J. Phys. Chem. 3980, 84, 307-309
907
Proton Solvation in the Lower Aliphatic Alcohols with Emphasis on Isopropyl Alcohol and fert-Butyl Alcohol R. De Lisi,' M. Goffredi, and V. Turco Liveri Istkuto di Chimica Fisica, Universita' di Palermo, 90123 Palermo, Italy (Received April 11, 1979; Revised Manuscript Received September 25, 1979) Publicatlon costs assisted by C.R.R.N.S.M.
The purpose of this paper is to show that the proton transfer mechanism in aprotic solvents is different frlom that in amphiprotic solvents. The hypothesis that in more bulky alcohols the anomalous proton transfer mechanism cannot occur is refuted, It is also clarified that the presence of small amounts of water in alcohols can give an erroneous evaluation of some physical parameters of acids such as conductivity, association constant, and solubility. In a recent piaper' C h a n h n i and Kolthoff have reported the hoof some acids and salts in 2-propanol (2-PrOH), tert-butyl alcohol (t-BuOH), and 1-hexanol (1-HexOH). From these results and the additivity rule, they have calculahd XoH+ in 2-PrOH and in t-BuOH, obtaining values very different from the l i t e r a t ~ r e . The ~ ? ~arguments used by the authorri to conclude that the literature values are abnormally large are questionable. On the basis, of the paper of Contreras-Ortega et aL4 one cannot decide whether the anomalous proton transfer mechanism in the more bulky alcohols is possible or not. In fact they find that the formulation of the solvated not only as ROH2+in 1-HexOH but also as H30+ is sufficient for interpretation of the thermodynamics of hydrogen isotope exchange reactions. Obviously, if this cannot question the proton jump mechanism in water, by analogy it cannot exclude that the same mechanism is possible in 1-HexOH. Moreover it will be clarified that their XoH+q in 2-PrOH depends on tlhe water content of alcohol and that the Conway, Bockris, and Linton5 model for the proton jump mechanism, even if inadequate for predicting the anomalous contribution to proton conductivity ( X o a ~ + )in anhydrous alcohols, seems to show that this is present also in higher alcohols. The proton mobility in hydroxylic solvents is given by two contributions: the normal diffusional mechanism and the anomalous proton jump mechanism, where, according to the only quantitative model proposed by Conway et al., the rate-determining step is the rotation of a solvent molecule. If a / b is thle eccentricity of the solvent molecules assumed as a oblate spheric particle, where a and b are, respectively, the major and the minor axes, the rotation velocity about the minor axis (rotation about the major axis does not contribute to orient the molecule) is given by (J = KT/8aqa2b (1) Consequently, the anomalous conductance should be proportional to w. Starting from eq 1the ratio between in a solvent s to that (XoaH+), in a reference the (Aoa,+), solvent r is
E%$
(AoaH+)s/(AoaH+)r
= (7a2b),/(qa2b),
(2)
To confirm this hypothesis two difficulties arise: the possibility of measuring the XoaH+ and of having the more probable valules of a and b for each alcohol. A complete check of eq 1 can be made by assuming the following: (i) the normal contribution to the total proton 0022-3654/80/2084-0307$01 .OO/O
mobility is given by the conductivity of the proton at minimum which is obtained when small amounts of water are added to alcohols,2Le., A o a ~ += A o R o-~ Ao,in; (ii) eq 1 can be written as o = K T / 6 ~ ( ~ / ~ a= a ~A/VV, b) (3) where V, corresponds to the volume of a prolate sphere rotating about the minor axis, while the volume of a prolate sphere in static condition is V, = 4/3rab2. Assuming that V, is given by the intrinsic volume Vi of the molecule, it follows that V, = Vi(a/b) (3 4 Consequently, the relative anomalous conductance, as in eq 2, can be written as (AoaH+)s/(AoaH+)r = (viVa/b),/(ViW/b), (4) From the atomic intrinsic volumes in A3 reported by 13dwards! Vi(C) = 5.6, Vi(H) = 5.7, and Vi(0) = 7.7 and from additivity rule,' the Vi values of alcohol molecules can be calculated. Starting from these values and from a geometrical evaluation of a / b and from literature valueci of q,2v9l3 it is possible to calculate the XoaH+ for all alcohols by using MeOH as reference solvent. For all alcohols the experimental AoaH+ results are greater than the calculated ones. For example, in the case of 2-PrOH the calculated AoaH+ is 13.1 while the experimental value is 25.1. Nevertheless, this calculated value is very different from zero, as postulated by Chantooni and Kolthoff. On the other hand, it is remarkable that the value (13.4) reported by these authors for (AoH+)sp,oHcorresponds to that found by us in a hydroalcoholic solution containing about 0.1%I of water. This is not fortuitous because Chantooni and Kolthoff report that the water content in alcohol, assumed as anhydrous, by KF titration ranged from 0.05 to 0.1%. In the same way the water content in alcohol can account for the difference in (XoH+)prOH between the literature values.9J4 Another approach can be used to verify whether the proton jump mechanism is still possible in the more bulky alcohols. Interpreting the proton exchange between two solvent molecules as a kinetic mechanism, we can treat the limiting ionic conductance as the rate constant of a zeroorder (time-independent) reaction AoaH+ = Fv = Fk = FA' exp(-E*/Rl") = A exp(-E*/Rn (5) where F is the Faraday constant. From the literature values8J1 of hoeH+as a function of temperature, the A and E* values in MeOH, EtOH, and 1-PentOH can be calculated from an Arrhenius plot. Bloth 0 1980 American Chemical Society
308
The Journal of Physical Chemistty, Vol. 84, No. 3, 1980
De Lisi, Goffredi, and Turco Liveri
TABLE I: Parameters of Eq 5 and Comparison between Calculated and Experimental Anomalous Contribution to Proton Conductivity in Some Solvents at 25 "C
MeOH EtOH 1-PrOH 1-BuOH 1-PentOH 1-HexOH 1-OctOH i-BuOH 2-PrOH 2-BuOH t-BuOH CH,CN (CH,),CO H*O
E*IR 370 1280 1785 2240 2685 31 55 3915 2175 1935 2400 3385 95 1745 (- 2200)
In D 3.485 3.190 3.016 2.862 2.711 2.554 2.297 2.886 2.966 2.807 2.477 3.584 3.030 4.364
In A 5.77 8.08 9.52 10.75 11.96 13.19 15.21 10.54 9.92 11.15 13.78 4.97 9.41 (- 1.4)
(A:ROH A min)
( I o a H +)calcd
92.7 44.1 34.2 25.5 19.2 13.6 8.0 25.7 30.9 22.2 11.3 104.7 35.1 (390)
hoH+h'Et4N+
93.W 42.2b 31.5' 26.Bbrd 19.5e 14.4f 7.1f 2 6.0 b g 25.1b 22.4d 8
13.gh - 3,4i
3183
'
Reference 8. Reference 2. Reference 9. Reference 10. e Reference 11. f Reference 12. Reference 13. From A ' H c ~ o , (ref 1 5 ) and AoEt,NC1O, (ref 17). From A ' H c ~ o , (ref 1 5 ) and A'Et,NC10, (ref 16). From h o ~ + (ref 18)and h o E t , N + (ref 19).
these parameters appear to depend on the structural properties of the alcohols. A straight line is obtained from the plot of both In A and E* as function of In D. From these plots the A and the E* values, for all alcohols, can be obtained by interpolating or extrapolating procedures. In Table I are reported the E* and A values and the anomalous conductivity of the proton in some alcohols calculated by eq 5. As can be seen the correspondence between experimental and calculated values is very close. This indicates that undoubtedly the anomalous proton jump mechanism can occur in more bulky alcohols than methanol and ethanol as postulated by Conway et al. Also shown in Table I is the anomalous contribution to conductivity in water, acetone, and acetonitrile, which can be calculated from the above plots. The difference between calculated and experimental values in water may be due to uncertainty in the extrapolation of E* and In A; at the same time the calculated value can be considered to confirm that the same anomalous mechanism occurs both in water and in all aliphatic alcohols reported in Table
I. On the other hand, the calculated anomalous contribution to proton conductivity in aprotic solvents such as acetonitrile and acetone shows that in these solvents this mechanism cannot occur. After all, the idea that the anomalous contribution to proton conductivity depends on the structural properties of solvent seems valid. As the water content in alcohols can be used to explain the difference in (XoH+)RoH between various literature values, the same can be sufficient to explain the anomalous behavior, in secondary vs. primary alcohols, of proton transfer activity coefficients from methanol to alcohols (MyH+S) reported by Chantooni and Kolthoff. This parameter depends on the difference of basic strength between the methanol and the other alcohols. The basic strength decreases both in primary and secondary alcohols as the alkyl chain increases as suggested by Dannhauser and Bahe,20consequently one should expect ('7"+S)2.PrOH > (MyH+S)2.BuOH. Also if the basic strength in liquid phase follows the same order as in gas phase21the basicity, and then MyH+S, of 2-PrOH should be larger than that of 1BuOH. This conclusion is obtained by starting from the equilibrium constants of the proton distribution between methanol and alcohols, "K: MeOH2+ + ROH
MeOH
+ ROH2+
(6)
I
L
/
1
2
*' 3
1
1
I
I
4
5
6
7
number o f carbon atoms
Flgure 1. Partition constants (0)and transfer activity coefficients of proton, H) corrected and (") uncorrected, for the Born effect between methanol and varlous alcohols as function of number of carbon atoms in the chain at 25 'C: (-) primary alcohols: (----) secondary alcohols.
which can be easily calculated from the equilibrium constants of the proton distribution between alcohols and water reported in the l i t e r a t ~ r e ~ , ~ - l ~ ROH2++ H 2 0 ==ROH + H30+ (7) In Figure 1 are plotted In M~ +scorrected and uncorretted for the Born effect, and InTuKF as a function of the number of carbon atoms in the alcohols. As can be seen in the case of primary alcohols the trend of In MKFis the same as that of the uncorrected In MyH+S whereas in the secondary alcohols they are in opposite direction. Also the are generally close but In MK,Sand the corrected In MyH+S it still emerges that the value of In MyH+S in 2-ProH, in spite of behavior of basic strength, is abnormally more negative than that in 2-BuOH. As stated above, this anomalous value probably can be explained in terms of the water content in the alcohol. On the basis of the Chantooni and Kolthoff paper the transfer activity coefficient is related to experimental parameters In MyH+S = MASp&(HPi) + In MyS(HPi)SAMpK,,(TABPi) + 1/,SAMpK,,(TABBPh)4(8) The first two terms on the right-hand side are mainly dependent on the water content in the alcohol. If one takes into account the PKd of HC1 in l-PentOH,l' of which the pKd is comparable to that of HPi in 2-PrOH, it emerges that the pKd decreases from 3.65 to 3.36 with an increase in the water content from 0 to 0.1%. The 0.3 unit decrease of PKd per 0.1% of water is close to that for HPi in methanol where the j%d decreases from 3.€Jn in anhydrous alcohol to 3.0823when the water content is 0.27% and in
J. Pbys. Cbem. 1980, 84, 309-314
809
(3) I n ref 2 is reported the koHtin 2-BuOH but not in t-BuOH as reported ethanol where the p& decreases from 4.122in anhydrous by M. K. Chantooni and I. M. Koithoff in ref 1. solvent to 3.4923in a hydroalcoholic mixture containing (4) C. Contreras-Ortega, C. Nash, and P. Rock, J. Solution Cbem., 5, 0.19% of water. 133 (1976). (5) B. E. Conway, J. 0. M. Bockris, and H. Linton, Jr., J . Pbys. Cbem., The In MySEW depends on the solubility of HPi in al24, 834 (1956). cohols and decreases with increasing solubility. Now the (6) J. T. Edward, J. Cbem. fduc., 47, 261 (1974). presence of water in alcohols gives an increase in the (71 A. Bondi. J. Phvs. Cbem.. 68. 441 (1964). solubility of HPi and consequently a decrease in In MrsHpi. (8) R. De Lisi, M. Gffredi, and V. Turco Lberi, j . Cbem. Soc., Faraday Trans. I, 74, 1096 (1978). Then the anomalous value for this parameter in 2-PrOH, (9) M. Goffredi, Atti Accad. Sci. Lett. Arfi Palermo, Ser. I V , 27 smaller (about 0.4-0,5 unit) than that expected from a ( 1966- 1967). comparison with the other alcohols,’ can be due to the (10) R. De. Lisi and M. Goffredi, flectrocbim. Acta, 16, 2181 (1971). (11) R. De Lisi and M. Goffredi, J. Cbem. SOC.,Faraday Trans. 1 , 70, water content in the alcohol. 787 (1974). From the sum of the probable effect of water content (12) R. De Lisi, M. Goffredi, and V. Turco Liveri, J. Cbem. SOC.,Faraday (0.4-0.5 unit) and that on the (0.170) on the In MySHpi Trans. 1, in press. (13) R. De Lis1 and M. Goffredi, flectrocbim. Acta, 17, 2001 (1972). MASpKd(HPi)(0.3-0.4 unit) a more reliable value for In (14) M. Goffredi and T. Shedlowsky, J. Pbys. Chem., 71, 2182 (1987). MyHtS can be obtained. (15) D. K. McGuire, Diss. Abstr., 26, 116 (1965).
Acknowledgment. The authors acknowledge support of this work by the C.R.R.N.S.M. (Comitato Regionale per le Ricerche Nucleari e di Struttura fell0 Matereo).
References and Nates (1) M. K. Chantooni and I. M. Kolthoff, J. Phys. Chem., 82, 994 (1978). (2) R. De Lisi, Mi. Goffredi, and V. Turco Lweri, J . Cbem. Soc., Faraday Trans. 1, 72, 436 (1976).
P. Walden, H. Ulich, and G. Bwch, 2.phys. Chem., 123,429 (1926). G. A. Forcier, Ph.D. Thesis, University of Massachusetts, 1966. T. Shedlowsky, J . Am. Chem. Soc., 54, 1411 (1932). D. F. Evans and R. L. Kay, J . Phys. Cbem., 70, 366 (1966). W. Dannhauser and L. Bahe, J. Chem. Phys., 40, 3058 (1964). J. Brauman and R. Blair, J . Am. Cbem. Soc., 90, 6561 (1968). G. Chariot and 8. Tremilion, “Chemical Reactions in Solvents (and Melts”, Pergamon Press, New York, 1969. (23) P. Majersky and M. Dybalova, Acta Fac. Rerum Nat. Univ. Comenianae, Cbim., 22, 99 (1975).
(16) (17) (18) (19) (20) (21) (22)
Conductance and Infrared Studies on Acetonitrile Solutlons Containing Crown Ethers and Alkall Metal Salts Harry P. Hopkins, Jr.;
and Alan B. Norman
Bparfment of Chemisfty, Georgia Sfate Univefsity, Atlanta, Georgia 30303 (Received May 17, 1979)
Conductance studies have been performed on acetonitrile solutions of LiI, NaBPh4,and KBPh4at difference concentrations of 12-crown-4,15-crown-5,18-crown-6,and TM-12-crown-4. Upon the addition of these crown ethers to the LiI solutions, the equivalentconductance increases. A decrease is observed for similar experiments with NaBPhl and KBPh4 solutions. Infrared studies were performed in the 500-200-~m-~ region, leading: to the unambiguous conclusion that the crown ethers are complexing the lithium cation. A model for the solvation of the lithium ion is proposed to account for the increase in conductance found for the lithium salts. Since a 1:l solid complex is isolated from the acetonitrile solutions containing LiBr and 12-crown-4or 15-crown-5, the compositionof the complexes in solution is assumed to be 1:l. Analysis of the conductance data at different mole ratios of crown ether to salt provides equilibrium constants for the 1:l association complex. For the lithium cation these are in the order: Keq(12-crown-4)< Keq(15-crown-5)C Keq(18-crown-6),whereas for the sodium cation Keq(12-crown-4)
