The Journal of Physical Chemistry, Vol. 83, No. 3, 1979 419
Partial Molal Volumes of Organic Cornpounds in CCI, (14) (a) W. W'est and R. T. Edwards, J Chem. fhys., 5, 14 (1937);(b) E. Bauer and M. Magat, J . fhys. Radium, 9, 319 (1938). (15) (a)A. D. Buckingham, Can. J . Chem., 38, 300 (1960);(b) A. D. Buckingham, T. Schaeffer, and W. G. Schneider, J . Chem. Phys.,
32, 1227 (1960).
e($),the possibility of "solvent sorting" casts doubts on the meaning of such correlations. (27) This is the original procedure used by Kirkwood to develop eq 1. (28)The expressions of the dipolar contributions to the volume and entropy are given by of
(16) Y. Ooshiita, J . fhys. Soc. Jpn., 9, 594 (1954). (17) VI. Liptap in "Modern Quantum Chemistry", Part 11, 0. Sinanoglu, Ed., Academic Press, New York, 1965,Chapter V. This work also contains references to previous theories.
(18) J. G. Kirkwood, J . Chem. fhys., 2, 351 (1934). (19) This is the original procedure used by Kirkwood to develop eq 1. (20) (a) For a recent survey of solvent effects on spectroscopic properties, see, e.g., M. Jauquet and P. Laszlo in "Solutions and Solubilities", Part I, Wiley, New York, 1974 Chapter IV. (b) Concerning the use and limitations of dielectric function to correlate infrared shifts, see, e.g., W. E). Horrocks, Jr., and R. M. Mann, Spectrochim. Acta, 19, 1375 (1963); S.Tanaka, K. Tanabe, and H. Kamada, Spectrochim. Acta, Part A, 23, 209 (1967);A. D. Buckingham, R o c . R . SOC. London, Ser. A , 248, 189 (1958);ibid., 255,32 (1960);M. L. Josien and N. Fuson, J. Chem. fhys., 22, 1169, 1264 (1954);J . Chim. fhys., 51!, 162 (1955). (21) (a) E. Fontaine, M. T. Chenon, and N. Lumbroso-Bader, J . Chim. fhys., 62, 1075 (1965);(b) P. Laszlo and J. I.Musher, J . Chem. fhys., 41, 3906 (1964),and references cited therein. (22) See,e.g., (a) A. M. Benson, Jr., and H. C. Drickamer, J. Chem. Phys., 27, 1164 (1957);R. R. Wiederkehr and M. G. Drickamer, ibid., 28, 3'11 (1958);(b) R. L. Schmidt, R. S. Butler, and J. H. Goldstein, J . Phys. Chem., 73, 1117 (1969),and references cited therein. (23)(a) R. J. Abraham and R. Bretschheider in "Internal Rotation in Molecules", W. J. Orville-Thomas, Ed., Academic Press, London, 1974, Chapter 13; (b) M. H. Abraham and R. J. Abraham, J. Chem. Soc., ferkin Trans, 2, 47 (1974);(c) ibid., 1677 (1975). (24) H. Frohliclh, Discuss. Faraday Sac., 42A, 3 (1946). (25) H. Block and S. M. Walker, Chem. fhys. Lett., 19, 363 (1973). (26) These studies were carried out in mixed solvents and even though heir experimental results are rather well represented by linear functions
and
where
(29) (a) M. H. Abraham in "Progress in Physical Organic Chemistry", A. Streitwieser, Jr., and R. W. Taft, Ed., Wiley, New York, 1974,p 31; (b) M. H. Abraham, J. Chem. Soc., ferkin Trans. 2, 1343 (1972); (c) ref 23b.
(30) Although most of the information available on this system comes
from ref 7c, WE! nave used the values gwen by Abraham and Abraham (ref 23c) (31)(a) E. Lippert, A?. Nektrochem., 61, 967 (1957);(b) C. J. F. Bottcher, "Theory Dielectric Polarization", Elsevier, Amsterdam, 1952, pp
135-138. (32) M. H. Abrahani and P. L. Grebbier, J . Chem. SOC.,ferkin 7rans. 2,1737 (19763,and referenced cited therein. (33) R. L. Fulton, J. Chem. fhys., 61,4141 (1974). (34)We are indebted to a referee for suggesting the use of this theory.
Partial Molal Volumes of Organic Compounds in Carbon Tetrachloride. 2. Haloalkanes' Fereidoon Shahidi, Patrick G. Farrell, and John T. Edward* Department of Chemistry, McGill University, Montreal, Quebec, Canada H3A 2K6 (F7eceived July 14, 1978) Publication costs assisted by the Natural Sciences and Engineering Research Council of Canada
The average number of gauche arrangements (2J involving 1:4 halogen/halogen, halogen/carbon, and carbon/carbon interactions in 43 mono- and dihaloalkanes have been calculated. The partial molal volumes of 40 of these compounds could be calculated with reasonable accuracy by addition of increments (chlorine, 17.02; bromine, 19.53; iodine, 25.45 mL mol-l; and reported values for methyl, methylene, methine, and quaternary carbon) to a covolume of 11.61 mLdmol-', and subtraction of decrements (Cl/Cl, 0.25; Cl/C, 0.92; Br/C, 1.53; X/C, 2.53 mL molu1)for each unit of 2,. The additive scheme did not work for vicinal dibromo compounds. The results show the halogens to have smaller increments, and to give rise to smaller decrements when involved in gauche interactions, than would be expected on the basis of their presently accepted van der Waals volurnes.
Introd uctiorx We have shown2 that the partial molal volumes Y" of straight- and branched-chain alkanes in carbon tetrachloride a t 25 " C are given with good accuracy by the equation
Po
=
v, + ?nkP + k1 z p 1
(1)
where V, is a constant covolume of 11.61 mE mol-', nk is the number of groups (methyl, methylene, methine, or quaternary carbon) of type k and Ik is the volume increment of such a group, and 2,' is the average number of gauche interactions of type 1found in the molecule and 6' the volume change associated with such an interaction. In alkanes I:he only types of gauche interactions encountered are those be tween methyl or methylene with 0022-3654/79/2083-Q419$Ql .OO/O
other methyl or rnethylene groups; these we designate as C / C . The change in volume g C j C associated with this gauche interaction was found to be -2.5 mL mol-l, about the value expected from the difference in volume between a cyclohexane isomer having a methyl group axial (Z,C/C = 2) and that having it equatorial (Z c/c = O).2 In the present paper we test the appkicability of eq il to the 43 haloalkanes of Table 11. To do this we must first calculate not only Z:iC but, where necessary, Z,x/x (e.g., in 1,2-dichloroethane)and Z9x'C (e.g., in 1-chloropropane), and then estimate the reductions in Poto be expected from such gauche interactions.
Calculation of Average Number of Gauche Interactions 2, The calculation of ZgCiC of alkanes by Pitzer's steric partition function, assuming AH = 700 cal mol-l for the 0 1979 American Chemical Society
420
The Journal of Physical Chemistry, Vol. 83, No. 3, 1979
TABLE I: -
F. Shahidi, P. G.
Farrell, and J. T. Edward
Calculation of Average Number of Gauche Arrangements 2, in Various Haloalkanes at 25 "C Z p X
haloalkane 1-chloropropane 1-chlorobutane 2-chlorobutane 2-meth yl-l-chloropropane 1,2-dichloroethane 1,2-dichloropropane 1,2-dichloropropane 1-bromopropane 1-bromobutane
calcd
0.21' 0.29a,g 0.29a,g
Z,XlC
exptl
0.21h 0.22' 0.34j
2,ClC
calcd
exptl
calcd
exptl
0.71a 0.68a,C 0. 84a9 1.39'
0.71b 0.78d 0.75d 1.2f
0.31e 0.36e
0.52d 0.52d
0.87a,g 0.87a,g 0.57' 0.52e,k
0.95' 0.77j 0.57b 0.401
0. 3lelk
0.40'
' Assuming AH^'^^ = 130 cal mol-'
in favor of the two gauche conformations over the anti conformation, K. Yanabe and 8. Sagki, J. Mol. Struct., 27, 79 (1975). C Assuming AHc'lc = 1500 cal mol-' when 6' Cl/C followed by g + C/C: cf. J. StGkr, S. Dirlikov, B. Obereigner, and B. Schneider, J. Mol. Struct., 8, 449 (1971). d T. Ukaji and R. A. Bonham, J. Am. Chem. SOC.,84, 3631 (1962). e Assuming AHclc = 700 cal mol'' in favor of anti. G . H.Pauli, F. A. Momany, and R. A. Bonham, J. Am. Chem. Soc., 8 6 , 1286 (1964). Assuming ~ H c l / c l = 890 cal mol'' in favor of anti: cf. footnote h. R. J. Abraham and E. Bretschneider, "Internal Rotation in Molecules", W.J. Orville-Thomas, Ed., Wiley, London, 1974, p 515. H. B. Dempster,J. Mol. Struct., 23, 193 (1974); J. Thorbjghmsrud, 0. H. Ellestad, P. Klaboe, and T. Torgrimsen, ibid., 15, 45 (1973). At 38 "C: Y. Shahab and M. S. Saeed, ibid., 40, 221 (1977). Assuming AHBrlC = 240 cal mol-' in favor of anti. F. A. Momany, R. A. Bonham, and W. FI. McCoy, J. A m . Chem. SOC.,85, 3077 (1963). TABLE 11: Partial Molal Volumes (To,in mL mol-') of Haloalkanes in Carbon Tetrachloride at 25 "C
1-chloropropane 2-chloropropane 1-chlorobutane 2-chlorobutane 2-methyl-1-chloropropane 2-me th yl-2-chloropropane 1-chloropentane 1,2-dichloroethane 1,2-dichloropropane 1,3-dichloropropane 1,3-dichlorobutane 1,4-dichlorotutane 2,3-dichlorobutane ( d l ) 2,3-dichlorobutane ( m e s o ) 1,3-dichloro-2,2-dimethylpropane 1,5-dichloropentane 1-bromopropane 2-bromopropane 1-bromobutane 2-bromobutane 2-meth yl- 1-bromopropane 2-methyl-2-bromopropane 1-bromopentane 1-bromohexane 1-bromoheptane 1-bromooctane 1-bromononane 1,2-dibromoethane 1,2-dibromopropane 1,3-dibromopropane 1,2-dibromo-2-methylpropane 1,3-dibromobu tane 1,4-dibromobutane 1,5-dibromopentane 1,6-dibromohexane 1,7-dibromoheptane 1,8-dibromooctane 1,9-dibromononane 1,lO-dibromodecane 1,12-dibrornododecane iodoe thane 1-iodopropane 2-iodopropane 1-iodobutane a
0.71
0.21 0.29
0.46 0.10
0.18 0.21 0.21
0.68 0.84 1.39
0.31 0.36
1.17
0.71
0.87 0.89 1.39 1.35 1.85 1.90 4.00 1.35 0.57
0.37 0.24 0.61 0.10 0.57
0.52 0.80 1.25
0.31 0.34
0.53 0.53 0.53 0.53 0.53
0.61 0.90 1.20 1.50 1.80
0.87 0.97 1.79 1.07 1.06 1.05 1.05 1.05 1.05
89.54 9 2.68 106.16 108.36 108.75 112.58 122.05 80.32 99.33 96.90 115.55 113.23 116.68 118.00 133.75 129.76 91.84 95.19 108.44 110.32 110.64 115.09 125.05 141.67 158.28 174.89 191.51 101.27
0.39 0.24 0.55 0.85 1.16 1.46
119.98 117.89 134.49 151.11 167.69 184.30
1.05
1.76
200.91
1.05 1.05
2.06 2.67
217.52 250.72 81.27 97.63 101.11 114.30
0.43 0.38
0.32
91.24 + 91.76 i 107.29 5 108.21 i 108.30 f 110.99 i 123.37 5 81.44 5 99.16 f 96.80 i 115.67 ? 113.07 i 116.04 i
0.42 0.40 0.40 0.38 0.40 0.30 0.24 0.20 0.41 0.50 0.32 0.23 0.25a
133.84 ? 129.60 f 91.80 i 94.35 f 108.28 i 110.27 f 110.67 f 112.73 i 124.32 i 141.12 i 157.56 f 173.98 i 190.69 i 87.10 'r 104.91 f 102.43 i: 122.80 ? 120.20 ?r 117.71 f 134.60 f 150.70 i 167.11 i 183.83 f
0.49 0.30 0.40 0.40 0.12 0.40 0.48 0.43 0.25 0.50 0.45 0.56 0.50 0.20 0.30 0.31 0.35 0.30 0.30 0.30 0.30 0.30 0.25 200.71 f. 0.43 217.72 2 0.70 252.64 f 0.90 81.20 i 0.32 97.78 i 0.21 101.20 i. 0.30 114.13 + 0.40
Aldrich compound: a mixture of d l and meso in undetermined proportions.
anti (a) .+ gauche (g) transf~rmation,~ has been described in detail by Essentially the same method was used for calculation of the ZgXicvalues shown in Table I; the calculation for 1-bromobutane is illustrated in the Ap-
pendix. The individual AH values on which the calculations were based are indicated in footnotes to Table I. Values of AH from different sources diverge considerably (cf. ref 6); we have chosen values which seem to be most
The Journal of Physical Chemistry, Vol. 83,No. 3, 1979 421
Partial Molal Volumes of Organic Compounds in CCI4
TABLE 111: Constituent (I)and-Structural ( 6 ) Contributions (in mL mol-') to V" in CCl, a t 25 "C
Vw
I
11.62' 14.40' 19.18' 13.67
17.02 19.53 25.45 26.85'
group C1
Br I CH,
I t v,
calculations for 1-bromoalkanes CnH2n+lBrfor n showed Z C i: to be given by
gauche interaction
6
Cl/Cl
-0.25
Cl/C Br/C I/C
-0.92 -1.53 -2.33 -2.50
1.46,'1.3gb 1.36,a1.34b 1.33,'1.2Sb 1.96
c/c
Z,CiC= 0.3(n - 3)
a Based on V, of halogen attached in primary position: A. Bondi, J. Phys. Chem., 68,4 4 1 ( 1 9 6 4 ) . b Based on V, of halogen attached in secondary or tertiary position. From ref 2.
'
reliable. Few of these values pertain to solutions in carbon tetrachloride, but the results of Eliel and Martin7 indicate that solvent effects on the conformational equilibria of monohaloalkanes will be slight. On the other hand, when two or more halogen atoms are present in a compound, it seems likely that the energy of interaction of the carbon-halogen dipoles will depend on solvent.8 Consequently, the AH adopted in footnote f of Table 1 is that for the anti -* gauche transformation of 1,2-dichloroethane in ethylene this solvent has a dielectric constant close to that of carbon tetrachloride, and should show similar solvent properties.8 It is apparent that agreement between calculated and observed values of 2, in Table I is only fair, possibly because the assumption that the enthalpy differences between various conformations can be obtained by adding up the separate AH contributions for each individual gauche or anti arrangement found in a given conformation holds less well for the polar haloalkanes than it does for the nonpolar (alkanes. However, many of the experimental data are not very reliable. Consequently, we have calculated our V o values using 2, values calculated for the AH data footnoted in Table I. These Z, values are given in Table 11. ]Errors in 2, introduced by such a procedure are likely at loast to be consistent, and to some extent to be compensated by errors of opposite magnitude in 6. In calculations for 1,3-dihalo compounds, it was assumed that arrangements having parallel carbon-halogen bonds could be excluded;Yalso excluded were arrangements having parallel C-C (and C-Br bonds (cf. ref 5). The number of possible conformations increases rapidly with chain length, being 99 for 1-bromoheptane or 01,wdibromohexane, and calculation of 2, by Mann's procedure becomes tedious for long chain compounds. Fortunately,
o c
with Z,B'/Cremaining constant at 0.53 for n 2 5. Similar calculations for a,w-dibromoalkanes Br(CH2),Br for n = 4-6 showed ZgC/' = 0.3(n - 4) 0.24 (3)
+
with ZgB'jCremaining constant a t 1.05 for n I 5. The Z values in Table I1 for 1-bromoalkanes having n > 7 and for a,o-dibromoalkanes having n > 6 were obtained using these two equations.
Results and Discussion The volume increments I for chlorine, bromine, and iodine, and the volume decrements 6C1/C1, @IC, aBrIC,and listed in Table I11 were obtained by a least-squares fitting of eq 1 to the experimental Povalues of Table 11, using ZgcIC, ZgXjC, and ZgXixvalues calculated as above, and the volume increments for V, and for methyl, methylene, methine, and quaternary carbon already es' values calculated using these various tablished.2 The P parameters are listed in Table I1 alongside the experimental values. It is evident that the additive scheme of eq 1works fairly well with most of the haloalkanes of Table 11. In particular, it accounts for the different partial molal volumes of isomeric compounds, such as 1-and 2-chloropropane and the four isomeric bromobutanes. However, application of eq 1 to the experimental data for the three uic-dibromoalkanes of Table I1 requires BB'/B' to be positive, and to vary considerably for each compound. We cannot explain these results. The decrease in volume P i C accompanying a gauche chlorine/carbon interaction recorded in Table I11 is in good agreement with the values calculated by Christian et al.1° to account for the effect of pressure on the equilibrium between equatorial and axial chlorocyclohexane (-0.93 mL mol-l) and diequatorial and diaxial trans-1,4-dichlorocyclohexane (-0.7 mL mol-l) in carbon disulfide at 50 "C. However, 6B''C of Table I11 is in poor agreement with the value (-0.95 mL mol-') calculated from the effect of pressure on the equilibrium between diequatorial and diaxial trans-1,4-dibromocyclohexanein CS2.I0 In even worse agreement is 6C1/c1from Table I11 with the reduction in volume (1.8 f 0.4 mL mol-l) accompanying the shift from the C1 (Zgc'/c'= 1) to the Cs (Zgc'/C1 = 2) conformation of 1,1,2-trichloroethane in CS2 under pressure;ll
6
0
2.45
0.299
0
0
0
0
240
3.25
0.396
1
0.396
0
0
700
1.5
0.183
0
0
1
0.183
940
1
0.122
1
0.122
1
0.122
-,1ZgBrIC=- 00.518
1
5
4
7
,2500
-0 8.2
a
9'
4-7 (2)
TABLE IV
B-,
=I
-0 1.000
-0 2, C'C 5-
422
The Journal of Physical Chemistry, Vol. 83, No. 3, 7979
it seems likely that for trichloro compounds solvent effects become more importantqS Qualitatively, the most striking fact to emerge from the results in Table 111is that halogen atoms behave as if their volumes were smaller than indicated by their van der Waals volumes V,,12 The partial molal volume 8" of a solute is made up of V , plus the void or "empty" volume Ve,I9which depends on the closeness of packing of the solvent molecules about N (Avogadro number) solute molecules. Bromine has about the same V , as methyl (Table 111) and, if the packing of carbon tetrachloride solvent molecules about it were similar, would be expected to have about the same volume increment I. In fact, I (and I / Vw)for bromine is considerably smaller. Similar considerations apply to the other halogen atoms,14as shown by their I / V, ratios (Table 111). Furthermore, the volume decrease (aBrIC)resulting from the gauche compression of a bromine with a methyl is less than that (clCIc)resulting from the gauche compression of two methyl groups. The ent,halpy increase AHBrlc resulting from the gauche interaction of bromine with methyl is also less than the increase resulting from the interaction of two methyls, but in this case part of the difference probably comes from the polar character of bromine. For the smaller chlorine atom the polar effect, becomes dominant, the gauche conformation of 1-chloropropane becoming more stable than the anti.15J6 The problem of the failure of van der Waals radii rv, to indicate the effects of atoms or groups on conformational equilibria is an old one.1s The van der Waals radii of halogens are usually derived from crystallographic data for perhalogenated compounds,12which necessarily have their molecules packed into the crystal with carbon-halogen dipoles opposed to each other. These dipolar repulsive forces may have the effect of slightly increasing nonbonded halogen-halogen internuclear distances along the line of the C-halogen dipole. It is possible that carbon tetrachloride solvent molecules can approach the halogen nucleus more closely in the direction normal to the Chalogen bond than in the direction in line with this bond, and that a van der Waals radius defined in terms of the latter approach only is too large. Similar considerations would explain the smaller 6 and AH values when methyl is replaced by bromine. The trend in I / V,,,values in Table I11 suggests that other factors in addition (e.g., polarizability) may affect the closeness of approach of solvent carbon tetrachloride molecules to halogen atoms attached to a carbon skeleton.
Experimental Section The haloalkanes were all commercial products; purification of them and of solvent carbon tetrachloride was carried out as described previously.2 Partial molal volumes were obtained as before from the densities of solutions
F. Shahidi, P. G. Farrell, and J. 1.Edward
measured with a Paar digital precision density meter.2
Appendix. Calculation of Z , for 1-Bromobutane If we consider only anti and gauche arrangements, 1kroxnohutane can exist in the nine conformations shown in Table IV (see ref 5 for symbolism). The enthalpy differences AH are obtained by adding together the separate AH values, footnoted in Table I, for each separate gauche interaction, with the exception of g*g' arrangements, as in 8 and 9. For these arrangements steric interference will be severe, and enthalpies sufficiently high for 819 to be neglected.5 We start with the next least stable conformation 617, and arbitrarily set the quantity R in 1 mol of the equilibrium mixture at 1. The conformation 415 will be more stable by AH = 240 cal mol-', which at 25 "C corresponds to a quantity R = 1.5;17bthe conformation 213 by 700 cal mol-', which corresponds t,o R = 3.25; and the conformation 1 by 940 cal mol-l, which corresponds to h?= 2.45 (when the differing multiplicities of 1 and of 617 are taken into account), Since CR = 8.2, the mole fractions y = R/8.2 of the various conformations are computed. Each conformation has zg gauche arrangements, and the average number 2, in 1 mol is given by 2, = Cyz,. References and Notes (1) Work supported by the National Research Council of Canada. (2) J T. Edward, P. G. Farreli, and F. Shahidi, J. Phys. Chem., 82, 2310 (1978). (3) As an exception to this ruie, it was assumed AH N 0 for the two possibie conformations of vic-1,Z-dimethyl compounds (cf. ref 4). (4) N. L. Allinger, J. A. Wirsch, M. A. Miller, I. J. Tyminski, and F. A. Van-Catledge, J. Am. C h m . Soc., 90, 1199 (1968);R. H. Boyd, ibid., 97, 5353 (1975). (5) G.Mann, Tetrahedron,23, 3375 (1967);G. Mann, M. Muhlstadt, J. Braband, and E. Doring, bid., 23, 3393 (1967). (6) K. Tanabe and S. Saeki, J . Mol. Struct., 27, 79 (1975). (7) E. L Eliel and R J. L. Martin, J . Am. Chem. Soc., 90, 689 (1968) (8) R. J. Abraham and E. Bretschneider, "Internal Rotation in Molecules", W. J. Orville-Thomas, Ed., Wiiey, London, 1974,p 481. (9) J. Stckr, S.Dirlikov, B. Oberelgner, and 9. Schneider, d Mol. Struct., 8,449 (1970). (IO) S: D. Christian, J. Grundnes, and P. Klaboe, J. Am. Chem. Soc., 97. -.. 3864 - - - (19751. (11) S.D. Christian and J. Grundnes, J . Chem. Phys., 65,498 (1976). (12) A. Bondi, J . Pbys. Chem., 68, 441 (1964). (13) A. Bondi, J. Phys. Chem., 58, 924 (1954). (14) Bondi'* has pointed out that V, for halogen atoms varies slightly according to whether they are attached to primary, secondary, or tertiary positions; the differences, however, are small, and we have ignored the possibility that volume increments Imay also be affected by the position of attachment of the halogen to the carbon skeleton. (15) K. Tanabe and S. Saeki, J. Mol. Struct., 27, 79 (1975),and references therein. (16) The gauche chlorine/methyl interaction may not always be stabillzing, as in the cases of isobutyl chloride and axial chiorocyclohexane, for reasons discussed in ref 17a. (17) E. L. Eliel, N. L. Allinger, S. J. Angyal, and G. A. Morrlson, "Conformational Analysis", Wiley-Interscience, New York, 1965: (a) pp 17,44; (b) p 1 1 . (IS) G.J. Karabatsos and D.J. Fenogiio, "Topics In Stereochemistry", Vol, 5,E. L. Eliel and N. L. Allinger, Ed., Wiley-Interscience, New York, 1970,pp 167-203. \
- I
