Tri-F-acetic Propionic
+ r.),
+
ASO(rigid1,
e.u.
-54.53 -59.18 -64.02 -61.67
the entropy associated with rotation of the methyl groups with respect to the rest of the molecule may be deduced from the barrier assumed and the reduced moments of inertia.5 For trifluoroacetic acid, the entropy contribution for free internal rotation was calculated by means of the relation Sf,i,r.= 2.287(10g T
+ log 1,
- 2 log n) + 89.93
and the increment due to restricted rotation was read from the available table^.^ Thus we found (at 160’) the values listed in Table IV. TABLE IV Sr.i.r.
(dimer), e.u.
Formic Acetic Tri-F-acetic Propionic
2Sr. i.r. (monomer), e.u.
We are now in a position to deduce the increment in entropy arising from the vibrational contributions. These are given in Table V. The fact t h a t the increment in vibrational entropy is so large is significant6; the conclusion is inevitable t h a t in the association process the monomer units become only weakly bonded to each other. Then the six new vibrational frequencies to be associated TABLE V e.u.
e.u.
Aso(vib-x), e.u.
Formic Acetic Tri-F-acetic Propionic
-35.98 -36.84 -36.30 -36.39
-54.53 -59.11 -62.70 -60.67
$18.55 +22.27 -i-26.40 +24.28
AS%igid+ r . r . ) ,
X-C(Z
remain rigid, and that the quadrilateral formed by the four oxygen atoms is a rectangle symmetric about a line joining the opposite carbon atoms. The force constants for the 0-H * ’ ’ ‘ 0 stretching motions were obtained by assuming an inverse power type of potential matched for the observed 0 * 0 separation and half of the heats of dissociation. The force constants for the 0-H * * a
-a /
bending were taken to be (0.97/1.0S)b~+~ bend, recorded for various monomer^^*^*^^ both for the inplane and out-of-plane motions. Six frequencies were thus deduced for each of three acid dimers. These are listed in Table VI, while a comparison TABLE VI
ASr.i,r. e.u.
0 0 0 5.62 5.55 0.07 10.44 9.12 1.32 (calculations not performed) Estimated 1
ASD(exp),
tween formic and trifluoroacetic acids could be accounted for by postulating a sufficiently extensive loosening of the bonds upon dimerization of the latter.’ On the other hand, if our conclusion regarding the proper description of the dimers is correct, a simple model should not only lead to vibrational entropy increments of the magnitudes observed, but should also account for their correct sequence. The following model is treated briefly in the appendix. In i t we have assumed t h a t the vibrational contributions to the entropy in the monomer units remain essentially unaltered upon dimer formation. Further, t h a t insofar as the six new vibrations are concerned, the units
with the dimer ring may be considered as arising from the relative vibrations of two massive subsystems; consequently they are very low. The naive assumption that the ring can be treated as a single unit vibrationally is indeed unsatisfactory since this not only would argue for of about one-half t h a t observed, but also would require t h a t the entropy increment associated with the dimer ring be about the same for all four acids. It is difficult to see how the 8 e.u. difference be( 5 ) 13. S. Taylor a n d S. Glasstone, “Treatise on Physical Chemistry,” Vol. I, D. Van Nostrand Co., New York. N. Y., 1942,p. 661. (6) A. Shepp a n d S. H. Bauer, THISJOURNAL, 76, 266 (1954).
c1
Formic Acetic Tri-F-acetic
172 165 126
i.2
348 332 286
Fa
t4
481 215 127
124 114 54
FS
145 143 89
Y6
96 35 16
TABLE VI1 e.u.
e.u.
Difference, e.u.
18.55 22.27 %G .40
17.G8 21.47 27.37
0.87 .80 - .93
ASovib.
Formic Acetic Tri-F-acetic
ASoiine-r,
(7) T h e extent of weakening of t h e vibrations which are characteristic of t h e monomer molecule as a consequence of dimerization is illustrated by t h e following table, for trifluoroacetic acid.8 Assignment O H stretching C=O stretching C-0 deformation C-0 stretching C-F stretching OH bending (in plane) C-F stretching (asymm). OH bending (out pl.) C-C stretching C=O bending
Monomer C, cm. - I 3587 1826 1465 1300 1244 1130 1162 804 825 708
Dimer i . , cm.-’
3248-2700 1788
1465 1203 1244
1203 1182 ( e ) 1123 825 708
\O T h e frequencies tabulated above account for 11 of the 18 vibrational degrees of freedom of CFaCOOH. Restricted internal rotation about C-C accounts for a twelfth. Three of t h e remaining frequencies are associated with C-F bending modes; by analogy with t h e C-F stretching modes these should not be much affected by association. There remain threelow frequencies, two CFs wagging, and one carboxyl group wagging, appreciable changes in which could contribute significantly t o ASQ. We estimate a n npper limit of five units if such a loosening were t o occur. (8) W. Fuson, h2. Josien, E. A. Jonesand J. A. L ~ W S O IJI ,. Chetn. l’hys., 20, 1627 (19.52). (9) V. Z. Williams, iDid., 16, 24.3 (1Y47). (IO) R. C. Herman and R. Hofstadter, ibid., 6, 534 (lY.38).
between -lSiJvib-x and the entropy contribution The ideal gas entropy increments for thc above rcdeduced from each set of frequencies (A.Soring-c action, a t 400°K., for four combinatioiis of symmetis presented in Table VII. ries are given below. The spectroscopic data" A considerable number of Kainan frequencies in IF, ulii Ilih ITthis range have been recorded" for the dimers; we were not successful in matching a set of six comJ . ~ C4v 1 - 4 2 51 ---13.80 puted values with those reported for a given acid. cj,. -43.13 -43 18 However, this is not surprising in view of the crudeness of our model and the absence of detailed in- favor the CAr-D5i, combination (the underlined formation on intensities and polarizations of the value). From the variation of the equilibriuin Iianian lines. -1careful reinvestigation of a series constant for the above reaction with temperature, of acids may prove worthwhile. In the meanwhile Bernstein and Katz'j reported -43.3 + 3 e.u. we believe that a rational treatment for the di- Since the D;j, structure is most implausible, the merization process may be presented in terms of the problem of distinguishing by means of thermoformation of weak bonds between monomers, with chemical data between the two possible configurathe latter practically niaintaining their identity. tions for IF5 reduces to checking predicted entropy This is consistent with the model assumed in the increments which are 0.0 e.u. apart. For a series of theoretical computatioii of heats of associ a t'1011 eleven measurements taken a t regular intervals for the aliphatic Furthermore, one may between (i00--1-OO0K., the ideal gas equilibrium argue that the order of tlecreasing hydrogen bond constants will have to be determined to an accustrengths is racy of 4% (equivalent to 0.04 mm.). For the reaction (BrF3 F2 = BrF5) sufficient acetic formic Iiropionic( > '\trifiuoroscctic data are not available to permit relating the symmetry number of the trifluoride to that of the penta:is is reflected by the experimental values for the fluoride. Spectroscopic datal6 favor the assignheats of association (Table I ) ; it is not distributed ment of the latter to Cj,.. On this basis, and with according to the magnitudes of the equilibrium the further assumption that the Br-F distances constants. The latter sequence is confused by the are equivalent and equal to the sum of the covalent effect of inass on the vibrational entropy decrement. radii, Stephenson and Jones16tabulated the thermoT h e difference between the calculated ring-vibra- dynamic properties of the pentafluoride. .4 third tional entropies and those deduced from experiment law entropy is available for bromine trifluoride. l 7 are probably due to : (a) the assumption of rigidity The value for the gas a t the normal boiling point 0 of the S - C i unit, which would tend tu make was corrected to 300'K. Thus the entropy clecre'0 nient for the addition of fluorine to bromine trifluothe computed value low; (b) a small amount of ride was deduced to be = -4221 e.u. Furweakening of the original bonds due to dimeriza- ther, by combining the above values with the availtion; and (c) the neglect of anharmonicity in the able data for RrF and Br?ISthe entropy change for ring vibrations. In the case of trifluoroacetic acid the reaction iSBrF = :%Br2f BrF3 BrF5) wm the calculated value was too high; arid this might estimated to be ASiJ = - 114 e.u. (ideal gas value). be explained as being due to an underestimation of The entropy decrement computed for the reaction the bending force constants for this acid, the cor- iClF f F? = ClF3) on the basis of the accepted rect values being probably closer to those assigned structure of the productl9 and the published specfor the other two (see Table IX). troscopic data for the reactants and The Fluorination of Halogen Fluorides.--The check with the value deduced from the observed F? = variation of the equilibrium constant with teniperentropy increment for the reaction (IF6 IF;) was computed for various combinations of atwe,'" 1s'' = -:;?.(; e.u. models, assuming the symnietries C4\- and C5,. for n'ith the aid of the above values, we found it posthc pentafluoride and the syninietries D5h and Dit, sible to solve for a rational set of aaernge bond enerfor the heptafluoride. Preliminary electron dif- gies (a.b.e.) based upon various heats of formation, fraction results13on the structures of 1177 and the dissociation energies from spectroscopic studies and vibrational frequency assignments reported by minimum values for AFO's. These are summarized Lord, et al.,'? for both fluorides were used. The in Table TTII. For the dissociation energies of 1 7 2 , lengths of I-F ban+ were assumed to be equivalent Br2 and 1 2 we used ;$7,i',214.j.tj,223j..j2?kcal. /inole, and equal to 1.88 A. in the C5, and Ditl configura- respectively. Then, the a.b.e. for IF5 follows froiii tions; in the ClV and D5il configurations the I-F the heat of formation of the gaseous compound as bonds along the principal rotation axis were taken reported by Qf = 194.6 kcal. ;mole, and the to be 1.93 A., while the I-F bonds exiending to the :I.:) R . Bernstein and J . J . Katz. J . P h y r . Cl!em., 66, 885 (l!ls52). girdle were assigned lengths of 1.83 A. The latter (I(;) C V. Stephenson a n d E. A. Jones, J . Chem. P h y s . , 20, 1830 two values are those which appear in the radial dis- (1!1.52). (17) 0 . D . Oliver and J . Ll-. Grisard, THISJ O U R N A L , 74, 2703 (1952). tribution curve for IFj, roughly with a ' / j weighing. (18) G . Iferzherg, "The Spectra of Diatomic 3folecules," 2nd Ed., I ~
+
+
+
: 1 1 ) Summary uf Conference o n Kecent Research o n t h e Hydrogen Bond in the Soviet Ir.:ion, O N K L Report 106-52 (1952). ( 1 2 ) 31. 11.Jones, v"? P. Gilkerson and G. A. Gallop, J . Chein. P h y i . , (1.3) S. H . B x u e r . i i n ~ u h l i s h e dd a t a . (14) R.C . I,ord, 11, A . Lynch. J r . . \Y, aki, Trris J O T T R S - \ I . , 72, ,522 ( I 0 , j O ) .
C .Schurnb a n d 1;. J . Slowin-
D. Van Nostrand Co., Kew York, N. Y , 1030. (19) (a) I,0 ! a x ~ l . ~ ~ ~ I:poii coiiibiriin~this with tlic. hi;lwr \.due for the litrat oi f the central L' t 0111. The large internuclear distance m c l low dissociation energy iii fliiorinc. has been csplained'6 in ternis of 11011-
hnntling electron iriteractioi;. Appendix Outline of the Normal Coordinate Treatment for the Mutual Vibrations of the Monomer Units, a s Present in the Dimer The foriii oE ~ l i cpotciiri,il fuiictioii p o t u 1;tted for the iii~eriictioiiIxt\veeil the osyge11 :rtoms, (I-I%""O, w i s V(r) = Q ( I < , ' t ) ' i ?(I( / t / r ) z , whereill (I \vas assigticd 11:iIf tile iusgnitude of the ALP of dissociatioii of the correspoiidiiig tliiiicr, xiid li is the ccluilil>ration, Froni this it follo\rs t h a t the force constant for stretching i\ k,, = 1 S @ / K 2 . The force cotist:tt!tb for thc bending motions a t the oxygen ntoills
e&2)
Iyrl)
Fig. 2.-Definition
( b ) Out-of-plane parameters. of the structural pdrdmeters for (:I) the .ind ( b ) the out-of-plane triotioils
i r
