J . Phys. Chem. 1991, 95, 1503-1507
since it is one of net H addition. Another possibility for. formation of 6-yl radicals is direct H addition to CS,where the H’s arise from the methyl via dissociative superexcitation. However, Das et al. found in aqueous solutions of uracil that direct H addition occurred at both C5 and C6 in the approximate ratio 2:l .Sd In view of this result, and the fact that the initial population in MeT included no significant contribution from 5-yl radicals, !i seems unlikely that the 6-yl radicals were formed by the direct H mechanism. Regardless of how 6-yl radicals form in MeT, they have been shown by Flossmann et a1.*Obto transform irreversibly into the 5-yl form under activation by either white light at 77 K or heat. The irreversibility of this 1,2 hydrogen shift indicates that the 5-yl form is more stable than the 6-yl form in thymine. Therefore, the evidence with thymine derivatives in solids indicates that 5-yl radicals will be the net result of any mechanism producing any combination of 6-yl and 5-yl radicals. Significance for DNA. The basic thymine-related fact from DNA studies that must be accounted for is the formation of thymin-5-yl radicals. In the discussion above, three mechanisms were proposed for producing 5-yl radicals of thymine: (1) direct protonation of T at C6: (2) protonation at C5 followed by electron addition; (3) direct H addition to C5 or C6. It is clear from a variety of studiesSbscthat the 5-yl radicals can be formed by direct protonation of the anion at C6. However, in the solid-state studies discussed above, it is not clear that this mechanism is a significant source of the considerable population of 5-yl radicals found after warming the sample to ca. 300 K. In particular, no direct connection was found between the anions in MeT and the production of 5-yl radicals. Recent results with oriented DNA fibers found that the spectral component assigned to T did not behave as
1503
expected upon incorporation of methyl-deuterated thymine into the DNA.36 This is evidence that the concentration of T is less than previously thought and thus that the thymin-5-yl radicals formed upon warming the DNA may arise from other precursors. The complete set of evidence, in particular the evidence that thymine 5-yl radicals do not require anions as precursors, divides into two parts the basic question of how the 5-yl radicals form in DNA: ( I ) What factors (molecular arrangement, hydrogenbonding mates, water presence and positioning, etc.) control the effectiveness of the possible mechanism? (2) What is the relative importance of these in DNA?
Summary and Conclusions In summary, the discovery of a proton at 0 4 in the anions of TdR raises the possibility that all “anions” of thymine derivatives reported so far in magnetic resonance studies of solids are similarly protonated. This discovery also shows that pK, values alone are insufficient to predict proton transfer across hydrogen bonds in solids. In addition, experimental evidence available at this time supports several plausible mechanisms for formation of thymine 5-yl radicals that do not require direct protonation at C6 of T. The basic result is the proposal that the appearance of the thymine 5-yl radicals in DNA is the result of the variety of possible reactions as affected by the local conditions within DNA. Acknowledgment. This work was supported by N I H Grant CA36810 and by NATO Travel Grant RG 0426/88. Additional travel support was obtained from Norges Allmenvitenskapelige Forskningsrad (NAVF). Discussions with W. A. Bernhard and S. Steenken concerning the nature and behavior of thymine radiochemical products are gratefully acknowledged.
Raman Spectroscopic Study of Hydrogen Bondlng in Aqueous Carboxylic Acid Solutions. 2. Deuterio Analogues in Heavy Watert Naoki Tanaka, Hiromi Kitano,* and Norio Ise Department of Polymer Chemistry, Kyoto University, Kyoto, Japan (Received: July 5, 1990)
Raman spectra of deuterio analogues of acetic acid and propionic acids in heavy water at 25 OC were measured. The carbonyl stretching region of the spectra was resolved into four envelopes by using band-fitting programs according to the assumption of the existenceof monomeric, dimeric, and polymeric acetic acid species formed by hydrogen bonding. Dimerization constants for the monomer-dimer equilibrium, KD, of carboxylic acid-d, were calculated from the normalized band areas. KD’s in heavy water solutions were greater than those in aqueous solutions. The contribution of hydrophobic interaction to the KD was thermodynamically discussed. Furthermore, normal-coordinate analysis of water-associated acetic acid molecules was carried out to clarify the reason for the splitting of C-C stretching vibration of acetic acid-dl heavy water solution.
Introduction It has henfound by various methdsI-4 that the dimerization constant of carboxylic acids tends to increase with increasing- alkyl . chain length. It is concluded that hydrophobic interaction stabilizes the carboxylic acid dimers in aqueous solution. In the previous study,s we investigated the dimerization of carboxylic acids in aqueous solution using Raman spectroscopy. The effects of alkyl chain length and the concentration of carboxylic acids on dimerization constants ( K D )in aqueous solution were investigated by the band resolution of the spectra. In the present study, KD’s of deuterio analogues of acetic acid and propionic acid in heavy water were estimated at various concentrations by the band resolutions of the spectra. The dif‘Presented at the 39th Annual Meeting of the Society of Polymer Science, Japan, at Kyoto International Hall in May, 1990. To whom correspondence should be addressed.
0022-3654/91/2095-l503$02.50/0
ference in KDvalues for normal carboxylic acids and their deuterio analogues were quantitatively discussed in terms of the hydroPhobic interaction.
Experimental Section Materials. Acetic acid and propionic acid were obtained from Nacalai Tesque, Kyoto, Japan, and used after distillation. Acetic acid-dl and acetic-d, acid-d, were guaranteed reagents from Aldrich Chemical Co., Milwaukee, WI, and CEA, Gif-sur-Yvette, France, respectively. Propionic acid-d, was prepared by hydrolysis ( I ) Nash, G. R.; Monk, C. B. J . Chem. Soc. 1957,4274. (2) Suzuki, K.; Taniguchi, Y.;Watanabe. T. J . Phys. Chem. 1973, 77,
1918. (3)Katchalsky, A.; Eisenberg, H.;Lifson, S.J . Am. Chem. Soc. 1951, 73, 5889. (4) Martin, D. L.; Rossotti, F. J . L. Proc. Chem. SOC.London 1959, 60. ( 5 ) Tanaka, N.; Kitano, H.; Ise, N. J . Phys. Chem. 1990, 94. 6290.
0 1991 American Chemical Society
1504 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
A
B
C
0
Figure 1. Water-associated acetic acid and its deuterio analogues: A, acetic acid i n water; B, acetic acid-d, in heavy water; C, acetic-d, acid in water; D,acctic-d3 acid-d, in heavy water.
of propionic anhydride in deuterium oxide for 4 h at 60 OC and distilled under reduced pressure. A Milli-Q grade water and heavy water obtained from CEA were used for preparation of sample solutions. Spectroscopic Measurements. The Raman spectra of aqueous carboxylic acid solutions were recorded by using an NR-1100 Raman spectrophotometer (Japan Spectroscopic Co., Tokyo, Japan) with a resolution of 5 cm-I. The spectra were excited at 488 nm by an argon ion laser (GLG 3200, NEC, Tokyo) at powers of 300-500 mW. The depolarization ratio was measured with a system consisting of a half-wave plate, lens, and a polarizer. All measurements were carried out in a thermostated chamber controlled at 25 f 0.5 O C by using a Peltier device (Model RT-IC, Japan Spectroscopic Co.). Normal-Coordinate Analysis. Normal vibration calculations were carried out according to Wilson’s G F matrix method6 by use of the Computation Center, University of Tohoku, Sendai, Japan, and the library programs R N C r B and NCTBL. Standard literaturc bond lengths and angles’O were used for molecular parameters of water-associated acid and its deuterated analogues (“monomer species” acid). The bond angle of the hydrogen bonding was assumed to be 180°, and the length 1.59 A, which are the theoretical values for the hydrogen bonding of the waters.’ The structural assumptions make all these molecules to be C, symmetry. The symmetry coordinates for these molecules were constructed using the assumed C,ysymmetry of the molecules, and all vibrational modes were separated into 18 vibrations belonging to A’ species and 9 vibrations belong to A” species. The initial values of the set of force constants were transferred from Fukushima’s works and adjusted by the least-squares procedure so as to give a satisfactory agreement of calculated frequencies with 43 observed frequencies of four kinds of waterassociated acetic acid (Figure I ) . Force constants related to the unobserved vibrational modes remained the same as the initial values (Le., K(O-H), H(CO-H), H(O--HO), etc. in Table I). Band Resolution. Spectra were resolved with the data decomposition program written by Drs Hiroshi Kihara and Toru Ozeki, Hyogo University of Teacher Education, Hyogo Prefecture, Japan, using Marquardt’s m e t h ~ d . ~
Results and Discussion Normal-Coordinate Analysis. Many works have dealt with the IR and Raman spectra of acetic acid dimer and monomer and their deuterated d e r i v a t i v e ~ , ~and J ~ some ~ ~ of them described ~~
(6) Wilson, E. 8. J. Chem. Phys. 1939, 7, 1047; 1941, 9, 76. (7) Goel, A.; Murthy, A . S. N.; Rao C. N . R. Indian J. Chem. 1971, 9, 56.
(8) Fukushima, K.; Zwolinski, B. J. J . Chem. Phys. 1969, 737, SO. (9)Marquardt, D.W. J. SOC.Ind. Appl. Math. 1963, / I , 431. (IO) Kishida, S.;Nakamoto, K. J . Chem. Phys. 1964, 41, 1554. ( I I ) Wilmshurst, J. K. J . Chem. Phys. 1956, 25, 1171. (12) Berney, C. V.;Redington. R. L.; Lin, K.C. J. Chem. Phys. 1970.53, 1713. (13) Annamalai, A.; Singh, S.Can. J. Chem. 1982,61, 263.
Tanaka et al. TABLE I: Urey-Bradley Acetic Acid‘ no. force const I K(C-H) 2 K(C-Cj 3 K(C=O) 4 K(C-0) 5 K(0-H) 6 K(O***H) 7 K(H‘-0) 8 K( H“-0) 9 H(HCH) 0 H(HCC) I H(CC=O) 2 H(CC-0) 3 H(OC=O) 4 H(C-OH) 5 H(HOH) 16 H;(CO..’.H)
Force Constants of “Monomer Species”of value
no.
4.45 I
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1.604 6.999 7.614 7.053 0.392 5.890 6.110 0.462 0.143 0.931 0.632 0.695 0.579 0.509 0.005
force const H,(CO*..H1 _. H,(O...HOj H z ( 0 . * .HO) X(CO2) T(C-C) T (c - 0 ) T(C=O)
F(CC-0) F(HCC) F(CC=O) F(CC-0)
F(OC=O) F(C-OH) F(H0H) K
value 0.005 0.066 0.036
0.411 0.003 0.098 0.161 0.073 0.657 1.085 1.222 0.255 0.366 0.472 -0.105
“ K = stretch; H = bend ( H , = in-plane; H2 = out-of-plane); F = repulsion; x = out-of-plane wag; T = torsion. Force constants are in (mdyn/A; mdyn/rad). H’ = hydrogen of water molecules associated with the acetic acid molecule directly; H” = another hydrogen of water molecules.
CC
Str.
CH3 asym.dei
l?f”(C“) Figure 2. Concentration dependence of Raman spectra of acetic acid-d, in heavy water: 100-90 wt % ’ D20solution at 25 O C ; arrows indicate the direction of dilution (100, 98,95,93,90 wt %).
aqueous sol~tions.~ Acetic acid forms several kinds of associated species in aqueous s o l ~ t i o n . ’The ~ spectrum of water-associated acetic acid (corresponding to “monomer species” in aqueous solution) is different from that of “monomer” acetic acid as vapor” because of the hydrogen bonding between acetic acid and solvent molecules. We carried out the normal-coordinate analysis of hydrogen-bonded “monomer species”, shown in Figure 1. Figure 2 shows the concentration dependence of spectra of acetic acid-d, in heavy water; the spectra are normalized by the CH3 asymmetric stretching mode. Remarkable spectrum changes were observed in the C=O stretching mode, COD bending mode, and C-C stretching mode in this wavenumber region. This is because the population of “monomer species” acetic acid-d,, which has a spectrum different from that of “dimer species” of acetic acid-d,, increases with dilution of the solution. The wavenumbers of the vibrations in monomer species of acetic acid-dl in heavy water are different from those of monomer acetic acid-d,. The differences in the wavenumber of the C=O stretching mode ( 1 768-1 792 cm-’ for monomer, 1713 cm-’ for hydrogen-bonded monomer species) and the COD bending mode (995 cm-’ for monomer, 1070 cm-l for hydrogen-bonded monomer species) are due to the hydrogen bonding with the solvent molecules. The obvious splitting is found in the C-C stretching mode of monomer species of acetic acid-d,, which we previously adopted as an internal standard for acetic acid aqueous solution.s (14) Haurie, M.; Novak, A. J. Chim. Phys. 1965, 62, 146. (IS) Ng, J. B.; Shurvell, H. F. J . Phys. Chem. 1987, 91, 496.
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 1505
Aqueous Carboxylic Acid Solutions 895
8L8
TABLE 11: Observed and Calculated Vibrational Frequencies and Assignments for 'Monomer Species" of Acetic Acid' wavenumber, cm-' obsd calcd assignment (PED,%) A'
3436.0 2946.0 1712.0 1650.0
851
799
-
2 L-J lb00
9'00
6'00
7'00
(cm-')
9'0B
8'00
7'00
(cm-')
Figure 3. C-C stretching vibration of water-associated acetic acid and its deuterio analogues: A, 50 wt % acetic acid in water; B, 50 wt % acetic acid-d, in heavy water: C. IO wt % acetic-d3 acid in water; D, 50 wt % acetic-d, acid-d, in heavy water.
Figure 3 shows the C-C stretching modes of monomer species of acetic acid and its three deuterio analogues. The deuterio analogues of acetic acid molecule associated with heavy water molecules obviously possess split C-C stretching modes. This is suspected to be caused by the Fermi resonance due to the combination or overtone of the vibration which is affected by the hydrogen bonding with heavy water molecules. The normal-coordinate computation was carried out to make this point clear. The "original" vibrational frequency of C-C stretching mode of monomer species of acetic acid-d,, which is unknown because of the splitting, and the other undetected frequencies whose combination or overtone possibly causes the Fermi resonance of the C-C stretching mode were calculated. The final set of force constants is shown in Table I, and vibration frequencies are compared with observed frequencies with the band assignment in Tables 11 and 111. As shown in Table 111, the C-C stretching mode of acetic acid-d, in heavy water is calculated to be 858.2 cm-I. This vibrational frequency is close to the combination of calculated frequencies of the C02out-of-plane wagging mode and the C-0 torsional mode (518.5 + 330.4 = 848.9 cm-I). In the case of acetic-d, acid-d, heavy water solution, the C-C stretching mode is calculatcd to be 802.0 cm-I, and this is close to the overtone of C=O torsional mode (408.0 X 2 = 816.0 cm-I). This would be the reason for the splitting of the monomer species of acetic acid-d,. Estimation of KD of Carboxylic Acid-d, in D20.In the former study, we estimated the dimerization constants KD for acetic, propionic, and n-butyric acids in aqueous solution by the decomposition of their Raman spectra in the concentration range 0.03-0.3 mol fraction.5 Using the same method, we estimated the KD for acetic acid-d, and propionic acid-d, in heavy water to investigate the effect of hydrophobic interaction on the dimerization constants (Figure 4). The Raman intensity is directly related to the concentration of a species, and integrated band area, I , is expressed as I = JC (1)
896.0 628.0
3596.9 3452.4 3335.1 2994.8 2936.2 1715.7 1650.3 1515.9 1510.0 1393.2 1286.7 948.5 893.0 743.8 627.6 391.4 209.0 17.2
2999.6 1436.0 1433.7 996.9 587.7 599.0 463.0 439.5 420.4 41.7 22.7
u(0-H) (100) u(O-H') (59) + u(0-H") (33). u(O-H';) '(67) u(0-H') (36) ~asym(CH3)(100) Usym(CH1) (99) u(C-0) (51) + u(C=O) (34) + CO2 rock (21) 6(HOH) (95) 6asym(CH3) (83) + 6asym(CH,) (8) 6(COH) (32) + 6,,,(C02) (19) + u(C-0) (15) 6,,,(CH3) (83) + WCOH) (21) u(C=O) (38) b(C0H) (35) + u(C-C) (20) Lym(CH3) (83) + 6,s m(CH3) (14) u(C-C) (66) + u(C-6) ( I I ) C 0 2 rock (63) + baSym(CH3) (IO) + u(C-0) (8) 6(COJ (66) + u(C-C) (8) + u(C=O) (8) 6(OH***O)(91) u(C=O***H) (90) 6(C=O..*H) (99)
+
I
.
+
A" ~asym(CH3)(100) 6a,ym(CH3) (100) G(CCH) (100) C=O torsion (96) w(C02) (72) C=O torsion (23) C - 0 torsion (75) + w(C02) (23) 6(OH** e o ) (96) C-C torsion (97) 6(C=O-**H) (95)
+
4 u = stretch; 6 = bend; x = out-of-plane wagging; H'= hydrogen of water molecules associated with acetic acid molecule directly; H" = another hydrogen of water molecules.
Wavenumber (cm')
Figure 4. Computer-resolved spectrum of the carbonyl stretching vibration of neat acetic acid-d, at 25 OC.
where J is the molar intensity coefficient, and C the concentration of the species. Using an internal intensity standard, normalization of the C=O stretching peaks was carried out for an exact comparison of the solutions of different concentrations. By using the internal standard, effects of variation such as instrumental factors and sample cell properties can be taken off. Ng and Shurvell15 used the C-C stretching mode of acetic acid at 893 cm-' as an internal intensity standard, and we adopted the same method as theirs for normalization of acetic acid and propionic acid. As mentioned before, the C-C stretching mode of deuterio analogues of acetic acid and propionic acid-d, was not adopted as an internal intensity standard because this mode split in dilute concentrations. Thus, CH3asymmetric deformation modes were adopted as a standard for the analysis of the spectra of these solutions. When I,, is the intensity of monomer species and Istadis that
Tanaka et al.
1506 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 TABLE III: Observed nod Calculated Vibrational Frequencies and Assignments for “Monomer Species” of Acetic Acid-d,”
wavenumber, cm-’ obsd calcd
T
O’(I
assignment (PED. 5%) A‘
3024.0 2994.8 2942.0 2936.2 262 I .O 2487.3 2493.0 2439.7 1713.0 1707.6 1515.8 1465.2 1354.7 1205.0 1206.1 1070.0 1068.0 948.7
Figure 5. Concentration dependence of KDof carboxylic acids at 25 OC: A, aqueous acetic acid solution; 0, aqueous propionic acid solution; A, acetic acid-d, in heavy water; 0 , propionic acid-d, in heavy water.
740.9 600.6 285.7 198.6 16.7
TABLE IV: Dimerization Constants (KD) of Acetic Acid and Prooionic Acid Comoared with Results of Several Workers“
2988.0 2994.6 1434.0 1433.8 1005.0 996.9 518.5 455.0 431.7 330.4 301.4 41.6 22.6
“ Y = stretch; 6 = bend; x = out-of-plane wagging; D’ = hydrogen of
water molecules associated with acetic acid molecule directly; D” = another hydrogen of water molecules. of internal standard peak, the normalized intensity of monomer species, Itmon, is derived as Imon
CmonJmon
[stand
CnominalJstand
I”,, = - -
=
J’monFmon
J’,,, = 0.16 f 0.05
Fmoncnominal
=
([”on/
J’mon)Cnominal
(5)
The concentration of dimers (both cyclic and linear) is therefore calculated as cdim
= (Cnominal
- cmon)/2
Drouionic acid
0.14 0.06 0.16 0.15 0.19 0.17
0.19 0.10 0.23 0.25 0.32 0.44
“ A t 25 OC. b A t 30 “C. stability constants).
ref 2b.c
I‘ 3c 4c 4
our previous works
= [adimcr]/[amonomer]2 (thermodynamic
with each other and much smaller than r d i m and I,,,. Consequently, dimerization constant, KD, is calculated as KD =
(7)
cdim/(cmon)2
For propionic acid-d, J’,,,/J’di,
= 1.15 f 0.1
(8)
The proportions of the concentrations of monomer and dimer can be calculated as Jbim -Cmon - ---
I’mon
2cdim
Ibim
J’,on
(9)
Consequently, KD is given by cmon
=
cnominalcmon/(cmon
+ 2cdim)
(4)
Using these values, we estimated the dimerization constant, KD, of acetic acid-d,. From eq 2, the following equation can be derived: =
acetic acid
(2)
where CnOminal is the total concentration of monomer that would be in the solution if there were no hydrogen bonding, Cmon is the concentration of monomer species, and Fmon is the molar ratio of the monomer species to the “nominal” concentration of carboxylic acid. Thc ratio of “normalized” molar intensity coefficient of monomer (J’mon) to that of cyclic dimer (Jbim) can be estimated from the ratio of the concentration dependence of I’,,, to that of [him. KD’s of the acids are calculated from these values. The details of the methods were described in our previous study.s The values neccssary for the estimation of KD of acetic acid-d, are obtained experimentally as follows: J’,,,/J’di, = 1 . 1 f 0.1 (3)
Cmon
0.2
Mole fraction
85 1.O 858.2 893‘0) 602.0
0.1
0
(6)
where c d i , is the concentration of dimer molecules and not that of carboxyl groups. This is based on the assumption that the polymer spccics almost exist as “linear dimer” in the concentration range 0.03-0.3 mol fraction bccause the intensity of the inner and the intensity of the group of linear dimer and polymer, linner. are comparable terminal group of linear dimer and polymer, I,erm,
Association of Carboxylic Acids. The results for acetic acid-d, and propionic acid-d, are given in Figure 5 together with the results of our previous study on acetic, propionic, and n-butyric acids. In all cases, the value of KD tends to increase with increasing alkyl chain length and decrease with increasing concentration. The former result is caused by the difference of the strength of hydrophobic interaction, and the latter is attributed to the nature of carboxylic acids as the structure breaker.I6 KD of carboxylic acid-d, is greater than that of carboxylic acid. This is caused by the difference in strength of hydrophobic interaction in water and heavy water. Oakenfull and Fenwick” ~~~~
( 16)
~
Oakenfull. D.;Fenwick, D. E. J. Chem. Soc., Faraday Trans. I 1979.
75, 636. (17) Oakenfull. D.; Fenwick, D. E. Ausr. J . Chem. 1975, 28, 715.
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 1507
Aqueous Carboxylic Acid Solutions TABLE V: Calculated Standard Free Energy of Dimerization and Hydrophobic Bond Formation of Carboxylic Acid-d, in Heavy Water formic acid acetic acid motionic acid AGD, kcal/ mol 1.9 1.1 0.82 AGHP, kcal/mol -0.8 -1.08
estimated the free energy of hydrophobic interaction between hydrocarbon chains in heavy water by the conductance measurements on micellar heavy water solutions. Using their results, we confirmed our results for KD of carboxylic acids. Table IV shows the compilation of the results of KD of aqueous acetic acid solution obtained by various Results by Martin and Rossotti4 were in good accord with our result. The other show the thermodynamic stability constants TKD (not dimerization constant), and the relationship between KD and TKDisI8
-log T K =~ -log KD - loghimer + 2 log fmonomer
(13)
wherefmnomerandhimcrare the activity coefficients of the monomer and dimer, respectively, in the solution. KD of carboxylic acid-d, in heavy water was estimated by using the data by Martin and Rossotti. Schrier et al.l* experimentally determined the standard free energy of hydrophobic interaction of carboxylic acid dimers in aqueous solution by the potentiometric method. The experimental TKDvalue is converted to the standard free energy of dimerization by eq 14. AGD = -RT In TKD
(14)
The frcc energy of hydrophobic bond formation, AGHp, was obtained by subtracting the free energy of the formation of the dimer, AGD, of formic acid from the AGD(HA) values of acetic and propionic acids: AGHP= ACD(HA) - AGD(formic acid) (15) We adopted the same method because this has been often used for the analysis of the hydrophobic i n t e r a ~ t i o n . ~ . ' ~ Table V shows the standard free energies of dimerization of formic, acetic, and propionic acid, which are given by TKDvalues of Martin and R o ~ s o t t i .The ~ standard free energies of hydrophobic interaction are calculated by the eq 15. Oakenfull et al. estimated the standard free energy of hydrophobic interaction per methylenc group as -0.33 and -0.42 kcal/mol in H 2 0 and D20, re~pectively.~'We can assume that hydrophobic interaction in D 2 0 is estimated to be 1.27 times greater than that in HzO. Using this assumption, we estimated the KD in D 2 0 from the data of Martin and Rossotti. (18) Schrier, E. E.; Pottle, M.;Scheraga, H. A. J. Am. Chem. Soc. 1964, 86. 3444. (19) Yamamoto, K.; Nishi. N. J. Am. Chem. SOC.1990, 112, 549.
Here we supposed that the standard free energy of the dimerization of formic acid AGD(formic acid) in H 2 0 is the same as that in D20. This is based on the fact that hydrophobic interaction does not work in the dimerization of formic acid.Ig Consequently, the standard free energy of the acetic acid in D 2 0 is calculated as AGD(acetic acid) = AGHP(D20)+ AGD(formic acid) = -0.8 X 1.27 + 1.9 = 0.88 kcal The thermodynamic stability constants, -log TKD,is calculated as - log TKD(aceticacid in D20) =
AGD(acetic acid in D20)/(2.303RT) = 0.645 Martin and Rossotti calculated -log TKD(aceticacid) and -log KD(aceticacid) in H 2 0 as 0.81 and 0.73, respectively. This means that logfdinler- 2 log fmon?mel = -0.08. Assuming that this is valid in D 2 0 solution, the stoichiometric equilibrium constant is calculated as -log KD(acetic acid in H 2 0 ) = -log TKD(aceticacid in D20) - 0.08 = 0.565 KD = 0.27 M-' KD for propionic acid in D 2 0 is calculated in the same way: -log KD(propionic acid in D 2 0 ) = 0.288
40 = 0.51 M-I These values are not far from our experimental values as shown in Figure 5. Conclusions The dimerization constants KD of acetic acid-d, and propionic acid-dl in heavy water were estimated on their Raman spectra. The KD values of these acids were greater than those of acetic acid and propionic acid. The greater value of the KD for the heavy water solutions are attributed to a stronger hydrophobic interaction in heavy water. The thermodynamically calculated KD value for deuterio analog of the acids was close to the experimental value. Acknowledgment. We thank Professor Katsunosuke Machida (Kyoto University) for his advice on the process of normal-coordinate analysis and to Professor Issei Harada and Associate Professor Hideo Takeuchi (Tohoku University) for the permission to use their programs RNCTB and NCTBL. We gratefully acknowledge Assistant Professors Hiroshi Kihara and Toru Ozeki (Hyogo University of Teacher Education) for their kind offer of the least-squares fitting program. Thanks are also due to Dr. Kensaku Ito (Osaka Economy University) for his advice on the computation. This work was supported by the Ministry of Education, Science and Culture (Grand-in-Aid for Specially Promoted Research 63060003).
