J. Phys. Chem. 1995, 99, 11673-11679
11673
High-pressure Mass Spectrometric Study of the Gas-Phase Association of C1- with a,mDiols Wan Zhang, Ch. Beglinger, and John A. Stone* Chemistry Department, Queen's University, Kingston, Ontario, Canada K7L 3N6 Received: March 7, 1995; In Final Form: May 22, 1995@
A high-pressure mass spectrometer with a pulsed electron beam has been employed to determine the standard enthalpies and entropies of association of diols (D) with C1- to form DC1- and DClD-. The -AZP (kcal mol-') and -AS" (in parentheses, cal K-' mol-') values for the formation of DC1- are 1,Zethanediol 25.3 (29.1); 1,3-propanediol 28.3 (34.0); 1,Cbutanediol 30.2 (42.6); 2-butene-1,4-diol 32.9 (44.4); and 2-butyne1,4-diol 28.9 (36.7). All the diols behave as bidentate ligands to give cyclic DC1-, and the values of -AH" for the C4 diols are the maximum expected when comparison is made with -AH" for the formation of the Cl--bound dimers of methanol and ethanol. The effect of diol size on the magnitude of -AZP is significantly less than for protonation. Although 1,2-ethanediol also has the smallest values of -AZP and -AS" for the formation of DClD-, the small entropy change results in this diol being the better clustering agent of all the diols at elevated temperatures.
Introduction
The thermodynamic data obtained on the clustering of molecules around gas-phase ions, both positive and negative, have been of considerable importance in helping elucidate the organization of solvent around ions in the liquid phase.'-6 Studies of the gas-phase solvation of halide ions have been predominant in studies of negative ion solvation, with C1- being generally favored for quantitative studies of absolute binding energies. There are several reasons for this: C1- is readily produced in the gas phase, usually by dissociative thermalelectron capture by a chlorinated molecule such as carbon tetrachloride or chloroform; its free energy of binding with many simple molecules has values which are in the optimal range of 10-25 kcal mol-' for a first molecule2 so that absolute values rather than relative values may be obtained for enthalpies of binding by high-pressure mass spectrometry (F- binds much more strongly than C1- and often participates in unwelcome side reactions such as HF production by proton abstraction; Brand I- bind less strongly); the presence of two isotopes aids the interpretation of mass spectra, a factor which has been of considerable value in the use of C1- as a reagent ion in chemical ionization mass spectromet~y;~.~ the spherical electric potential associated with the ion aids in simplifying theoretical calculation. In this paper we report the results of a study of the association of C1- with apalkanediols, which are expected, as in their association with the proton, to behave as bidentate ligand^.^,'^ The objective was to (a) ascertain bidentate behavior via measurements of absolute values for enthalpies and entropies of association and comparisons of these values with those of monodentate alcohols and (b) to determine the effect of carbon number on these values, since for protonation the size of the cyclic structure formed has a very significant bearing on the thermodynamics of the interaction, the maximum binding enthalpy not being attained until 1,4-butanediol, when the O-H-.O linkage can be linear, or almost linear.''-i4 To this end 1,2-ethanediol, 1,3-propanediol, and 1,4-butanediol were chosen for study since comparative data are available from our laboratory on their proton affinities and the intramolecular hydrogen bond energies of the protonated molecules." In @
Abstract published in Advance ACS Abstracts, July 1, 1995.
0022-365419512099-11673$09.00/0
addition, the effect of the geometrical constraints, if any, on bidentate behavior due to the presence of a double or a triple bond in the 2,3-position of the C4 a,w-diol has been examined. Data for the formation of symmetrical and nonsymmetrical C1-bound diol dimers were also obtained to provide further information on the thermodynamics of solvation by these ligands. Experimental Section
The high-pressure mass spectrometer equipped with a pulsed electron beam has been described previously in detai1.I5.I6 Ion source pressures which may be used in the instrument are in the range 2-6 Torr (1 Torr = 133 Pa), and the available temperature range is 300-625 K. Premixed samples of known composition are fed into the ion source from a 5 L glass reservoir via a variable leak, both held at a temperature of 400 K to prevent problems due to diol condensation. Mass spectra may be obtained by scanning the spectrometer electromagnet with continuous electron ionization. Thermodynamic data are obtained using an electron beam which is repetitively pulsed, with ionization periods of 50 ,us followed by 10-25 ms without ionization, during which the intensity of a selected ion is monitored as a function of time. For each selected ion, data for (1-2) x lo3 pulses are accumulated. The time-resolved intensities for ions of interest in a given spectrum are processed to give normalized ion intensities (ion counts) as functions of ion residence time. A modification of the data acquisition procedure from previously reported work with this instrument was the substitution of a personal computer for the hard-wired multichannel analyzer. Each sample consisted of -0.3-2 mol % diol and -0.05 mol % carbon tetrachloride in methane as buffer gas. All the liquid diols were added to the flask in known quantities by weight using microliter syringes. 2-Butyne-l,4-diol (mp 326 K) was first dissolved in methanol. No ions containing methanol were observed with this sample since, as was found in this work, the C1- affinity of a single alcohol molecule is much smaller than that of a diol. The methane was Matheson Purity grade with a stated purity of greater than 99.99%. All other chemicals were from the Sigma-Aldrich Chemical Co. and were of the highest punty 0 1995 American Chemical Society
Zhang et al.
11674 J. Phys. Chem., Vol. 99,No. 30, 1995 1.o
0.8 -
6o
1
t
0.6 -
D,.CI-
I &
20-
v)
cI-
D,.CI-
D.CI-
0.2 0.4
0.0 ’
=gm 100
(3)
80
0.8
60
0.6 .
40
0.4 .
20
ButanediolSI’
0
I
t
0
100
200
300
400
Figure 1. Mass spectra of CI&/1,3-propanediol/CCl~mixtures: (a) 0.96 mol % diol, 2.5 Torr, 484 K; (b) 1.95 mol % diol, 2.7 Torr, 301 K.
available. The 2-butyne-1,4-diol was 95% cis. Allowance was made for this in all processing of data, it being assumed that the trans form could not compete for C1- with the cis form because of its monodentate behavior. All the chemicals were used as received.
Results C1-, formed by dissociative electron attachment to carbon tetrachloride, associates with diol D at ion source pressures from 2 to 5 Torr to give D,Cl-, the value of n depending on diol concentrationand ion source temperature. The typical low- and high-temperature spectra for D = 1,3-propanediol, shown in Figure 1, illustrate the “clean” spectra obtained. At the lower temperature of 301 K in methane containing 1.95 mol % 1,3propanediol the association of C1- with from 1 to 5 diol molecules is observed, but at the higher temperature of 484 K, for a diol concentration of 0.96 mol %, its association with only one molecule is evident. The very small non-chlorine-containing peak at m/z 70 observed at the higher temperature was not identified. By judiciously matching ion source temperature and diol concentration,it was possible to obtain thermodynamic data for the formation of DC1- and DClD- for the linear amalkanediols with carbon numbers from 2 to 4 and also for two unsaturated C4 diols, cis-2-butene-1,4-diol and 2-butyne-1,4diol. Examples of the experimental data from which thermodynamic information was obtained are shown in Figure 2. The normalized ion intensities for C1- and DC1- (D = 1,4butanediol) as functions of ion source residence (reaction) time in Figure 2a show a constant ion current ratio iDcl-/icl- after 300 p s which extends beyond 3000 ps, suggesting the attainment of equilibrium for the C1- association reaction, reaction 1.
The equilibrium constant K1 can be calculated from the constant ion current ratio and the known diol concentration (pressure PO)in the ion source: lDC1- Po K 1 =-: n ‘C1- D ‘
I
cr
o.2 0.0 I
0
I
1000
0
2000
3000
Time (microseconds)
Figure 2. Normalized ion intensities as functions of ion residence time for (a) D C1DCI- (D = 1,4-butanediol,0.07 mol %), 2.6 Torr, 443 K; (b) D DC1- 2 DClD- (D = 2-butyne-1.4-diol.0.1 1 mol %), 2.7 Torr, 379 K.
+
+
*
The standard pressure Po is 760 Torr. The computed value of K Ifor a given sample at constant temperature was found, as required if it is indeed a true equilibrium constant, to be independent of ion source pressure for a given mixture and, in different samples, independent of the amount of diol within the narrow range of diol concentration that was available for experimentation. With increased diol concentrations, above those required for the study of the association of a first diol molecule, equilibrium constants could be measured for the formation of Cl--bound diol dimers. DC1-
+ D =DClD-
(3)
Po
~DCID-
K2=--
(4)
‘DC1- D ’
A typical plot of normalized ion currents for dimer formation, in this case for D = 2-butyne-l&diol, is shown in Figure 2b. Again, the constant ion intensity ratio after -400 ps implies the attainment of equilibrium in the reaction, and again this attainment was ascertained as described above. Equilibrium constants K1 and K2 as functions of temperature for the five diols studied are shown in the van’t Hoff plots of Figure 3. The standard enthalpy and entropy changes for each equilibrium, obtained respectively from the slope and intercept of the van’t Hoff plot, are shown in Tables 1 and 2. The 95% confidence limits for each value, obtained by linear regression, are given. A check on some of the data in Tables 1 and 2 was obtained by determining the equilibrium constants for several C1- transfer reactions (reaction 5) and diol exchange reactions (reaction 6) (Di and D2 are different diols). D,ClD,ClD;
+ D,=D, + D2C1-
(5)
+ D, == D,ClD;
(6)
-I- D,
Figure 4 illustrates the rapid attainment of equilibrium in a typical C1- transfer reaction. The thermodynamic data for reactions 5 and 6, which are presented in Figures 5 and 6,
Gas-Phase Association of C1- with a,w-Diols
J. Phys. Chem., Vol. 99, No. 30, 1995 11675
t
14
6
(a)
1.5
2.0
18 I
2.0
I
3.0 I
2.5
1.50
2 00
2.0
3.0
2.5
2 50
2.5 (1R) x lo'
16 I
I
2.0
1
1
2.5
3.0
3 00
3.0
K"
(1m) s Id K'
Figure 3. Van't Hoff plots for the equilibria D,Cl-
+D
D,+lCl-: D = (a) 1,2-ethanediol;(b) 1,3-propanediol;(c) 1,4-butanediol; (d) 2-butene-
1,Cdiol; (e) 2-butyne-l,4-diol.
TABLE 1: Thermodynamic Data for the Association of Diol 0) with Chloride: D C1- = DCl-
+
D
-
1,2-ethanediol 1.3-propanediol 1,4-butanediol 2-butene-1&diol 2-butyne-l,4-diol methanol' ethanolc 2(methan01)~ 2(ethan01)~
m
-AS"
a
25.3 f 1.0 28.3 f 1.7 30.2 f 1.7 32.9 f 1.5 28.9 f 1.1 17.4 17.6 31.1 33.7
29.1 f 0.3 34.0 f 0.7 42.6 f 0.7 44.4 f 0.5 36.7 f0.4 24.1 23.7 48.3 49.6
-AG02ga
-AGos~"
16.6 18.2 17.5 19.7 18.0 10.2 10.5 16.7 18.9
10.8 11.3 8.9 10.7 10.6 5.4 5.75 6.95 8.9
a kcal mol-'. bcal K-I mol-]. cData for solvation of C1- by one alcohol molecule, from ref 17. dData for solvation of C1- by two alcohol molecules, from ref 17.
TABLE 2: Thermodynamic Data for the Reaction W l D = W1.D-
+
E
Butsnediol.CI-
0.6 . 10.4
E
2 0.2
~
1 ButenedioLCI-
0.0 1 0
2000
1000
3000
I
Time (microseconds) Figure 4. Normalized ion intensities as functions of ion residence time for DICI- + D2 D I + D2Cl- (D1 = 1,4-butanediol,0.10 mol %; D2 = 2-butene-1,4-diol), 0.05 mol %, 2.5 Torr, 473 K.
~
D
-
1,2-ethanediol 1.3-propanediol 1,Cbutanediol 2-butene- 1,4-diol 2-butyne-1,4-diol kcal mol-'.
m
a
15.9 f 1.2 20.8 f 0.7 21.2 f 0.8 22.9 f 0.4 22.3 f 0.7
-20.8 (-36.2)
-AS" 22.1 f 0.6 36.2 f 0.3 35.4 f 0.3 37.3 f 0.2 34.7 f 0.3
-28.3 (-34.0)
CI-
cal K-'mol-'.
illustrate the consistency of the data in Tables 1 and 2 and confirm that the absolute values for the enthalpies and entropies of association in Tables 1 and 2 are probably well within their assigned confidence limits. Discussion The Bidentate Behavior of (%,@Diols. The behavior of a diol as a gas-phase ligand can be evaluated with reference to the hydroxyl-containing ligands, water, and the alcohols. Hiraoka and Misuze find that the enthalpies of binding of one to seven water molecules to C1- show a small but regular decline for each successive molecule, from 14.7 kcal mol-' for the first
P
t
.
C
I
-
h
P.CI.P-
i
-3.1 +/- 0.4 (-83+I- 0.2)
-2.3 +I- 0.1 (-4.8 +/- 0.1)
(-29.1)
E.CP
P.CI.E
-I
-3.4+I- 0.3
(-7.1+I. 0.2)
E.CI.E
-15.9 (-22.1)
Figure 5. Standard enthalpy (kcal mol-') and entropy (in parentheses, cal K-' mol-') values for C1- transfer and diol exchange reactions. The data with no attached confidence limits are from Tables 1 and 2. E = 1,2-ethanediol; P = 1,3-propanediol.
to 8.1 kcal mol-' for the seventh.17 These data are in reasonable agreement with those of other workers who have studied the association up to the fourth m o ~ e ~ u ~ The e . ~association * ~ ~ ~ of methanol molecules with C1- shows behavior similar too that of water; however, the two sets of published data for the
Zhang et al.
11676 J. Phys. Chem., Vol. 99, No. 30, 1995 -22.9 (-37.3) -32.9 (-44.4)
/
CI-'
\
-2.2 +/- 0.2 0.1) (-2.7 +/- 0.1)
-30.2
I
f
-1.7 +/- 0 4
BA.CI- A BA.CI.BA -21.2 (-35.4)
Figure 6. Standard enthalpy (kcal mol-') and entropy (in parentheses, cal K-I mol-') values for C1- and diol exchange reactions. The data with no attached confidence limits are from Tables 1 and 2. BA = 1,4-butanediol;BE = 2-butene-l,4-diol.
association of one to four methanol molecules are slightly different.'7.20 Because data for the association of one methanol molecule in ref 17 are in agreement with later data,2'.22all the data for methanol are considered to be the more reliable and will be used in all pertinent discussions; they were obtained with a pulsed electron beam, whereas those from ref 20 were not. The first and second methanol molecules have respectively enthalpies of binding 2.7 and 1.1 kcal mol-' greater than water, but the next five molecules have values identical with those of water. A first molecule of ethanol, surprisingly, binds only 0.2 kcal mol-' more strongly than a methanol molecule, but each successive ethanol binds 1-2 kcal mol-' more strongly than either water or methanol." The small differences between water and the two alcohols show how small a part polarization of the molecule beyond the hydroxyl group plays in the stabilization of the Cl-/molecule adduct. Theoretical calculations show that the interaction between a water molecule and C1- is mainly electrostatic with little charge transfer o ~ c u r r i n g . Although ~ ~ . ~ ~ the main interaction of C1- is with the acidic hydrogen which is bonded to oxygen, other hydrogens may participate to a small extent, for example, the second H in water and the alkyl hydrogens of alcohols. This is demonstrated by the small deviation from linearity of the 0-H. C1 group, which has computed angles of 162°24,25 for water and 163°26and 171°25for methanol. The nonlinearity of the group for water is accounted for in a newly developed interaction potential for Cl-sH20 that treats water using a foursite This shows an attractive C1-. * .O interaction due to an ion-induced dipole r-4 term which accounts for 18% of the calculated 12.32 kcal mol-' potential well. The Cl--bound dimer of methanol CH3OH. C1-** aHOCH3 is computed to have a linear H.* C1-- *Hgeometry with equal H* C1- distances of 2.29-8, and hence no direct participation of methyl hydrogens in the binding.26 This distance is increased only 0.03 8, compared with that in the monosolvated ion. The small increase may be in part due to the elimination of the weak interaction between C1- and the methyl hydrogens which is present in the monosolvated ion but not in the disolvated one. It must, however, be mainly due to the electrostatic nature of the binding in both complexes, with no significant electron-demanding covalent character. An a,w-alkanediol has an acidic hydrogen on each of its two oxygens, which allows the formation of an intramolecular hydrogen bond. There is little experimental information on the strengths of these hydrogen bonds. Knauth and Sabbah have described combustion and vaporization calorimetric studies from which they deduce that the intramolecular hydrogen bond enthalpies in the liquid phase for 1,2-alkanediols are -1 kcal mol-' .27 Traettenberg and Hedberg estimate, from electron
diffraction studies, the hydrogen bond in 1P-butanediol to be in the range 2.4-2.6 kcal mol-'.28 The most detailed information is provided by ab initio calculations. There are 27 possible conformers for 1,2ethanediol, most of which are degenerate. Of the 10 unique isomers, six are gauche and the remainder trans rotamers about r ~ ~ used very large the C-C bond. Cramer and T r ~ h l a have basis sets to obtain the energy of each of the isomers. Only the two lowest energy gauche rotamers are hydrogen bonded, the first non-hydrogen-bondedform being 1.3 kcal mol-' higher in energy and the rest, higher by -3 kcal mol-'. The trans isomers are all > 3 kcal mol-' above the energy of the most stable isomer and constitute only 2.4% of the isomer population at 298 K. These results are in accord with those from other c a l c u l a t i ~ n and s ~ ~also ~ ~ with experiments which find that there is no evidence for the presence of the trans isomers in the gas phase at ambient t e m p e r a t ~ r e . ~There ' . ~ ~ is a barrier of -6 kcal mol-' for rotation from gauche to trans?s3' which should prevent significant population of the latter form under the conditions of our experiments. No evidence was found in our work for the increasing presence of the trans form by, for example, a change in slope of a van't Hoff plot with increasing temperature. An assumed energy of 1 kcal mol-' to break the hydrogen bond in 1,Zethanediol would appear to be appropriate in this study. This value is significantly lower than the accepted 3-4 kcal mol-' for hydrogen bonds in oxygen-containing dimers of molecules such as water and alcohols33and may be too low for the higher alkanediols because of their increased ring size, which allows a stronger, more linear hydrogen bond and a lessening of the destabilizing C - 0 dipole-dipole repulsions. In the absence of definitive information on their hydrogen bond strengths the value of 1 kcal mol-' will be used for all the alkanediols. Only 1,Cbutynediol cannot form an intramolecular hydrogen bond. The length of the possible hydrogen bond in this molecule can be determined using standard bond lengths and angles and assuming a planar structure. It is found that the presence of the linear carbon chain leads to the impossibly large minimum 0--H distance of 4.9 8,. This is to be compared with the computed intramolecular hydrogen bond length of 2.2 8, in 1,2-ethanedi01.~ The two 0 - H groups of 2-butyne-1,4diol will be independently and freely rotating. It is anticipated that when a diol associates with C1-, both acidic hydrogens will participate, if the diol structure permits, and the hydrogen bond of the neutral will disappear. Proof that a diol behaves as a bidentate ligand is obtainable from comparison of the thermodynamic data for the diol with those for the association of two alcohol molecules. The latter data for methanol and ethanol from ref 17, presented in Table 1, show that the experimentally determined range of 25-32 kcal mol-' for the association of C1- with a diol is therefore considerably greater than for the association with one alcohol molecule and, for the most strongly bound (C4) diols, is equivalent to that for two. The diols must be behaving in the bidentate manner, the result being the formation of cyclic adduct ions. 1,CButanediol has only a slightly higher enthalpy of binding than 1,3-propanediol, but each has a measurably higher value than 1,2-ethanediol. This is superficially similar to the observations of their enthalpies of binding to the proton, 1,2-ethanediol having by far the lowest proton affinity. The major reason for this difference must be that, as for the protonated diols, increasing ring size in the adduct leads to a more favorable geometry with less strain and less bond-dipole-dipole repulsion. As noted earlier for the association of C1- with methanol and ethanol, polarization of the molecule does not appear to be
J. Phys. Chem., Vol. 99, No. 30, 1995 11677
Gas-Phase Association of C1- with am-Diols an important factor in determining the enthalpy of association. This favoring of larger rings might be offset to a small extent by the more favorable geometry in the larger hydrogen-bonded rings of the neutral molecules, leading to a stronger hydrogen bond, which is lost in the C1- adduct. We cannot, however, find any data, experimental or theoretical, on the relative strengths with increasing ring size of such bonds in diols. The largest enthalpy of association of a single diol molecule with C1- is that of cis-2-butene-1,4-diol. This is not surprising since the geometry of this diol with its planar carbon skeleton would be expected to favor bidentate behavior with formation of a complex not requiring, as maybe for the a,o-alkanediols, some restriction of rotational motion about the two central carbon atoms. The large enthalpy of association of 2-butyne1,4-diol, even somewhat larger than that of 1,3-propanediol,was initially surprising. Bidentate behavior is proven by this large value. A confirmation that this is consistent with the diol’s molecular structure may be obtained by a rough calculation. With standard bond lengths and angles and with a linear carbon skeleton, the calculated minimum distance between the two hydroxyl hydrogens in the planar neutral molecule of the diol is 4.2 A. Since the enthalpy of association with C1- is about twice that of a single methanol molecule, the H..C 1 distances in this adduct may be taken as 2.3 A, the computed value for the methanoVC1- adduct.26 Then for a planar structure and standard bond lengths, the H- C1. *Hangle is 86” and the center of the C1- is situated 2.9 A from the center of the triple bond. A deviation from planarity could increase the angle somewhat and bring the C1- closer to the triple bond, but the distance cannot be changed too much and still accommodate the C1radius of 1.7 A, the repulsion by the triple bond, and the measured large enthalpy of association, which implies Cl-H distances similar to those computed for the Cl--bound dimers of alcohols. However, in comparison with the saturated diols, the only geometrical requirement is the elimination of the free rotation of the 0 - H groups. There is no geometrical impediment to the bidentate behavior of this diol. Enthalpies of Cyclization of DCl-. The term enthalpy of cyclization was coined to interpret the thermodynamic data obtained from studies of protonated molecules which may form intramolecular hydrogen bonds. It gives a measure of the strength of the intramolecular hydrogen bond which “closes” the ring. Although the term was initially used in the discussion of the protonation of a p d i a m i n e s and is still mainly applied to protonation, it is useful in the present discussion. The experimental enthalpy change for the association of a diol with C1-, AWcyCllc, may be evaluated as the sum of the enthalpy changes for three steps: (1) M o b the breaking of the hydrogen bond in the neutral diol, (2) AWDthe association of C1- with one of the hydroxyl hydrogens, and (3) A W c y c l i c the formation of the cyclic structure by association with the second hydroxyl hydrogen.
(7) As discussed previously, m b may be taken as 1 kcal mol-’ for each of the diols. = -17.5 kcal mol-’, the enthalpy of association of a single molecule of methanol or ethanol with C1-. This value could be a little too negative since computation shows that C1- interacts with both the hydroxyl and the alkyl hydrogens of methanolz6and, if this is the case, almost certainly interacts with the ethyl group in ethanol. The computed enthalpies of cyclization are (kcal mol-’) 1,2-ethanediol -8.8; 1,3-propanediol, -1 1.8; 1,4-butanediol, -13.7; 2-butene-1,4diol, - 16.4; and 2-butyne-1,4-diol, - 11.4. The maximum value expected for .4HocyC~icis the enthalpy of association of a second M
O
D
alcohol molecule to a alcoholC1- complex since the resultant ion has a linear H- C1-* *H geometry with no strain energy or steric interference. The average experimental value for association of a second methanol or ethanol is 15:l kcal mol-’. Therefore, among the alkanediols, 1,4-butanediolhas almost the maximal and, presumably, optimal interaction with C1-. 1,3Propanediol has a slightly lower value, and 1,2-ethanediol has a significantly lower value, presumably because of geometrical constraints attributable to the smaller ring size of the adduct. These constraints are certainly much less than those encountered in the cyclization engendered by protonation when the enthalpy of cyclization of this diol is only 20% of the maximum value, and the maximum enthalpy of cyclization is not attained in a,wdiols until the ring contains four carbon atoms.” There are several reasons for this difference in the effect of diol size on cyclization enthalpy between C1- association and protonation. In the first place, a cyclic structure containing n 3 atoms ( n = diol carbon number) is formed upon protonation, whereas the C1- participates in a cyclic structure containing n 5 atoms. A larger ring size implies a more stable structure with less strain. More importantly, the proton is mainly covalently bound and has a directional bond with oxygen. Maximum hydrogen bond strength can be attained only when the hydrogen bond to the second oxygen is collinear with the first O-H.’2-’3 Although the Cl--bound dimer of methanol is computed to have a linear H- Cl-*Hgeometry,26the potential energy change with respect to bending is probably very small, and a collinear geometry is probably not necessary for maximum enthalpy of cyclization in the diolC1- complex. This has been found to be the case for the water hydrates of F-, the computed binding enthalpies of which for one to three water molecules show that “(the notion of) optimal geometry has little meaning”.34 Preliminary ab initio calculations do indeed show that the 1,2-ethanediolC1- complex has an H. C1- *Hangle of 69°.35 The geometrical requirements are small for the mainly electrostatic interaction between the electrically centrosymmetric C1- and the hydroxyl dipoles, and the structural geometry will be govemed mainly by energetic considerations, a linear geometry being preferable, as in the C1-bound alcohol dimer and the higher a,w-alkanediols, but not at the expense of the introduction of significant strain energy in the cyclic structures formed with bidentate ligands such as the diols. 2-Butene- 1,4-diol has the most negative entropy of cyclization, presumably by being able to accommodate C1- with the least molecular strain of all the diols, while retaining its planar carbon structure. The value is, within experimental uncertainty, equal to the expected maximum. When the carbon chain is linear in 2-butyne- 1,4-diol, the cyclization enthalpy decreases considerably. Further Solvation. As expected, the enthalpy change for the association of a second molecule of diol is considerably less negative than that for a first (Tables 1 and 2). Surprisingly, the decrease is most marked for 1,2-ethanediol, whose binding enthalpy is only 60% as large as for the first molecule even though steric hindrance is expected to be least for this smallest diol; for the other diols it is about 70%. That both diol molecules in the complex are acting as bidentate ligands is proved by comparing the data with those for the alcohols shown in Table 3. The enthalpy of association of dissolvated C1- with a further two methanol molecules is 72% of that of the first two, and the analogous value for ethanol is 74%. Both these values and the near equivalence of the enthalpies of association with C1- of two molecules of diol with four molecules of alcohol speak for the formation of almost strain-free structures by the
+
+
-
11678 J. Phys. Chem., Vol. 99, No. 30, 1995
Zhang et al.
TABLE 3: Free Energies of Association of C1- with Four Alcohol or Two Diol Molecules molecule -AG0298' -AG"sw" 1,2-ethanediol 25.9 15.6 1,3-propanediol 28.2 14.0 1,4-butanediol 28.2 12.4 2-butene-1,4-diol 31.5 14.9 2-butyne-1$diol 30.0 15.5 methanol 25.7 6.65 ethanol 27.2 6.05 a
kcal mol-I.
TABLE 4: Entropy Changes (cal K-l mol-') for the Association Reaction D C1- = DCl-
+
1,2-ethanediol 1.3-propanediol 1,4-butanediol 2-butene-l,4-diol 2-butyne-1,4-diol
-29.1 -34.0 -42.6 -44.4 -36.7
-37.6 -37.8 -38.0 -38.0 -38.0
+3.4 +2.9 +2.0
+
f5.1 f1.0
+2
-6.6 -8.5
+3.9
-2.7
Data calculated for 470 K.
higher diols. The only exception is 1,2-ethanediol, with significantly lower binding enthalpies for both one and two molecules. Entropy Changes. The experimentally measured entropy change ASoexpt which accompanies an iordmolecule reaction may be discussed in terms of statistical thermodynamics when the assumed separation of the energies of translation, vibration, and rotation allows independent computation of their individual contributions to the total entropy change.
+
ASoexpt= ASotrans As",,, 4-AS",,, The computed values of AS'trans, AS'vib, and AS',,,, are temperature dependent, while, within experimental accuracy, ASoexptis temperature independent over the experimental range studied. For purposes of comparison of experiment with theory for the formation of DC1-, the most appropriate temperature is 470 K, roughly the midpoint of the range of reciprocal temperatures of the van't Hoff plots. The formation of DCl- by the association of two particles is accompanied by a large decrease in entropy as three translational modes are replaced by intemal modes. The contribution of translational changes to the change in total entropy, ASotrms,is accurately calculable by the Sackur Tetrode equation. The results are presented in Table 4. The accurate calculation of hS",ib and ASorOtrequires knowledge of the rotational and vibrational levels of reactants and products, which are at present not available. Some insight into the association of C1- with an OH-containing molecule can be obtained from the work of Truhlar and c o - w o r k e r ~who , ~ ~ have modeled H2OC1-, the ion formed by the association of water with C1-. They found that the loss of translational modes in the formation of H20C1- leads to the appearance of three new low vibrational frequencies between the participants at -700, 275, and 155 cm-I. There are only small changes in the other frequencies of the water molecule following association, and these cannot make any contribution to the change in entropy. From the information provided in ref 24 for H20Cl-, we compute for this complex ASotrans -I- AS"vib f AS",,, = -34.5 4.6 -I-9.4 = -20.5 cal K-' mol-' at 370 K. This is in excellent agreement with the experimental value of -19.2 cal K-' mol-' obtained from a van't Hoff plot with a midpoint of the range of reciprocal temperatures of 370 K.17 AS",,,, which encompasses only the difference in extemal rotation between the C1- complex and the neutral molecule,
+
should be much smaller for the diols than for water because the ratio of moments of inertia will be much less. AS",,, = 3.4 cal K-' mol-' has been estimated for 1,2-ethanediol using a preliminary, ab initio structure.35 AS",,, can be estimated with some confidence for another of the diols, 2-butyne-1,4-diol, because of the geometrical limitations imposed by the linear carbon structure. Using accepted bond lengths and angles and an 0 C1 distance of 2.3 A, the calculated value of AS",,, is 3.9 cal K-' mol-'. The values for the other diols are estimated to be positive but less than that of 1,2-ethanediol, with assumed values of 2.9 kcal mol-' for 1,3-propanediol and 2 kcal mol-' for 1,4-butanediol. These values are shown in Table 4. The difference between ASoexpt and AS",,, ASorOt is hSovlb, which is shown in the last column of Table 4. The association of C1- with the heavier, bidentate diols compared with that of the essentially monodentate water will lead to lower frequencies for the three new vibrations of the complex and hence to a higher ASovlbthan for water. The increase in reduced mass from water to diol suggests that the expected new frequencies in the diol adducts would be roughly 25-50% lower than those for the water adduct. At the same time the vibrational or torsional low frequencies associated with the intemal hydrogen bond of the neutral diol are modified by changes due to expansion of the ring when hydrogen is replaced by C1- as the link in the adduct. This might be especially marked for l,Z-ethanediol, which has the smallest ring and therefore the greatest ring expansion. The saturated diols show an increasing negative value of ASov,bwith increasing carbon number. The significantly positive value for 1,2-ethanediol implies a relaxing of the constraints of the fivemembered ring of the neutral when the seven-membered C1complex is formed. The negative value for 1,Cbutanediol indicates a loss of some torsional motion of the carbon chain when the complex is formed since it would be expected that what was probably the strongest hydrogen bond of any of the neutral diol molecules would have the lowest entropy contribution of all the saturated diols. This limited restriction of the torsional motions could be due to dipolar interaction between the C1- and the C-H bonds of the central methylene groups. The unsaturated diols show behavior different from the alkanediols. 2-Butyne-1,Cdiol has a very small ASov,b,and since there is no hydrogen bonding in the neutral, the entropy of all newly introduced vibrations and torsions must almost exactly balance the lost free rotations of the two OH groups. This difference is contained in Asovtb. The entropy of a freely rotating OH group at 470 K is -5 cal K-' mol-',36 and hence ASov,b= -2.7 cal K-' is composed of - 10 cal K-I mol-' for the loss of the internal rotations and +7.3 cal K-I mol-' for the formation of the five new modes. The average entropy of each of the new modes is then 1.5 cal K-' mol-', corresponding to an average vibrational frequency of 350 cm-' at 370 K, a not unreasonable value. The other unsaturated diol, 2-butene1,4-diol, has the largest ASovlb,which is somewhat surprising but in line with its high enthalpy of association. An ab initio calculation of this system is warranted. Solvation of C1- by Alcohols and Diols. The standard free energies at 298 K and 500 K for the association of one and two diol molecules and one, two, and four alcohol molecules are presented in Tables 1 and 3 to illustrate the solvating abilities of the different diols and the alcohols. The enthalpies of association of one and two molecules of 1,2-ethanediol with C1- are significantly lower than those of the other diols; the associated entropies, however, are also much smaller. This has consequences when the effect of temperature on the solvating powers of the diols is considered. The free energies of association of C1- at 298 K with one diol molecule favors
Gas-Phase Association of C1- with a,o-Diols solvation by the higher diols, but at 500 K the association with one diol molecule is less dependent on the particular diol. 1,2Ethanediol is favored at 500 K over all except 2-butyne-1,4diol when solvation by two diol molecules is considered. Surprisingly, the least favored diol at 500 K for both monoand disolvation is 1,Cbutanediol, its large entropy decrease for adduct formation being the major factor. It is to be noted that at 298 K the free energies of association with C1- of two and four methanol molecules are essentially identical with those for one and two 1,2-ethanediol molecules, respectively. A fortuitous difference in enthalpy matches the exceedingly large entropy differences. At 500 K the entropy term dominates and association with diol is strongly favored. Acknowledgment. The authors thank the Natural Sciences and Engineering Research Council of Canada for continuing support. References and Notes (1) Kebarle, P. Ann. Rev. Phys. Chem. 1977, 28, 445. (2) Keesee, R. G.; Castleman, A. W. J . Phys. Chem. Re$ Data 1986, 15, 1011.
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