3359
Gas Phase Ion Equilibria Studies of the Hydrogen Ion in Wa ter-Dime thyl Ether and Me thanol-Dime thyl Ether Mixtures K. Hiraoka, E. P. Grimsrud, and P. Kebarle" Contribution f r o m the Chemistry Department, University of Alberta, Edmonton, Alberta, Canada. Received December 18, 1973
Abstract: G a s phase ion equilibria involving clusters W,E,H' and M,E,H+, where W, M and E are water, methanol and dimethyl ether molecules, were measured with a high-pressure pulsed mass spectrometer. The temperature dependence of the equilibrium constants for equilibria of the types W,EH+ E = W,EzH' (addition) and MmEeH+ E = M,-lE,+l M (exchange) permitted evaluation of the corresponding AGO, AH', and ASo changes. Data involving many possible combinations of W and E and M and E were obtained for a total of up t o five molecules in the cluster. These detailed results can be utilized in several ways. The proton affinity difference between E and W was determined t o be 23 kcal/mol by means of thermodynamic cycles involving mixed clusters. The proton affinity difference of 9 kcal/mol between E and M was determined by direct proton transfer and thermodynamic cycles involving mixed clusters. Comparing clusters of the types W,EH+ and W,WH+ one finds that the difference between their basicities decreases rapidly with increase of n. These results suggest that the basicity of W might be higher than that of E in aqueous solution. The decrease of relative basicity of the cluster W,EH+ is due t o two factors: weaker hydrogen bonding of W t o EHT and removal of two H bonding positions by the methyl groups present in E. The energy changes observed o n build-up of clusters like W,E,H+ and M,E,H' show that hydrogen bonding is dominant. Clusters where the last molecule cannot hydrogen bond since all positions are blocked by methyl are very unstable. The preference for the more methyl substituted molecule decreases with cluster size. More energy is released if the incoming molecule can hydrogen bond t o a position close t o the (expected) location of positive charge.
+
+
+
a s phase ion equilibria studies c o m p a r i n g the reactions
G
+ + +
H+(HzO)n = HT(HzO)n- 1 Hz0 H+(CH30H)n = H+(CHsOH)n- 1 CHsOH H+(CHsOCH,)n = H+(CH30CH3)n- 1 CHaOCH3 were published recently.
T h e s e studies s h o w e d t h a t
the stabilities of t h e proton h e l d d i m e r s B2H+ were B deq u i t e similar, the AGO f o r dissociation t o BH+ creasing slightly i n the o r d e r B = HzO, C H 3 0 H , (CH& 0. T h e p r o t o n a t e d water a n d m e t h a n o l species c o u l d f o r m s t a b l e clusters c o n t a i n i n g m o r e than t w o molecules. In c o n t r a s t , the (CH30CH&H+ and higher e t h e r clusters were very unstable. This confirmed t h e expected i m p o r t a n c e of h y d r o g e n bonding. S t u d y of equilibria of t h e higher clusters of p r o t o n a t e d w a t e r and m e t h a n o l indicated that s o m e structures like the sym-
+
m e t r i c s t r u c t u r e H 3 0 + ( H 2 0 ) 3 h a v e s o m e w h a t higher stability. T h i s s h o w e d that in H b o n d e d structures a s y m m e t r i c build-up of molecules around a center (a p r o t o n o r a p r o t o n a t e d molecule) leads to greatest stability. The present w o r k deals with mixtures of w a t e r and dimethyl e t h e r and m e t h a n o l and d i m e t h y l ether. In mixtures of water a n d d i m e t h y l e t h e r t h e clusters H+(H20),(CH30CH3), are observed i n equilibria w i t h w a t e r and d i m e t h y l e t h e r molecules. M i x t u r e s of m e t h a n o l and dimethyl e t h e r l e a d to t h e observation of the mixed H + ( C H 3 0 H ) , ( C H 3 0 C H 3 ) , species. S t u d y of these equilibria as a f u n c t i o n of t e m p e r a t u r e leads to d e t e r m i n a t i o n of AGO, A H " , and A S o f o r dissociation and exchange reactions of t h e t y p e s h o w n below. H+(CHIOH),(CH~OCH~)~ = H+(CH3OH),(CH30CH3),-
1
+ CHBOCH~
(1) E. P. Grimsrud and P. Kebarle, J . Amer. Chem. SOC.,95, 7939 (1973).
+
H+(CH3OH),(CH30CH3), CH30H = H+(CH30H)n+i(CH3OCHa)e- 1
+ CH30CH3
The t h e r m o d y n a m i c quantities o b t a i n e d provide inf o r m a t i o n on stability changes with c o m p o s i t i o n of t h e cluster, effect of h y d r o g e n b o n d i n g , c h a n g e s of basicities of m e t h a n o l and dimethyl e t h e r i n t h e presence of water molecules, and o t h e r related properties. Experimental Section The high-pressure ion source mass spectrometer with which the measurements were done was described ear1ier.l Only a brief account of the procedures followed will be given here. Methane buffer gas at a pressure of 4 Torr containing known amounts of water (130-320 mTorr) and dimethyl ether (2-8 mTorr), for water-dimethyl ether system, and of methanol (160-300 mTorr) and dimethyl ether (6-30 mTorr), for methanol-dimethyl ether studies, was passed (-1 m/sec-1 measured at STP) through the thermostated ion source. The 2000-V ionizing electron beam ( 5 X 10-8 A) was pulsed "on" for 150 psec and off for 2-4 msec. The ions escaping from the field free ion source into an evacuated region were magnetically mass analyzed and collected in a multichannel analyzer as a function of their arrival time after the electron pulse. A good temporal profile for ions of a given mass can be obtained after some lo4 electron pulses. The ratios of the ion intensities become constant some 100 psec after the electron pulse. These constant ratios were assumed equal to the ion concentration ratios at equilibrium. Experiments at elevated ion source temperatures were made by heating the ion source block with an electrically heated jacket. Experiments below room temperature were made with an ion source of otherwise identical dimensions but with channels in the ion source block through which a cooling liquid (ethanol) was circulated.
Most measurements were done at a single solvent pressure. Occasional checks were made in which a variation of the solvent pressure by a factor of 10 led to an equilibrium constant differing by less than 20%. (2) A. J. Cunningham, J. D. Payzant, and P. Kebarle, J. Amer. Chem. SOC.,94,7627 (1972).
Hiraoka, Grimsrud, Kebarle / H+ in H 2 0 - C H 3 0 C H 3and C H ~ O H - C H S O C H ~
3360 1 0 4 ~ , ,,
,
I
,
I
,
,
, , , , ,
I
_ , , , , ,
,
, , 4
1000/T["K)
1000/ T ( O K ]
Figure 1. Van't Hoff plots for water (W) and dimethyl ether (E) equilibria: WwEeH+ E = WwE,+lHf or W,E,H+ W = W,+lEeH+. The Van't Hoff lines are identified by the subscripts corresponding to number of water and dimethyl ether molecules 1) in ion on left and right side of equation, i.e. (w, e -+ w , e and (w,e w 1, e ) for the above two equations.
-+-
-
+
Figure 3. Van7 Hoff plots for methanol (M) and dimethyl ether (E) equilibria of type M,E,H+ E = M,E,+,H+ and M,E,H+ M = M,+lEeH+. Van't Hoff lines identified by the same notation as used in Figure 1.
+
+
+
io3 IO4
+
r t
10-1
20
30
40
lCCO/T(°K)
Figure 2. Van? Hoff plots for water (W) and dimethyl ether (E) exchange reactions of the type W,E,H+ E = W,-lE,+lHe W. Van't Hoff lines identified by the same notation as used in Figure 1.
+
Figure 4. Van't Hoff plots for methanol (M) and dimethyl ether (E). Exchange reactions of the type M,E,H+ M = M,+lE,-lH' E. Van't Hoff lines identified by the same notation as used in Figure 1.
+
+
-+
Results and Discussion (1) Results. The experimentally obtained Van't Hoff plots for the water-dimethyl ether mixtures and methanol-dimethyl ether mixtures are shown in Figures 1-4. The corresponding AG, A H , and A S values are summarized in Figures 5 and 6 and Tables I and 11. Included are results obtained earlier for the pure protonated water,2 methanol, and dimethyl ether clusters. Some of the values shown in Figures 5 and 6 are marked by an asterisk. Such values were obtained not by direct measurement of the equilibrium but by the application of thermodynamic cycles. This was necessary when the direct measurement of the equilibrium was difficult. An interesting example of such a situation is given in the following section. The thermodynamic data obtained from direct equilibria measurements are amenable to cross checks by application of thermodynamic cycles. As can be verified in Figures 5 and 6 the AGO values in most cases do cancel within 1 kcal for a complete cycle. The direct measurements in general involve different conditions of concentration and temperature such that thermodyJournal of the American Chemical Society
4
96:11
namic consistency is not automatic. The errors observed in cycles involving the A H and A S data, Table I, are generally larger. They reflect the larger uncertainty of these determinations, particularly in cases where the temperature interval covered was comparatively narrow. (2) Proton Affinity Differences between Water, Methanol, and Dimethyl Ether. Shown in Figures 5 and 6 are the AG" values for the proton transfer W --t E and M 4 E, corresponding to reactions 1 and 2. AGIO =
23.3 kcal/mol was obtained indirectly following the path I outlined in Table 111. A partly independent path 11, Table 111, leads to 22.3 kcal. Values for AG20 can be obtained from the direct determination of K2 since the basicity difference between methanol and dimethyl ether is much smaller. In addition to the direct value of 8.7 kcal/mol a number of indirect values can be obtained. Thus paths IV-VI, Table 111, lead to values of 9.3, 9.1, and 8.7 kcal/mol. Munson3 has summarized available proton affinities of oxygenated compounds, The "best values" given:'
May 29, 1974
(3) J. Long and B. Munson, J. Amer. Chem. Soc., 95,2427 (1973).
3361
Figure 5. Free energy changes for addition and exchange reactions of protonated clusters containing water (W) and dimethyl ether (E) molecules. The value in parantheses gives -AGO300 (kcal/mol) for the reaction leading from one to the other cluster. The proton is omitted from the clusters. Example: W1 + Wz (24.3) means AGO = -24.3 kcal for reaction WIH+ W = WzH+. Values with a star were obtained indirectly from cycles involving directly measured values. Standard state 1 atm. Values from ref 1 and 2 have "a" as a superscript.
Figure 6. Free energy changes for addition and exchange reactions of protonated clusters containing methanol (M) and dimethyl ether (E) molecules. Same conventions used as in Figure 5. Values fromref 1 and 2 have "a" as a superscript.
+
Table 11. Thermochemical Data from Protonated Mixed Clusters in Equilibria (Methanol and Dimethyl Ether)" Reaction
Table I. Thermochemical Data from Protonated Mixed Clusters in Equilibria (Water and Dimethyl Ether)" Reaction
-AH"
-ASo
-AGO
(1) Addition Reactions WEHT E = WEzH+ 18.5 i 2 10.7 i 2 8.9 i 1 WEzH+ E = WE3H+ 16.8 i 1 9.6 i 1 WzEH+ E = WzEzH- 16.4 i 1 WzEzHE = WzEzH+ 1 5 . 8 i 1 4.9 i 1 W3EH+ E = W3EzH+ 16.9 f 1 7 . 1 zt 1 14.6 f 1 EH+ W = WEH+ 22.6 i 1 WEH+ W WzEH+ 15.3 i 1 7.5 i 1 WzEH+ W W3EH+ 13.8 i 1 6.2 i 1 W3EH+ W = WaEH+ 10.2 i 2 4.5 i2 EzH+ W WEzH+ 16.3 i 1 4.7i1 6.3 i 1 WEzH+ W = WzEzH+ 13.6 f 1 WzEzH+ W = 11.6 i 1 3.611
+
+ + + + +
+ + + + + + + W3EzHA
W I E ~ H ++ W WzE3H+
+ + +
=
WEH+ E = EzH+ W WzEH+ E = WEzH+ W WaH+ $- E = W3EH+ W W3EH+ E = WzE*H+ +W WzEzH+ E = WE3H+ W WbH+ E = WaEH+ +W W4EH+ E = W3EzH+ W W3EzHt E = WzEaH+ W
+ + + + + + + + + +
11.4
1
2.4f 1
(2) Exchange Reactions 6.8 i 0.5 6.5 i0.5
26.3 i 4 26.6 i 2 22.8 i 2 36.5 i 3 32.9 i 2 26.5 i 1 26.3 i 2 25.4 zt 2 19.0 i 6 38.8 i 2 24.6 i 2 26.8 i 3 30.3 i 3
1.0f 0.5
5.0 i 1
3 . 5 5 ~1
5.1 i 1
5.9 i 1
5.0 i 1
2.9 i 2
4.8 i 0.5
3.6 f 0 5
4.0 f 1
3.4 i 0.3
2.6 i0.5
2.4 i 1
5.2 i 1.0
3.7
1
5 . 0 3 ~3
4.8 f 1
2.7 i 1
7.0 i 2
4.4 i 1
1.3 i 1
10.5 f 3
f
All values are in kcal/mol, AG" values for 300"K, A S o in eu, standard state 1 atm. Only data from directly measured equilibria are shown. Data for related reactions can be obtained from thermodynamic cycles as shown in Figure 5 and Table 111. a
are: PA(H20) = 165 f 3, PA(CH30H) = 182 f 3, and PA(CH30CH3) = 190 f 5 kcal/mol. The differences between these values give 25 for reaction 1 and 8 kcal/mol for reaction 2 with a probable error of some 5 kcal. This is close to the average values of about 23 and 9 kcal shown in Table 111. It should be noted that
-AH"
-AG"roa
(1) Addition Reactions 35.0 i 2 27.6 f 2 20.2 i 0 . 5 11.3 f 1 21.9 f 0 . 5 14.4 i 1 16.6 i 0 . 5 7.1 i 1 17.2 f 0 . 5 8.7 f 1 12.5 f 0 . 5 4.8 f 1 15.3 f 0 . 5 5.9 i 1 26.3 i 0 . 5 18.2 i 1 18.8 zt 0 . 3 10.2 i 0 . 5 15.9 f 0 . 3 6.6 i0.5 13.7 f 0 . 3 4 . 5 zt 0 . 5 18.1 f 0 . 4 9.0f 1 15.1 f 0 . 4 6.0 f 1 12.2 i 0 . 2 4.3 f0.5
+ + + + +
MH+ E = MEH+ MEH+ E = MEzH+ MzH+ E = MzEH+ MzEH' E MzEzH+ M3H+ E = M3EH+ M3EH+ + E = MaEzH+ MaH+ + E = M4EH+ EH+ M = MEH+ MEH+ M = MzEH+ MzEH+ M = M3EH+ MaEH+ M = MdEH+ EzH+ M MEzH+ ME2H+ M MzEzH+ MzEzH+ M = MaEzH+
+
+ + + + + + +
MH+ E = EH+ MzH+ E = MEH+ +M MiEiH+ E = EzH+ M M3H+ E = MzEH+ M MzEH+ E = MiEzH+ +M MdH+ E = MIEH M E = MsEH' MzEzH+ M MzEzH+ E = ME3H+ M MjH+ E = M4EH+ M MaEH+ E = MaEzH+ M
+ + + + + + + + + + + + + + + +
-ASo 24.7 f 3 29.8 f 2 25.2 i 1 31.8 i 2 28.6 i 1 25.6 i 2 31.5 i 2 27.1 i 1 28.9 zt 1 31.2 i 1 30.8 i 1 30.6 i 1 30.6 i 2 26.5 i 1
(2) Exchange Reactions 7.6 f 1 8 . 7 i 0 . 7 -3.9 i 1 3.6 i0.2 4 . 4 zt 0 . 2 - 2 . 8 i 1
+M
2.9 f 0.2
2.6 f0.2
1.0i 1
2.2 i0 . 2
2 . 3 i0.2 -0.4 f 1
1.4 f 0.2
1.2 f 0.2
0.9 i 1
1.6 i0.2
1 . 4f 0.2
0.6 i 1
0 . 9 i0.2
0.5 f 0.2
1.4 f 1
-5.7b 1.8 f 0.5
1.0 i0.5
2.7 i 1
0.0 i 0 . 5
0 . 3 i 0 . 5 -0.8 f 1
a All energy values are in kcalimol, AGO values for 300"K, AS' in eu, standard state 1 atm. Only data from directly measured equilibria are shown. Data for related reactions can be obtained from thermodynamic cycles as shown in Figure 6 and Table 111. Value obtained by measurements at a single temperature (300°K) using 4 Torr of dimethyl ether. The signal from the ME3H+cluster was only slightly above noise level. Assuming possible error due to background AGO for reaction ME2H+ + E = ME3H+probably larger than +5.7 kcal/mol.
the proton affinities quoted in the literature are often obtained by a bracketing technique involving gaseous proton transfer reactions. More recently proton
Hiraoka, Grimsrud, Kebarle
H+ in H20-CH30CH3 and CH30H-CH30CH3
3362 Table 111. Thermodynamic Data for Proton Transfer Reactions
between Water, Methanol, and Dimethyl Ethera (1) (CH&OHr
+ HBO = (CH3)zO + HaO+
Path of thermodynamic cycleb
(2) (CH8)zOH-
(111) (IV) (V) (VI)
AGiO.
AHi".
kcal/ mol
kcal/ mol
AS,'. eu
+ CH8OH = (CH8)rO + CHaOHz-
El, Mi El, MiEi. Mi Ei, Ea, MiEi, Mz, MI El, EQ,MIEB.MzEi, M B . Mi
A G O ,
AH,',
kcal/ mol
kcal/ mol
ASB', eu
8.7 9.4 9.1 8.7
7.6 8.7 8.9 7.6
-3.9 -2.4 -0.9 -3.6
a Data obtained from Figures 5 and 6, Tables I and 11, and ref 1. Values of AGO at 300"K, all energies in kcal/mol, A S in eu, standard state 1 atm. * For notation used see Figures 1 , 5 , and 6.
transfer ion equilibria have also been sed.^-^ In both of these cases one obtains values corresponding to AGO for proton transfer. These are assumed t o be close to the AHo values since the entropy change of the proton transfer reactions is generally small,6 i.e., around 1-3 eu. The bracketing technique and the equilibrium technique depend on proton transfer studies involving many compounds with similar proton affinities such that each proton transfer step involves a relatively small AG change. The proton affinity difference between water and dimethyl ether of 23 kcal obtained in the present results also involves many steps since the direct measurement of the equilibrium constant Kl is not possible. In the present case the intermediate compounds are mixed clusters whose proton affinities change more gradually. We do not think that the present technique necessarily gives more accurate results. The relatively good agreement with the literature data might also be due to fortuitous cancellations of errors in the values shown in Figure 5 . Nevertheless, it is significant that the present completely independent determinations are close to those obtained by other methods. Obviously, the much lower AG and AH values obtained by Bennett, Beggs, and Field7 for the H+(H20)?and H+(H20)3formation (W, + Wp W,) hill not lead to proton affinity differences in agreement with literature data3 when substituted in the thermodynamic cycles of Figure 5 or 6. The A H and A S values for reactions 1 and 2 can also be obtained from the present determinations. Unfortunately, the Van't Hoff plots for the clusters containing water and dimethyl ether were taken over a rather narrow temperature range. Furthermore, because of the large proton affinity difference between these two compounds several of the equilibria were difficult to measure. For this reason the A H and particularly the A S values are less reliable. The two
-
(4) M. T. Bowers, D. H. Aue, H. M. Webb, and R. T. McIver, Jr., J . Amer. Chem. Soc., 93, 4314 (1971). (5) E. M. Amett, F. M. Jones 111, M. Taagepera, W. G. Henderson, D. Holtz, J. L. Beauchamp, and R. W. Taft, J . Amer. Chem. Soc., 94, 4724 (1972). (6) J. P. Briggs, R. Yarndagni, and P. Kebarle, J . Amer. Chem. Soc., 94, 5128 (1972). (7) D. P. Beggs and F. H . Field, J . Amer. Chem. Soc., 93, 1567 11971). F. H . Field and D. P. Beggs. ibid., 93, 1576 (1971); L. Bennett and F. H. Field, ibid., 94, 5186 (19fj).-
major cycles available for AHl and ASl give for the enthalpy 22.8 and 18.7 kcal and the entropy -1.8 and -7.2 eu. We believe the first value to be more reliable since A S is expected t o be small. More consistent results are obtained for the proton transfer from dimethyl ether to methanol. The values for several paths are summarized in Table 111. The AH values are between 7.6 and 8.9 kcal, while the A S values are in the range - I to -3.9 eu. (3) Changes of Basicities of Methanol and Dimethyl Ether with Increasing Hydration. A number of interesting relationships can be observed from a study of the data shown in Figures 5 and 6. One of these is the change of basicity of methanol and dimethyl ether with increasing hydration. As discussed in the preceding section, the basicities (or proton affinities) increase in the order H 2 0 , C H 3 0 H , and (CH3)20. This is a consequence of the stabilizing effect of the methyl group on the positive charge in the protonated species. The basicity order in aqueous solution has been difficult to determine.6 Data from Figure 5 corresponding to the reaction H+W, E = H+EW,-l W are shown below.
+
H-W
+
+ E = H+E + W
H"W2 + E HCW3 E H'W? E H-W, E
+ + +
= = =
=
H+EW + W H-EW:! + W H+EW3 + W H'EWA + M.'
- 23
-13 3 -7 8
-5 0 -3 7
The G o values (kilocalories per mole) demonstrate that the exothermicity in replacing a water by an ether molecule decreases progressively with increasing water content in the cluster. This means that the greater basicity of ethanol rapidly decreases with increasing water content of the cluster. An extrapolation of the present results to aqueous solution is not possible; however, the rapid fall off of the values does suggest that the ether is probably a weaker base than HOH in aqueous solution. The reasons for the rapid decrease of basicity of the ether with water content are probably twofold. A big decrease is observed already between the first and second proton transfer reaction (W, E) and (W2, WE). This decrease cannot be due to steric blockage of hydrogen bonding by the methyl groups since steric effects probably play only a minor role in the stability of the EWH-. The initial decrease from 23 to 13.3 kcal should be due to the fact that the stabilizing charge dispersion caused by the methyl groups in EH+ makes the additional stabilization by one water molecule less important than is the case for WH+. Earlierg l o we had observed that the strength of hydrogen bonding in charged species increases with the acidity of the proton donor and basicity of the proton acceptor. Applying this to the present hydration reactions (EH+ W = WEH+ and WH+ W = W2H+),we conclude that the smaller energy release in the first reaction is due to the lower acidity of EH+ when compared with WH+. Thus, the higher basicity of E relative to W automatically reduces the energy gain of the hydration reaction.
+
+
(8) E. M.Arnett, Progr. Phys. Org. Chem., 1,223 (1963). (9) R. Y a m d a m i and P. Kebarle, J . Amer. Chem. Soc., 93, 7139 (1971). (IO) J. D. Payzant, A. J. Cunningham, and P. Icebarle, Can.J. Chem., 51,3242 (1973).
Journal of the American Chen~icalSociety 1 96.11 / May 29, 1974
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3363
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