Jan. 5, 10.54
DONOR-ACCEPTOR REACTIONS [CONTRIBUTION FROM THE
DEPARTMENT O F CHEMISTRY,
265
CORSELL UNIVERSITY]
Computation of Entropy Increments in Gaseous Bimolecular Associations. I. DonorAcceptor Reactions BY ALLANSHEPP ilND RECEIVED JUNE
s. H. BAUER
8, 1953
Iri this paper, it is first demonstrated that good values for the over-all entropy increments in gaseous bimolecular addition reactions, of the type A B = AB, can be computed from our knowledge of, or from judicious estimates of, the structural and spectroscopic parameters of each species involved. These values were combined with available AHO's, t o deduce equilibrium constants. This was done for several systems for which direct equilibrium studies do not appear feasible. It is also shown that the vibrational entropy increment in addition compound formation, which may be computed by subtracting 4.Sot,+,, from the available 4.SOtotal,has particular significance in that it gives a measure of the tightness of the new A-B bond. A plot of 4.9, against the reduced mass a t the A and B groups is proposed as a quantitative measure of this bond tightness.
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In this paper we wish to report on the calculations we have made for the entropy changes which accompany homogeneous gas phase reactions between Lewis type acids and bases; in particular, reactions of acids in which the acceptor atom is boron. Calculations were first carried out for a system for which experimental data were available. The resulting agreement between experimental and calculated A 9 values, served to check the structural and spectroscopic parameters assigned to the species involved, and to give an indication of the accuracy to be expected for calculations done on other reactions. The calculations of As0 values were then carried through for several reactions for which the enthalpy increments only were available, so that the equilibrium constants could be estimated. As yet, these constants cannot otherwise be determined. Thermodynamic data are available for the decompositions of borine carbonyl (OC :BH,) and deuterated borine carbonyl (OC :BD3), as reported by Burg.' Our values of ASo were obtained by Experimental
= = 9.142 kcal./mole + 2c0 { 4Ho AS0 = 32.51 0.5 e.u. = 4Ho = 8.465 kcal./mole + 2c0 { 4S0 = 32.47 =t0.5 e.u.
(1) 20C:BH3 BZH6 (2) 20C:BD3 BZD6
=IC
Computed
32.11 +0.5 31.64
&O.T computing the entropy of each species in the usual manner, from structural and spectroscopic parameters, as indicated below. The translational plus rotational entropies of B2H6 and BsDc were computed from the structural parameters given by Hedberg and Schomaker.2 The vibrational assignment for diborane used was that given by Anderson and Barker.3 For the frequencies of B2D6, the eight infrared bands reported by Webb, Neu and Pitzer4 were considered along with those of diborane, and by using the Teller-Redlich product rule, all the fundamental frequencies were estimated. The resultant entropies for the ideal gases are
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B2H6: S0300(l atm.) = ( 5 3 . 2 6 ) ~ , + ~ . (2.34)" = 55.60 e.u. B z D ~ :S o 3 w ( 1 atm.) = (55.22)tr.+r. (4.39)" = 59.61 e x .
This value for diborane is in agreement with that
e)
A. B. Burg, THISJOURNAL, 74, 3482 (1952). (2) R. Hedberg a n d V. Schomaker, ibid., '79, 1482 (1961). (3) W. E. Anderson and E. F. Barker, J. Chem. Phys., 18, 898 (1950). (4) A. N. Webb, J, T. Neu and IC. S P i t x e t . J , P h y v . C k r m . . 1'7, lOOP (1949In
reported by Webb, et aI. (55.74 e.u.), based on their own frequency assignments, and earlier structural work. The translational plus rotational entropies of OC : BH3 and of OC : BD3 were computed from the structural parameters given by Gordy, Ring and Burgs5 The fundamental frequencies of OC : BH3 were reported by Cowan,6while those for OC : BD3 were computed from Cowan's secular equation for the W3X-Y-Z molecule. To correct for non-ideality, critical constants were estimated from the vapor pressure curve,' and were used in the Berthelot equation in the usual manner. The resulting entropies are OC:BH:$:So,300(latm.) = (55.62)tr.+,. 4-(3.52)" (0.043),.i. = 59.10 e.u. OC:BD3: S o d ~atm.) ~ ( l = (56.94)tr.+,. (4.44)" (O.O43),,i. = 61.34 e.u.
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The entropy of CO as determined by Johnston and Davis8 is 47.357 e.u. a t 300°K. and one atmosphere. Using the above entropies, our values given in equations 1 and 2 are readily deduced; the assigned limits of error result from an analysis of the uncertainties in the calculations. These check the experimental values rather well. The key reaction to further calculations is the equilibrium between diborane and borine (BH3), for which we have reported thermodynamic constants in a previous letter9 (3)
2BH1 = B2H6
4H0271 =
-28 kcal.!mole
ASoJoo = -34.22 e.u.
The entropy increment is 0.4 unit numerically larger than the published value, resulting from slight revisions in the calculation ; the enthalpy increment is 4 kcal. smaller, based on a reanalysis of kinetic data. The absolute entropy of borine was estimated as follows. A planar structure, with H-B-H angles of 120" (sp2 type bonding) was assumed. The B-H distance is very likely of order 1.16 to 1.18 A., and it is known that the B-H stretching force constants in B3N3H6 and in 0C:BHB are 3.42 X lo5 and 3.21 x lo5 dynes/cm., respectively.6-10 Consistent with these ( 5 ) W. Gordy, H. Ring a n d A. B. Burg, Phys. REV.,78, 1482 ( 6 ) R. D. Cowan, J . Chsm. Phys., 18, 1101 (1950). (7) A. B. Burg a n d H. I. Schlesinger, THIS JOURNAL, 69, 780 18) H. L. Johnston a n d C. 0.Davis, i b i d . , 66, 271 (1934). (9) S. H. Bauer, A. Shepp and R. E. McCoy, ibid., 7 6 , 1003 (10) B.T.. C r a w f w d a d J. T. Gdsall, J . Chem. Phys., 7 , 1 2 3
(1951). (1937). (1953). f1938),
ALLANSHEPPAND S. H. BAUER
?GO
Yol. 7G
values, one rnay apply Badgers rule," which relates bond Gistance to stretching force constant to deduce 1.16 A. and 3.38 X lo5 dynes/cm. for the B-H distance and stretching force constant, respectively. To compute all vibrations of borine two more force constants are needed; k d for in-plane bending, and k n for nut-of-plane l>ending. Thcsc force constants are available" for RCl,, and RBr3, and by comparing ratios of k , ' h and k 'k11 for the three halides we were able to estimate the values of k,1 a n d k~ i n RH; to be 0.13 x I O 6 and 0.30 X IO5 dynes, cin., respectively. These lead to the fundamental frequencies: 2384 cm.-l (a), 802 em.-' (a), 29iG em.-' (e) and 176.7 cm.-' (e). I t is to be emphasized that these structural and spectroscopic parameters are estimates only. Severtheless, the ideal gas entropy, depending only slightly on the magnitude of the frequencies, and on the logarithm of the products of the moments of inertia, should be accurate to half an entropy unit or better. Hence the entropy for the ideal gas is HH?:S";o~(l atm.) = ( 4 l . i i H i r..+I. + (0.22),, = 11.91 e.u. This value, combined with that for leads to the ASo given in equation 3. The Reaction of Borine with Carbon Monoxide.One may combine equations 1 and 3, and their respective A T P l-alues (1) RH,: 4-CO = OC:RH, l l I G = -18.6 kc:i1. 'mole The A S u for this reaction follows from the above listed absolute entropies. The equilibrium constant (which cannot be determined by experiment) rnay then be estimated.
ing Cowans6 values for OC:BH3and our estimates for OC:BD8. The -BF3 rocking frequency was taken to be 365 cm.-', which is the assigned value for the rocking of the -CF3 group in F3CCH3.1i These estimates lead to 72 h 1 e.u. for gaseous OC:RF3, a t 300°K. and one atmosphere (ideal state), and to the value ASn300 = -36 e.u., for 5. The fact that OC : BF3 has not been prepared in the laboratory indicates either that equilibrium had not been attained in these experiments, or that the equilibrium constant for reaction 5 must be such that undetectably small amounts of the addition compound exist a t equilibrium. If we assume the maximum value for the equilibrium constant to be of order lo-? atm.-', the maximum value (in the negative sense) of AIIO is of order -8 to -10 kcal./mole. \\Then this enthalpy increment is compared to that of 4 and of 1, i t appears that RFa is a weaker acid than BHs by about 10 to 12 kcal./mole, while i t is stronger than B2H6by about 3.5 to 3.5 kcal./mole, with respect to CO as the reference base. [n'ith trimethylamine as a reference base, BF3 appears to be weaker than BH3 by 1 to 2 kcal.l3 Hence we believe that it was lack of activation of the CO rather than the weakness of BF3 which led to no addition compound,] Reactions of Boron Acids with Trimethylamine. -The entropy of gaseous trimethylamine (Me3N) may he computed at any temperature from the data given by Aston, et nl.,19 and the tables by Pitzer") for the entropy contribution due to restricted rotation. A4t300°K. and one atmosphere, i t is 09.41 e.u. To compute the entropy of the addition compound Ne3N:BH3 first note that it is A S " = -33.17 e.u., and isoelectronic withneopentane ( hle3CCH3)and, there4065iT log (Ke'Jztm = - 7.25 fore, to a good approximation, the vibrational plusrehh = 2.0 X lo6 stricted rotational entropies of the two molecules are The Hypothetical Reaction of Boron Trifluoride the same. .kcording to Pitzer,*' the value of .T,~,, with Carbon Monoxide.-Efforts to prepare the for neopentane, and hence for Me3r\::BH3,is 13.1.5 addition compound OC : BF3 according to the reac- e.u., at 300°K. To compute the translational plus rotational entropy, we used the interatomic distion tances determined for Me3N: BH3 by electron difiS) BF,(g) C O ( g ) = OC:BF:i(g) fraction,22but for the angles, we used the more achave not been successful. One may nevertheless curate values determined in the solid for tllc moleestimate the anticipated entropy change. The cule Me3N:RF3,23,24 which has been shown to he entropy of BF3 has been determined by SpencerI3 isomorphous with hIeaN: BHa. The resultant a t 300°K. and one atmosphere; i t is 60.77 e.u. In translational plus rotational entropy a t 300°K. and the structure of OC : BFs, we assigned the B;F dis- one atmosphere is 62.27 e.u., and the total entropy tance and F-B-C angles the values 1.38 A. and (ideal gas) is estimated to be 76.42 e.u. Thus we lo?", respectively, corresponding to the ones ob- arrive a t the estimates served in crystalline H3N:BF3.I4 The B-C and (7) M e n s + BH, = hIesS:BH3(g) C-0 distances were taken to be the same as in ASO,,, = -37.80 e.u. OC:BH3. For the vibrational spectrum, the six M e 3 S f lluR?Ha = RlesX:RHl(g) ( 8 ) BF3frequencies were taken to be the same as found ASolno = -20.69 e . u . in the compound hie2O: BFa, for which preliminary raman'j and infraredI6 spectra have been recorded, For the addition compound Me3N:BF3,we felt i.e., 804(a), .?30(a), 1216(e), 396(e), in cni.-'. that we could deduce an approximate value for the The B-C, C-0, and B-C-0 frequencies were J. R. h-ielsen. H. H. Claa-en and TI. C . Smith, J . r h e i n . P h y s . . taken to be 500, 1500 and 280 ern.-' by extra.po1at- 18,(17) 1471 (1950).
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J. Chrm. Phys., 2, 128 (1934). (12) G. Herzberg, "Infrared and R a m a n Spectra," D. Van Xostrand Co., Inc., A-ew York, N. Y., 1945, p. 178. (13) H. 11.Spencer, J . Chem. Phys., 14, 729 (1946). (14) J, L. Hoard, S. Geller and W. AT. Cashin, Actn Cryst., 4, 396 (1951). (15) F. V. Bunderman a n d S. H. Bauer, J . Ph>'s. Chrm.. SO. 32 (1946). (IO) S. H. Bauer. unpublished work. (11) R. hl. Badger,
(18) R. E. McCoy, Doctor's Thesis, Department of Chemistry, Cornel1 University, 1952. (19) J. G. Aston, hi. Sagenkahn, G. Szasz, G. >loessen and H. Zuhr, THISJOURNAL, 66, 1171 (1941). (20) K. S. Pitzer, J. Chem. Phys., 6, 469 (1987). (21) K. S. Pitzer, ibid., 6 , 473 (1937). (22) S. H. Bauer, THISJOURNAL, 64, 1804 (1937). (23) S. Geller a n d J. L. Hoard, A c f a C r y s f . ,4, 399 (1951). (24) S. Geller, R. 6. Hughes a n d J. L. Hoerd. i b i d . , 4. 380 (1951).
Jan. 5 , 1954
267
DONOR-ACCEPTOR REACTIONS
vibrational plus restricted rotational entropy by correcting Me3N:BH3 for the replacement of a BH3 group by a BF3 group. To do this, we noted that in the cases of OC : BH3and OC :BF3, a detailed comparison of the spectra showed that such a replacement caused a change of 4.5 e.u. We assumed that the same increment may be assigned in comparing N e 3 N:BF3 with Me& : BH3. Also, we assumed that the change from BH3 to BF3 would reduce the restricted rotational entropy by one unit, Using the structural parameters available for Me3N:HF3,23we determined the translational plus rotational entropy a t 300" and one atmosphere to be 6 W 7 e.u. .is a result, we estimate the total entropy of the ideal gas to be 84.0 e.u., and
From this, we may estimate the minimum value for A s 0 of the reaction (10) Me.O(g)
+ BFJ(g) = Me,O:BFa(g)
( ASoa~,),,,i, = -36.7 e.u.
where the subscript implies a minimum absolute quantity. This is in contrast to the experimental value which has been reportedz7to be -32.2 e.u. Two other entropy changes were quoted in the same paper, and are likewise too small (11)
(12)
+ BF:j(g) CjHaO(g) + BFa(g)
EtpO(g)
Et?O:BF:i(g) A S 0 = -27.5 e.u.
THF:BFs(g) AS0 = -27.1 e.u.
(THF
=
tetrahydrofuranc)
JIe.jS(g) f BF,(gJ = Me:3S:BF3!g)
Qualitatively, one may compare these ASu values with those for other reactions of two to one stoiThe AIIO values for reactions 8 and 9, and by us- chiometry appearing in Table I. SVhen this is irig ,'$, that for 'i also, have been measured in this done, it becomes apparent that the values for these ~ actual meas- three reactions are appreciably smaller than what Laboratory by I
