C. V. KRISHNAN AND HAROLD L. FRIEDMAN
1572 getics.28,26Whether or not such factors are involved in the reactions of e- in a polar solid such as cysteine we cannot say. However, simple dissociative attachment of e- need not necessarily be involved in steps 18 and 18a. An alternate explanation is that e- is captured by the sulfhydryl group to give RSH- and that chemistry then ensues as a consequence of proton transfer from an adjacent NH8+ group.26 Some evidence for such concerted action is to be found in the fact G (Hz) G ( HzS) from N-acetylcysteine, that CHsCONHCH ( CHzSH)COOH, is markedly lower than the corresponding value for cysteine as shown in Table 11. However, as formulated here, reactions 18 and 18a represent only the overall stoichiometries. The reaction scheme given in eq 14-21 leads to the
+
+
+
product relationship G( Hz) $G (HzS) +G (NH,) = G (RSSR) . We find experimentally that G (Hz) +G(HzS) iG(NH3) = 4.8 and that G(RSSR) = 5 . The combined yields of the radiation-induced steps 14 and 15 is given by GM GK,= G(H2) G(H2S) G(NH3) = 6.4. We cannot separately evaluate the contributions of ionization and excitation via reactions 14 and 15, respectively, since we have no knowledge of the relative yields of the branching reactions 16 and 16a, and 18 and 18a.
+
+
+
-
+
+
( 2 5 ) For a discussion of the effects of solvation energy on reactions of the type RXR X-, see J. A. Ward and W. H. Hamill, J . Amer. Chem. Soc., 87, 1853 (1965). (26) As noted in our discussion of reaction 9, the evidence is that the NHs+ group itself does not react with e- to yield hydrogen. See also ref Bb.
+
Solvation Enthalpies of Various Nonelectrolytes in Water, Propylene Carbonate, and Dimethyl Sulfoxide1 by C. V. Krishnan and Harold L. Friedman Departmenl of Chemistry, Staie University of New York at Stony Brook, Stony Brook, New Y o r k (Received November 1 8 , 1 9 6 8 )
11 790
The heats of solution of a number of nonelectrolytes, mostly alcohols and hydrocarbons, have been measured in the solvents water, propylene carbonate, and dimethyl sulfoxide at solute concentrations low enough so that solute-solute interactions are negligible. The solvation energies for the aliphatic compounds exhibit additive group contributions in propylene carbonate and dimethyl sulfoxide and a nonadditive “structural” contribution in water. This simple analysis is less successful for the aromatic compounds. The structural effect in the enthalpy of hydration of the normal alcohols ranges from about -2.5 kcal/mol for methanol to about -8.5 kcal/mol for amyl alcohol. Its plot as a function of chain length tends to level off near amyl alcohol. The enthalpy of the hydrogen bond from a normal alcohol to the solvent is near -8.1 kcal/mol in dimethyl sulfoxide and -6.2 kcal/mol in propylene carbonate.
I. Introduction The measurements reported here were made in the course of a study of solvation enthalpies of ionic species2 where, in the attempt to interpret the results, a need developed for the corresponding data for uncharged species. These a.re reported separately because a number of unexpected features make them of interest in a wider context than the study of ion solvation alone. The data are treated to see to what extent the enthalpies of transfer of various molecules from one medium to another can be decomposed into group contributions. In the simplest such treatment one would organize the data so that, in each case, one of the two The Journal of Phyeioal Chemistry
media was the dilute gas phase; the resulting enthalpies of transfer would be solvation enthalpies. In the present work this practice has been followed only to a limited extent for two reasons. The primary one is that in the work with ionic solutes2 the enthalpies in the gas phase are often not accessible to experiment. Indeed, they almost never are for polyatomic ions. There is evidence that one may circumvent this by employing a nonhydrogen-bonding solvent of high dielectric constant having only minimal basic and acidic tendencies as a reference medium for enthalpies of (1) Grateful acknowledgment is made of the support of this work by the National Institutes of Health. (2) H. L. Friedman, J . Phys. Chem., 71, 1723 (1967).
SOLVATION ENTHALPIES OF VARIOUSNONELECTROLYTES
1573
transfer of ions to more chemically active media.2 A promising solvent for this purpose is propylene carbonate, and, to see to what extent this practice may be misleading, we have mostly employed propylene carbonate as the reference medium in the present study. The solvation enthalpies of the nonelectrolytes in propylene carbonate can be used to check deductions made from the enthalpies of transfer to propylene carbonate from other solvents. The second reason is that often the absolute experimental error in the heat of vaporization i s large compared to the errors in measured heats of solution so that the solvation enthalpies are considerably less accurate than the enthalpies of transfer; the experimental uncertainties may tend to obscure interesting features. In the work with ionic solutes, dimethyl sulfoxide is useful for comparison with propylene carbonate so it has been included in the present study. The solvents used in the present work and some relevant properties are listed in Table I. 11. Experimental Section The chemicals used were of reagent, "certified," or spectral grade except t-amyl alcohol and biphenyl which were of the practical grade and ethanol which was 200 proof USP. The alcohols were dried over calcium oxide except n-amyl, t-amyl, and benzyl alcohols which were dried over calcium sulfate and then fractionally distilled over magnesium, the middle fraction being retained. Halobenzenes and hydrocarbons were washed with concentrated sulfuric acid and then with water, dried, and distilled. Nitrobenzene was washed with dilute sulfuric acid, steam distilled, dried over magnesium sulfate, and redistilled. Biphenyl was crystallized from benzene. Conductivity water was used for all of the measurements in aqueous solutions. Propylene carbonate (PC) and dimethyl sulfoxide (DMSO) were purified by distillation a t 4 and 12 Torr, respectively. The middle cut, used in both cases immediately after collection, Table I: Solvent Properties
HzO
dielectric constant, 25" PI D a,molecular polarizability, da Estd pK. of H(Solvent)+(aq) Abbrevixtion, this paper E,
Solvent
r
78
HsCCHCHzOCOO
65. l a
7
(HsC)zSO
45
1.84
4.94*
3.96
1.47
8.56c
7.97
0.0
7
0
PC
DMSO
W
a M . Watanabe and R. M. FUOSS, J . Amer. Chem. Xoc., 78, 527 (1956). b R . Kempa and W. H. Lee, J . Chem. Soc., 1936 (1958). CCalculatedfrom the data given by W. S. Harris, Ph.D. Thesis, University of California, Berkeley, Calif., 1958; UCRL Report 8381.
Figure 1. Enthalpies of transfer of normal alcohols to various media from water. The scale for the transfer to the gas phase from water is on the right; for the others, the scale is on the left, The scale for the transfer to € 1 9 0 from DzO (w +-d) is multiplied tenfold.
had specific conductivity 2-5 X and 4-8 X lo-* ohm-' ern-', respectively. The final solute concentrations in this study were well below 5 X M. The calorimeter and sample handling have been described e1sewhe1-e.~ The mixing or dissolution process was found to be practically complete in 2 4 min except as follows. The time required for n- and t-amyl alcohols in water was 10-12 min, and for aliphatic hydrocarbons in DMSO and P C it was 30-60 min. The heats reported in Table I1 are averages of duplicate measurements which differ by at most 0.1 kcal/mol except as follows. The heats reported for isopropyl, namyl, t-amyl, and benzyl alcohols are averages of 3 or more measurements selected from a larger number on the basis of purity criteria. The heats for hydrocarbons differ by a t most 0.2 kcal/mol. The heats reported for benzene and toluene are averages over 12 measurements each. These values differ considerably from the heats reported from solubility measurements. The purity criterion used is that further purification of the solute produces no change in the heat of solution. (3) H. L. Friedman and Y. 0.Wu, Rev. Sci. Znstr., 36, 1236 (1965). Volume Y3,Number 6 May i9B9
C. V. KRISHNAN AND HAROLD L. FRIEDMAN
1574
Table 11: Standard Enthalpies (kcal/mol) of Solution of Pure Compounds at 25" DMSO
W
-1.27, -0.34,
-1.73, -1.74," -1.75," -1.754,g 1.733f -2.42, -2.45," -2.39,L -2.42," -2.415; -2.4388 -2.43, -2.48," -2.20,by8 -2.422; -2.419@ -2.20, -2.16," -1.95,b -2.217; -2.15," -2.2649 -1.83, -1.52," -1.93," -1.8680 -3.08, -3.121,o -3.102' -4.11, -4.15,g -4.137; -4.10" -4.29, -4.4380 0.13,0.130
0.11, 0.72d 0.20,0.77d
PO
-1.28" -0.34'
2. o o c 1.50
0.29,O. 28"
2.02
0.61,0.61"
2.27
0.95,0.995
2.53
1.29 0.87 I . 19, 1.21" 1.16 -0.67 2.75 3.18 3.62 2.72 0.63,0.65" 0.90,0.89" 1.12 1.36,1.30° 1.16 4.98 0.31 0.52 0.52 0.31 0.55
2.77 2.36 2.51 2.47 1.22 2.19 2.52 2.84 2.12 0.37 0.56 0.76 0.89 0.81 4.53 0.13 0.41 0.54 0.82 0.27
a E. M. Arnett and D. R. McKelvey, J. Am, Chem, SOC., 88, 2598 (1966). b R. Aveyard and A. S. C. Lawrence, Trans. Faraday SOC.,60, 2265 R. L. Bohon and W. F. Claussen, J. Am. Chem. Xoc., 73, 1571 (1964). CY. C. Wu and H. L. Friedman, J. Phys. Chem., 70, 501 (1966). (1951). 0 R. Aveyard and R. W. Mitchell, Trans. Faraday Soc., 64, 1757 (1968). f D. J. T. Hill, Ph.D. Thesis, University of Queensland, 1965. 0 E. M. Arnett and W. B. Kover, to be submitted for publication.
111. Alcohols The enthalpy of solution data for several alcohols are presented in Table 11. Enthalpies of vaporization and enthalpies of transfer to H20from DzOsummarized in Table I11 are taken from the literature. The enthalpies of transfer between water and a number of other media, deduced from these data, are shown in Figure 1. Although it is sometimes assumed that plots of solvation energies as a function of carbon number for the straight-chain primary alcohols are linear, this is decidedly not the case here. On the other hand, the general similarity of the shapes of all of these curves suggests that a dominant contribution to the shape of each may be the structural (iceberg) effect in This effect is considered to be larger in D2O than in H2O and absent in DMSO, PC, and the dilute gas. It is possible to reach more quantitative conclusions about this structural effect by proceeding in the following way to elaborate on the common approximation that the solvation energy of a complex molecule is the sum of the solvation energies of its parts. The Journal of Phvsical Chemislrz,
We assume the following contributions to the partial molar enthalpy of an infinitely dilute solute species x in solvent a ~ ( xa);
=
H(x; g)
+ CAV(x; a) + I/'DW(x;a) + HB(x; a) + S T R ( x ;a)
(1)
H ( x ; g) is the enthalpy of x in the gas phase a t infinite dilution, CAV is the enthalpy increase in the process of making a cavity in the solvent to accommodate the solute molecule, VDW includes the van der Waals interaction of the solute and the solvent and polariza(4) H. S. Frank and M. W. Evans, J . Chem. Phys., 13, 507 (1945). (5) H.S. Frank and W.-Y. Wen, Discussions Faraday Soe., 24, 133 (1957). (6) G. Nemethy and H . A. Scheraga, J . Chern. Phys., 3 6 , 3382, 3401 (1962). (7) R. L. Kay and D. F. Evans, J . Phys. Chem., 69, 4216 (1965). ( 8 ) G. E. Walrafen, J . Chem. Phys.. 47, 114 (1967). (9) A. Ben-Nain, ibid., 42, 1512 (1965). (10) E. M Arnett in "Physico-Chemical Processes in Mixed 801vents," F. Franks, Ed., Elsevier Publishing Co., New York, N. Y., 1967. (11) F. Franks and D. J. G. Ives, Quart. Rea. (London), 20, 1 (1966).
1575
SOLVATION ENTHALPIES OF VARIOUSNONELECTROLYTES Table 111: Enthalpies of Vaporization a n d of Transfer to H20from DzO at 25” (kcal/mol) Compound HzO CHIOH CrHsOH n-C3H?OH n-CaHQOH n-C5H11OH i-CaH7OH t-CdHQOH ~-CIHI~OH CeHsCHzOH n-CsH12 n-cdh n - ~ , ~ ~ , 6
C-CsHrz CeHs C0H5 H 3 CeIIaCHzCH3 CeHsCH(CH3)z m-CeHa(CHa)z CsH5F C&5C1 c6H~Br CeH5I CeHsNOs C6IIsC6H5
c
AHwp
AHtra
10.51b 8.94,’~9.07d 10.12,b 10.18d 11.36c 12.581 12.62d 13.8OC 10. 8g6 11.200 11.960 14.6@ 6 . 32h 7,54h 8.74h 7.89h 8.0gh 9.08h 10.097h 10. 7gh 10. 195h 8.4Qh 10. 17n 10.87h ll.S5h 13.19h 18.87i
0. 030° 0.182 0.311 0.383 0.469 0.495 0.405 0.450
0.285
G. C. Kresheck, H. Schneider, and H. A. Scheraga, J. Phys. Chem., 69, 3132 (1965). b “Selected Values of Chemical Thermodynamic Properties,’’ National Bureau of Standards Circular 500, U. S. Government Printing Office, Washington, D. C., 1952. “ E . Doehlemans and E. Lange, Z . Elektrochem., 41,539 (1935). J. H.S. Green, J. A p p l . Chem., 11, 397 (1967). E J. H. S. Green, Trans. Faraday Xoc., 59, 1559 (1963). f J. H. S. Green, ibid., 61, 1869 (1965). J. A. V. Butler, ibid., 33, 229 (1937); J. A. V. Butler and W. S. Reid, J. Chem. Soc., 1171 (1936). h “Physical Properties of Chemical Compounds I, 11, 111,” Advances in Chemistry Series, No. 15, 1955, No. 22, 1959, and No. 29, 1961, American Chemical Society, Washington, D. C. J. C. Warner, R. C. Scheib, and W. J. Svirbely, J. Chem. Phys., 2, 590 (1934).
tion-dipole and dipole-dipole interactions (aside from H bonds) if any, H B is the enthalpy of formation of solute-solvent hydrogen bonds, and STR is the enthalpy a,ssociated with the structural change produced in the solvent by the solute (or by the cavity) and is particularly relevant to aqueous ~olutions.~~-15 Now we assume for any straight-chain primary alcohol CNHZN+~OHthat we have (see Appendix for discussion of notation)
C A V + VDW
+ HB = (HO*..H). + N(CH2).
(2) where (HO- .H) and (CH2) are coefficients which are independent of the species of the primary alcohols and where (CHZ). encompasses mainly the effect of a CHZ group on CAV (larger volume) and on VDW (larger polarizability). This equation is consistent with the linear dependence for the enthalpy of transfer to the gas from PC
.
Figure 2. Enthalpies of transfer of alcoholfi: 0 , to the gas from propylene carbonate (scale on right); A, to propylene carbonate from dimethyl sulfoxide (scale on left).
shown in Figure 2; according to eq 1 and 2 we have, for the normal alcohols = - (HO. * * H ) P c N(CHz)pc (CNH~N+IOH)~+PC
(3)
and the plot determines the coefficients given in Table IV. The two tertiary alcohols studied determine another set of coefficients, also given in Table IV, which are not very different from those for the normal alcohols. This tends t o support the usefulness of the assumption of group additivity of solvation energies. The small deviation of methanol on the primary alcohol line is an example of a commonly observed “end (12) When the structural term is important, there are ambiguities in the definitions of the other terms, especially C A V. For example, according to the ideas underlying the structure effects’a the “iceberg” structure would be induced just by the formation of a small cavity11 if the forces tending to orient the water molecules in the interface are negligible.1a In such a case it seems there would be no operation, whether calculational or experimental, which would enable one to separate the energetics of cavity formation into a structural part and a remainder. What the actual situation is around a small cavity in water is not clear. Pierotti14 has shown that intriguing correlations of solvation energetics in water with other properties are obtained by a theory which emphasizes the CAV term while neglecting explicit treatment of the STR term, as would be justifled if the cavity induced the structure and if the calculation of its energetics in the underlying theory were accurate. However, the consistency of this calculation has been questioned.16 For the present it seems useful t o assume that the structural term can be separated from the others although a complete separation is not achieved in the present paper. (13) F. H. Stillinger and A. Ben-Naim, J. Chem. Phys., 47, 4431 (1967). (14) R. A. Pierotti, J. Phys. Chem., 69, 281 (1965). (15) A. Ben-Naim and H. L. Friedman. ibid., 71, 448 (1967). Volume YS, Number 6 May 1969
C. V. KRISHNANAND HAROLD L. FRIEDMAN
1576 Table IV: Solvation Enthalpy Parameters (kcal/mol) H1 0
PC
DMSO
Primary Alcohols (HO***H) (CH2)
-6.20 -0.96
-7.68 0.32-0.07
-8.13 -0.87
6
Tertiary Alcohols (HOB OH) (CH2)
. . I
...
-5.52 -0.79
-6.89 -0.78
-0.61
-0.46
-7.5
-7.7
t
Alkanes (CHJ
...
(CBHO)
...
Aromatic ~~
~
~
~
effect” which may reflect a variation in the intrinsic hydrogen-bond donor strength in the beginning of a series N = 0, 1, 2, . . . . In Figure 2 we also plot
(CNH~N+IOH)PC+DMSO = ( E O * .H)PC+DMSO
+ N(CHZ)PC+DMSO(4) for the primary alcohols. The derived parameters for the transfer PC t DMSO are combined with those for g t PC to get the parameters for g c DMSO with the results given in Table IV. An interesting feature of Figure 2 is that the N = 0 intercepts for the primary alcohols come reasonably close to half of the enthalpy of transfer of HzO. The agreement seems quite satisfactory in view of the possibility of interference between the two hydrogen bonds which water presumably forms in each of these solvents. Having an empirical basis for the assumption of the linear dependence of enthalpies of transfer of alcohols upon N in the absence of structural effects, we now turn to the problem of isolating the structural term in aqueous solutions, We compare the transfers PC t w and d c w (DzO from HzO)
(CNHzN+1OH)pc+w = (HO* ~ H ) P c + ~
+ N ( C H Z ) P C +-~STRw(N) (C”zN+1OH)d-w
=
(5)
( H o r n*H)d+w .
N(CHz)d+w f STRd(N)
- STRw(N)
(6)
where STR(N) is the structural effect for the N-carbon normal alcohol in the water or DzO as indicated by the subscript. Now it is convenient to define the coeficients y, z, and z’ by the equations
XTRd(N)
E
(HO.**H)d
(1
+ y)STRw(N)
(7)
(1
+ Z) (HO***H),
(8)
(CH2)d E (1 4-
2’)
(CHZIW
(9)
We also make an additional postulate, namely, that The Journal of Phyaical Chemialry
‘
N
4
Figure 3. Reduced enthalpies of transfer of normal alcohols.
y is independent of N. If this is allowed, we can eliminate the structural term between eq 5 and 6 by defining a reduced enthalpy of transfer
-Wed
E
(CNH~N+IOH) pc c w
4-IP(CNHz,v+IOH)d+w = J’
+ Nj‘
(10)
where the coefficients are given by j~
- (1 - (z/y))(HO**.H), (11) (CHz)pc - (1 - (z’/Y)) (CHz), (12)
(HO...H)pc
jE
Equation 10 is plotted for various values of y in Figure 3. We find a good linear plot for y = 0.060 giving j = 1.16 kcal/mol andj‘ = -0.98 kcal/mol. The good linearity in Figure 3 demonstrates that the curvature of each plot in Figure 1 indeed has the same origin, the structural effect in water, and that the postulate that y is independent of N is consistent with the real situation. The same postulate has been made before, for example, by Wu and Friedman,’“ and indeed the factor y determined here is similar to what was estimated16 on the basis of the Nemethy-Scheraga calculations! On the other hand, the great utility of this postulate in isolating the structural effect makes it important to test it further when additional data on HzOt DzO transfers become available. (16) Y . C. Wu and H. L. Friedman, J . P h y s . Chem.. 70,166 (1966). See also R. H. Wood, R. A. Roomy, and J. N. Braddock, $bid., in press.
1577
SOLVATION ENTHALPIES OF VARIOUS NONELECTROLYTES Table V:
Saturated Hydrocarbon Transfers from PC (kcaljrnol)
-
RH Pentane
Hexane
Heptane
Cyclohexane
4.13 1.25 0.56 0.29
5.02 1.18 0.66 0.30
5.90 1.10 0.78 0.33
5.77 0.01 0.60 0.06
(RH)~+Pc (RH),+pc f N(CHz)pc (RH)DMSO+PC (RH)DMSO+PC - NCHZ)DMSO+PC
Now we may combine eq 5-9 using the parameters determined by Figure 3 as well as (HO..*H)PC and (CH2)pc from Table IV to obtain the result STRw(N)
=
16.67 (C"zrq+lOH)
dew
7.362 +--0.06 -z
0.02x'N 0.06 - Z'
(13)
where the parameters,z and z' are defined in eq 8 and 9. If z = 0 = x', which is equivalent to the assumption made by Kresheck, Schneider, and Scheragall in their discussion of the w t d transfer data, then our result for the structural term is given by the solid line in Figure 4. Certain data for aliphatic hydrocarbons discussed in the next section allow an estimate of z to be made; a t that point we return to a discussion of Figure 4.
IV. Aliphatic Hydrocarbons Data for several aliphatic hydrocarbons in PC and DMSO are summarized in Table V. Here these are formulated as R H = ( C H Z ) N ( C H ~ where ) N ~ N' = 0 or 2. Following the ideas introduced above we write
- N'(CHs)pc
(RH),+-pc = -lV(CHz)pc
As shown in Table V these data are in quite satisfactory agreement with this equation, using (CH2)pc = - 0.96 kcal/mol determined from the alcohol data, and lead to (CH3)pc = -0.59 kcal/mol. It may be remarked that a (CH3) term was not employed in treating the alcohol data. However, in the framework of the assumptions employed here, we
have the following identity, for any solvent a 2(CH3)a = z(CH2)a
+ (H.'*H)a
(14)
where (H. -H)a is the contribution of the end groups if the CH2 groups are all assumed to make the same contribution. The present result for this coefficient is (Ha .H)pC = 0.74 kcal/mol. The former way of presenting these results seems more physical but the latter is more closely analogous to what was done with the alcohols. However, the essential point is that because of eq 14 it is trivial to go from one to the other. As sho& in Table V the PC t DMSO transfer data for these hydrocarbons are also in satisfactory agreement with the formulation employed here. Then we turn to the transfers involving water (Table VI). Unfortunately, we did not succeed in attempts a t calorimetric measurement of the heats of solution of the hydrocarbons in Table V in water and the hydrocarbons in Table VI are too volatile for calorimetric investigation with our apparatus, so we do not have any overlap between the group which are shown to obey the additivity rules in DMSO and PC and the group for which we shall assume these rules in water. According to the formulation in section I11 we may write 0
(C~Hz~+z)g+w = -(H**.H)w
- N(CH2)w - STRw(N) (C ~ ~ H ~ ; V +g+w ~ O= H )- (HO
*
(15)
* H )w
- N(CH2)w - STR,(N)
(16)
where, in addition to the assumptions in the general formulation, we have assumed that the structural term does not depend on whether one of the end groups is CHI or CH20H. However, this also really follows from Table VI: Saturated Hydrocarbon Transfers from Water (kcal/mol) CH4
-10 I
I 2
I
I
N
4
I
Figure 4. The structural effect for normal alcohols: -: = 2' = 0; - - - z = 0.003, z' = 0.02 or x = 0.003, x' = -0.02.
(RH),, (RH),,,
- (ROH).,,
3.15 -7.65
CnHsR H- CaHs
4.10 -8.50
5.3 -8.5
C4HlO-.-.
5.9 -8.9
(17) G. 0.Kresheck, H. Schneider. and H. A. Scheraga, J. Phys. Chem., 6 9 , 3132 (1965). Volwrne Y3, Number 6 M a y 1969
1578
C. v". KRISIINAN AND HAROLD L. FRIEDMAN
Table VII: Aromatic Hydrocarbon Transfers from PC and DMSO (kcal/mol) r -
PhH
PhMe
r
(PhX)g+pc (PhX),-pc 0.96N (PhX)Pc+DMBo (PhX)pc+nMso -k 0.09N
-
0
1
7.72 7.72 -0.26 -0.26
8.52 7.56 -0.34 -0.25
the underlying additivity assumption and any interference between the effect of the hydroxyl group and the structural effect would be included in the term (HO.*-H),. As we see, the difference of eq 15 and 16 should be independent of the species and this is well borne out by the data in Table VI. Even the discrepancy of the N = 1 datum is not serious compared to the large quantities involved, but neglecting it we have
(HO*.*H), = -8.50
+ (H**.H),
(17)
The t,erm (He O H ) ,which involves neither structural effects nor solute-solvent hydrogen bonding, is not very large in PC or DMSO. Assuming it is the same in water as in DMSO (0.82 kcal/mol) , we have (HO.*.H),
-7.68,
z = 0.003
The result would not be very different if we used (H. *H),= 0.74 kcal/mol, the value for PC. Unfortunately, we still have no way to determine z', the coefficient in eq 9, although it seems it should be small. If we allow what seems a generous range for it, -0.02 5 z' S 0.02, then using eq 13 we can construct the curves in Figure 4. It is seen that even with these uncertainties in z and z' this analysis of the data yields an STR,(N) function whose accuracy is significant for many applications. The parameters (HO- -H), and ( C H n ) wfor z = 0 = z' are given in Table IV.
-
PhX PhEt N 2
9.34 7.42 -0.36
-0.18
m-Xylene
i-PrPh 1 1
--. ?
2
3
9.39 7.47 -0.35 -0.17
9.90 7.02 -0.47 -0.20
and ( C ~ H ~ . * * H ) Din M Table S O IV would be much affected. The same enthalpies of transfer together with some others are shown in Figures 5 and 6. They are plotted against the polarizability because of the possibility that, for these highly polarizable solutes in highly dipolar solvents, the ap2/re dipole-polarizability interaction term in the solvation energy would be the dominant one. This aspect is discussed further in the following section. Apparently the correlation works quite well for the compounds in Table VI1 but not for the others. In this connection it is important to note that all of the monohalobenzenes have dipole momentsI8 of 1.66 to 1.71 D so perhaps the dipole-dipole term in the solvation energy could account for their behaving differently from the hydrocarbons in Figure 5. However, in Figure 6 we see that the data separate into the same two families as before for the most part. This is not expected from any of the terms in eq 1 but may be a manifestation of the so-called charge-transfer interaction which often is invoked to elucidate the solution thermodynamics of aromatic hydrocarbon^.^^-^^ The PC c w transfers for a few aromatic compounds are shown in Table VIII. A simple additivity test shown here fails spectacularly. It is hard to believe that such large discrepancies could arise except through the failure of the additivity of the structural terms for the phenyl group and side chain. This nonadditivity is consistent with the finding that for the alcohols STR, is not linear in N .
V. Aromatic Compounds VI. Discussion of Group Contributions It might be supposed that, the number of assumptions and parameters employed in analyzing the data In this section a brief study is made of the extent to for alcohols and saturated hydrocarbons being so large, which molecular properties can give some understandthe consistency tests which are satisfied do not provide ing of the parameters in Table IV. While any but much verification of the assumptions employed. Howthe most elementary consideration would be outside ever the behavior of the aromatic compounds provides the scope of this paper, it is of interest to see whether some counter examples to this. we can recognize the dominant effect in each parameter. Data for several aromatic hydrocarbons in PC and DMSO are summarized in Table VII. The additivity (18) A. L. McCleliian. "'Table of Experimental Dipole Mornants,'" tests shown in the table arc based on the formula W. H. Freeman and Go., New York, N. Y., 1963. csHs(CH2)~for all of these hydrocarbons. The con(19) R. P. Rastogi, J. Nath, and J. Misra, J. Phys. Chcm., 71, 2524 (1967). sistency could perhaps be improved by detailed treat(20) W. A. Duncan and F. L. Swinton, Trans. Faraday SGC.,62, ment of different effects of ring substituents and of 1082 (1966). chain branching but this would require more data and (21) D . V. Fenby and R . L. Scott, J. Phys. Chem., 71, 4103 (1967). it seems unlikely that the results for (C~H~.**H)PO (22) A. Sandoval and M. W. Hanna, i b t d . , 70, 1203 (1966). The Journal of Physical Chemistry
1579
EOLVATION ENTHALPIES OF VARIOUS NONELECTROLYTES Table VIII: Aromatic Hydrocarbon Transfers from Water (kcal/mol) 0 Ph-Ph
e
(PhX)pc+w (PhX)p c c w - (PhH)~ (X)PC+W
Ph-Br,
c c w
PhH
PhMe
PhCHzOH
0.26 0
0.36 0.10 -0.13”
1.09 0.83 3.23b
... (1-pentanol)pc- - (l-butanol)pc+,.
0 Estimated as as (methanol)pc+,.
Polarizability, A3/molecute Figure 5. Enthalpies of transfer of aromatic compounds to the gas phase from propylene carbonate. H Dipole-Polarizability Interaction. We takez3~ C = 1.83 A3, a C H 3 = 2.56 A 3 , and a C e H B = 9.89 Aa. Then for r = 4 A and for the interaction of one polarizable center with one propylene carbonate molecule the a,u2/rs term gives contributions of -0.16 kcal/mol for CH2, -0.22 kcal/mol for CH3, and -0.86 kcal/mol for C6H0 to the solvation enthalpies of these groups in PC. All of these are so small compared to the observed parameters, -0.96, -0.59, and -7.5 kcal/mol, respectively, that even reasonable allowance for solvation numbers larger than unity and r less than 4 A would not allow one to conclude that this interaction is the dominant attractive one in these solvation parameters. This is especially clear because there is expected to be a sizable repulsive contribution from the cavity term in such a strongly dipolar solvent. It also may be noted that even with such strongly dipolar solvent molecules the dipole-hyperpolarieability interaction, whose magnitude may be estimated from molecular hyperpolarieability parameters collected by B u ~ k i n g h a m is , ~ much ~ smaller than the dipole-polarizability interaction.
/ OPh-Br
Ol-
I
b
I
t
I
PoiariZat3ty, I ~3/moiecd~
--.
---PhX
/
QPh-NO2
I
I
20
Figure 6. Enthalpies of transfer of aromatic compounds to pmpylene carbonate from dimethyl sulfoxide.
~
Estimated
The same comparison may now be made for the transfers to PC from DMSO (Table IX). For CH2 and CH3 the calculated and observed figures are close enough so that it seems likely that, with allowance for uncertainty in solvation number (i.e., number of dipoles interacting with each group) and in r, this interaction may account for the observed effect, but it is clear that in the case of C6Hs.*.H something else is happening which contributes a small extra stabilization in DMSO conipared to PC. This may be another manifestation of the charge-transfer interaction. What is most remarkable is that the CAV VDW sum which dominates the group solvation enthalpies in PC and DMSO is sufficiently the same in the two solvents so that apparently the dipole-polarizability interaction dominates the PC t- DMSO transfer. It also seems remarkable that the presumably positive CAV term is overcome by the VDW term in the solvation of all of these groups in PC or DMSO. Hydrogen Bonding. In the solvents considered here the solvation parameter (HO- OH)is expected to consist mainly of a positive cavity term and a dominant negative hydrogen-bond term. Therefore in the aprotic solvents the alcohol-solvent hydrogen bond must be somewhat stronger than the (HO- * H ) term in Table IV. Such strong hydrogen bonds were deduced for the interactions between alcohol molecules by Daviesz6 by a procedure somewhat similar to that used here. The relative strengths of the hydrogen bonds to PC and to DMSO are consistent with the enthalpy of transfer of water between these solvents (Figure 2) and with the order of the proton nmr shift for CHCls in several solvents measured by Delpuech.26 His results for the upfield shift in ppm relative to pure CHCla are: acetonitrile, 21 ;ethylene carbonate, 41 ; dimethyl sulfoxide, 105. It would clearly be of the greatest interest to have more comparisons of the energetic and spectroscopic properties of hydrogen bonds in systems in which the interaction was this well defined,
+
-
(23) R. J. W.LeFevre, Advan. Phys. Org. Chem., 3 , 1 (1965). (24) A. D. Buckingham and B. J. Orr, Quart. Rev. (London), 21, 195 (1967). (25) M . Davies, quoted by G . 0.Pimentel and A. L. McClellan, “The Hydrogen Bond,” W. H. Freeman and C o . . New York, N . Y.. 1960,pp 215, 216. (26) J. J. Delpuech, Bull. Soc. Chtm. France, 1624 (1966). Volume ‘73,Number 6 May 1969
C. V. KRISHNANAND HAROLDL. FRIEDMAN
1580
Table IX: Transfer to PC from DMSO (kcal/mol) CHa
Obsd
-( a / r s ) A p a
-0.09
-0.055
Group OH:
-0.15 -0.077
C4HS.. . H
-
-0.26 -0.30
but the only other one seems to be a study by several methods of carefully selected hydrogen-bonded systems by Arnett, Schleyer, Taft, and their coworkers.27*28 In fact their method I1 is equivalent to methods used in this paper to deduce the hydrogen-bond enthalpies, It is noteworthy that they find that AH of hydrogenbond formation does not order the strengths of some hydrogen bonds in the same way as two other criteria investigated. It is also of interest that ?Li shifts are not a useful measure of the strengths of the Lewis acid-base interaction of Lit with these and similar solvents.2g The term (HO*-*H), is more difficult to interpret since there could be a net increase of up to 3 in the number of hydrogen bonds when an ROH molecule is added to water, 1 in which ROH is the proton donor, and 2 in which it is the acceptor. There is only indirect evidence that in fact the increase in number of hydrogen bonds in this process is just 1, since some water-water bonds are broken when the ROHwater bonds are made." The hydrogen bonds associated with the structural effect are not to be included in these considerations, which relate only to the (HO * .H) term. The Structural E$ect. Two things about the structural effect in water, exhibited in Figure 4,are remarkable. The first is its magnitude; for the larger alcohols it exceeds the enthalpy of the alcohol-solvent hydrogen bond. The second is the apparent saturation of the effect with increasing carbon number. The apparent saturation is much sharper than would be expected if the effect were proportional to the surface of the cavity made by a coiled chain of N methylene groups. It suggests that if the effect is due to the cavity itself, rather than to the interaction of the contents of the cavity with the water, then it is an effect characteristic of small cavities. Although the Frank-Wen model of the structural effect5 does not automatically provide for this, it may be speculated that the surface polarization of water leading to its large surface potential becomes developed only as the cavity surface becomes flat enough80 and that the surface polarization interferes with the Frank-Wen flickering structures, the icebergs. Again it must be remarked that the cavity term may not be separable from the structural term.12 Other evidence for the saturation of the structural effect with increasing size of the solute, although at
The Journal of Physical Chemistry
much larger size levels, is exhibited by the enthalpies of transfer of tetraalkylammonium ions to PC from water.a1 Still other evidence is provided by certain data on partial molar volumes a t infinite dilution.a2Ja
VII. Appendix on Notation In this paper it is necessary to keep account of the enthalpy contributions of molecules or parts of molecules at infinite dilution in various media. In order to do this as clearly and simply as possible we replace the standard notation for the partial molar enthalpy of species x in phase a, say, H(x; a), by ( x ) ~ . We also replace the standard notation for the change in enthalpy per mole of x when x at infinite dilution is taken to phase b from phase a, say AHb,a(X) = H ( x ; b)
- H(x; a)
by the notation (X)b+a. Thus the parenthesis about the formula of a molecule or a group represent the partial molar enthalpy of the species and the subscript represents either the phase or the transformation. Some examples follow; in each line the last form on the right is the preferred one in this paper. H(CH3OH; HzO) = (CHsOH), AHvap(CHaOH)E (CHaOH), AHtv(CHa0H)
E
- (CHa0H)i
H(CH3OH; PC)
- H (CHSOH; DMSO)
=
(CHaOH) PC-DMSO
The last examples indicate why the arrow in the subscript is written from right to left; this corresponds to the order of the terms in the subtraction in the usual definition of a AH. All solute enthalpies pertain to standard states of infinite dilution in the specified media at 25' so we may omit the usual indications of standard state and temperature in most places. Similarly the units of (x) a and (x) b c a are always kilocalories per mole of x so these units are omitted except in the figures and tables. (27) E. M. Arnett, T . 9. 9. R. Murty. P. von R. Schleyer, and L. Joris, J . Amsr. Cham. Soc., 89, 5955 (1967). (28) D. Gurka, R. W. Taft, L. Joris. and P. von R. Schleyer, i b i d . , 89, 5967 (1967). (29) G. E. Madel. J. K. Hancock, L. F. Lafferty, P. A. Mueller. and W. K. Musker, Inorg. Chem., 5 , 554 (1966). (30) There is an obvious source of the postulated dependence of surface potential upon cavity size: As the cavity becomes smaller, the electric fleld associated with the surface potential at one side of the cavity tends to suppress the surface potential on the opposite side. (31) C.V. Krishnan and H. L. Friedman, unpublished results. (32) K. Nakanishi, N. Kato, and M . Maruyama, J . Phys. Chem., 71,814 (1967). (33) M.E. Friedman and H . A. Scheraga, ibtd., 69, 3795 (1965).
