KOTES
293
fore, the direct application of the treatment for a large number of organic compounds is not tenable. Inokuchi and his eo-workers have reported the conductivities of a few polycyclic aromatic compounds under 160 kbars at 15°.3J0 Figure 2 shows the plot Of log pi bar VS. log (pi60 kbar/pl bar) Of these compounds. The results indicate that the linear relationship also holds at high pressure for aromatic hydrocarbons and organic free radical compounds.
Solvent Deuterium Isotope Effects on Intramolecularly Hydrogen-Bonded Dicarboxylic Acid Monoanions'
by E. M. Eyring and J. L. Haslam Department of Chemistry, University of Utah, Salt Lake City, Utah 84118 (Received July 88, 1966)
There are many dicarboxylic acids having a much larger ratio of first to second acid dissociation constants than the value of 4 predicted from statistical theory. Such large differences have been ascribed to a strong intramolecular hydrogen bond in the acid monoanion.2 Equilibrium data in water and DzO at 25" for several such acids are given in Table I. Kinetic studies of the reaction kh'
LA-
15
Figure 2. Effect of pressure on resistance, under 160 kbars : 1, a,a'-diphenyl-p-picrylhydrazyl; 2, quaterrylene; 3, violanthrone; 4,pentacene.
,4s a result of limited data, the proposed pressureresistance relationship of organic compounds, eq. 1, cannot as yet be discussed at length. However, the linear function would be expected to curve for very conductive compounds (p1 bar < 1 ohm em.), in such a way that it becomes asymptotic to 0, because the effect of pressure on highly conductive compounds would be very small and the term R/R1 bar or p / p ~bar approach unity. The data so far reported are not suflicient to allow one to generalize the proposed relationship. We hope that the applicability of this treatment will be able to establish and aid in our prediction of the electrical resistance of organic compounds under various pressures.
Acknowledgment. The author is grateful to Drs. M. Pope and Y. Matsunaga for many stimulating discussions, and the U. S. Air Force Cambridge Research Laboratories for their financial support (Contract AF 19(628)-2482).
+ OL- E A'- + LzO
(1)
where L denotes hydrogen or deuterium and LAthe monoanion of the dicarboxylic acid have shown that the rate constant kLz3' expressed in M-' sec.-I of the forward reaction is inversely proportional to pKLz pKLlfor the acids in three different homologous series.a" Several such rate constants, measured by the temperature-jump relaxation method,6 are also shown in Table I. As will be shown below, such data lend credence to the intramolecular hydrogen-bond hypothesis and may elucidate the structure of the transition state. Bunton and Shiner have suggested a way of calculating both equilibrium' and kineticssgsolvent deuterium isotope effects that could be compared with the data of Table I. In essence, they ascribe such effects to differences in zero point energies of vibration, assign stretching frequencies to the relevant bonds in solution,lo ignore bending modes because their contri(1) This work was supported by the Directorate of Chemical Sciences, Air Force Office of Scient& Research, Grant AF-AFOSR-476-64, and was presented at the American Chemical Society physical chemistry symposium on relaxation techniques in chemical kinetics at Buffalo, N. Y., June 1965. (2) For a bibliography see L. Eberson and I. Wadso, Acta Chem. S c a d . , 17, 1552 (1963). (3) J. L. Haslam, et al., J. Am. Chem. SOC.,87, 1 (1965). (4) M. H. Miles, et al., J . Phys. Chem., 69, 467 (1965). (5) J. L. Hadam, et al., J . Am. Chem. SOC.,87, 4247 (1965). (6) G. Czerlinski and M. Eigen, 2.Elektrochem., 63, 652 (1959). (7) C. A. Bunton and V. J. Shiner, Jr., J . Am. Chem. SOC.,83, 42 (1961). (8) C. A. Bunton and V. J. Shiner, Jr., ibid., 83, 3207 (1961). (9) C. A Bunton and V. J. Shiner, Jr., ibid., 83, 3214 (1961).
Volume 70,Number 1 January 1066
NOTES
294
Table I: Isotope Effect Data and Calculations at 25"
-x, Acid
pKHP
pKH~b
Tetramethylsuccinic Tetraethylsuccinic Racemic (Y, 01 '-di-t-butylsuccinic cis-3,3-Dimethylcyclopropane-l,2-dicarboxylic" cis-3,3-Diphenylcyclopropane-l,2-dicarboxylic
3.56' 3.39' 2.2P
7.41' 8.06' 10.25'
pKDP
Theorye
7.75' 8.50" 10.92"
0.84 0.94 1.36
cm. -1
0-
N~
-KH/KD~-
Expt.!
kHst,i
101 M-1
bend?
Bend.'
0.34 0.43 0.73
1546 1800 2122
2116 2370 2692
mc.-1
--kHa~/P,rr
E-
SecondExptGZ arym
25'
5.3q
l.lq 1.2q
0.23*
Primsry"
4.4 4.2
1.7q
0.25 0.29 0.36
4.8
2.3Sq
8.25q
8.57'
1.04
0.31
1178
1748
6.3q
1.1'
0.28
3.9
2.30q
9.20'
9.57*
1.17
0.36
1246
1816
0.44*
1.6'
0.30
5.3
a Experimental: log ([H+] [ElA-]/[HzA]) in water. * -Log ([H+] [A+]/[HA-]) in water. Same as b, but in DzO. See eq. 6. See eq. 7. Bending modes negSee eq. 5. Calculated intramolecular hydrogen-bond stretching frequency in the monoanion. Bending modes included as in eq. 10. Experimental rate constant for the reaction HAlected as in eq. 9. OH- + A2HzO in water. Kinetic deuterium isotope effect for this same reaction. Experimental value. Secondary solvent kinetic isotope effect calculated as in eq. 12. Primary kinetic isotope effect calculated from eq. 13. " cis-Caronic acid. P. I(. Glasoe and L. Eberson, J. Ph.ys. Chem., 68, 1560 (1964). ' See ref. 5. e
'
+
'
butions are comparatively small, and calculate equilibrium effects from the expression7 =
antilog
ZVH
-
ZYE'
12.53T
where KH is the equilibrium constant in water, ZYH is the sum of the relevant frequencies in the reactant species expressed in cm.-l, ~ Y H ' is a similar sum for the products, and T is the absolute temperature. Their analogous expressiona for the kinetic isotope effect derived from absolute rate theory by Bigeleisenl' is (3) where kH is the rate constant in water and ZYH*is the sum of the relevant frequencies in the postulated activated complex, etc. Since Bunton and Shiner explicitly refuse to apply their model to cases of intramolecular hydrogen bonding: it is interesting to postulate first the structures for reaction 1.
+
The dotted lines denote hydrogen bonds to solvent. By analogy to their calculation for acetic acid we have for the specific case of cis-3,3-diphenylcyclopropane1,2-dicarboxylic acid pKBl = 9.20, pKb(A2-) = 14.00 - 9.20 = 4.80, pKb(A2-, per 0 atom) = 5.40, = 14.00 - 2.30 = 11.70, and pKb(HA-, pKb(i%i-) per 0 atom) = 12.00. Using eq. a and b of ref. 7, we estimate the following hydrogen-bond stretching frequencies: accepted by HAY
=
3040
+ 22.9 X 12.00 = 3314 cm.-'
donated by HAY
=
2937
+ 28.8 X 9.20
=
3202 cm.-'
accepted by A2-
+ 22.9 X 5.40 3164 cm.-' For the initial state ZYH= 3202 + 5 X 3314 + 3600 + 3 X 3000 + 2 X 3400. The two frequencies at 3400 cm.-l are added to conserve bonds (rule e of ref. 7). For the final state ZVH' 8 X 3164 + 4 X 3400. Y =
3040
=
=
Thus, the calculated equilibrium deuterium isotope effect at 25" is
K=/K=
=
antilog
39,172 - 38,912 = 1.17 3734
(5)
A n experimental value of the concentration ratio (10) For instance, they chose 3600 cm.-l for the nonhydrogenbonded OH stretching of OH- ion, 3000 cm.-l for the hydrogens of Hz0 donated for hydrogen bonding to OH- ion, and 3400 om.-' for the OH stretching in liquid HzO. (11) J. Bigeleisen, J. Chem. Phys., 17, 676 (1949).
NOTES
295
K H / K D= ([A2-] D201P A - ] [OD-]) X ( [A2-] [DzO][ U - ] [OH-])-'
(6)
can be obtained from Table I by noting that at 25' = 10-14*00, and according to Salomaa, et uD+uoD= 10-14.sl in D20. Using the DebyeHuckel activity coefficients for 0.1 M ionic strength solution yHt90H= 0.83 and yDCSoD= 0.81, we have UH+UOH-
K H / K D antilog (-9.20
- 14.81 + 14.00
+ 9.57) = 0.36
(7)
derived from the experimental data of Table I. The agreement between eq. 5 and 7 is far less satisfactory than that obtained by Bunton and Shiner for systems like acetic acid? Sjmila,r disagreement between theory and experiment is found for our other acids M shown in Table I. Let us postulate instead the structures 0
II
,KO.
with an intramolecular hydrogen bond presumed to exist in the monoanion. From the experimental K H / K D we , can then deduce a value for the stretching frequency x of this intramolecular hydrogen bond in the following manner. For cis-3,3-diphenylcyclopropane-l12-dicarboxylic acid we now have in the initial state ZVH= x 4 X 3314 3600 3 X 3000 3 X 3400. The value of XVH' = 38,912 remains the same, and hence
+
+
K ~ / = K 0.36 ~
=
antilog
+
x
+
+ 36,056 - 38,912 3734
anion has none, and H2O has one 1640-cm.-1 bending and three 710-cm.-' librational frequencies. Then, for cis-3,3-diphenylcyclopropane-l,2-dicarboxylicacid we would have
K H / K D= 0.36 = x 36,056 antilog
+
+ 3200 - 38,912 - 3770 3734
(10)
from which x = 1816 crn.-'. Values of x for our other acids calculated with the same assumed 1000-cm.-l value, etc., are shown in Table I. While a spectroscopic verification of these frequencies at relevant aqueous solution concentrations appears impossible, the importance of the calculation should not be discounted since its qualitative success lends support to the hypothesis of intramolecular hydrogen bonds in this type of monoanion. The other important consequence of the above equilibrium calculation is that the values of x can be used to calculate the secondary solvent kinetic isotope effect for each acid. The term secondary, as used by Bunton and Shiner, means summing all relevant frequencies in our activated complex except those directly involving the transferring proton. Thus, with the assumed mechanism for cis-3,3-diphenylcyclopropane-l,2-dicarboxylic acid 0 II
0.
: '*3314 i314
(9)
from which it follows that x = 1246 cm.-I. A low frequency is consistent with a high intramolecular hydrogen-bond strength.l8 However, this value is implausibly low since even the very strong hydrogen bond in HF2- has a higher frequency,14 1405 crn.-I. The lowest stretching frequencies used in the BuntonShiner calculations are around 2500 crn.-I. The inclusion of bending modes would have the effect of raising the intramolecular hydrogen-bond stretching frequency to a more plausible value. Following Bunton and Shiner15let us suppose that OH- haa two 600-~m.-~librations, the monoanion of mechanism 8 has two N1OOO-cm.-l bending frequencies, the di-
products
(12) P. Salomaa, et al., J . Am. C h . SOC.,86, 1 (1964). (13) The stretching frequency in a hydrogen bond is inversely proportional to hydrogen-bond strength in contradiction to the superficial application of Hooke's law; this is necessarily a consequence of an increase in reduced mass of the vibrating system that exceeds any possible simultaneousincrease in force constant. (14) G. L. Cote' and H. W. Thompson, Proc. Roy. SOC.(London),
A210, 206 (1951-1952).
Volume 70,Number 1 January 1966
NOTES
296
we can calculate a secondary solvent kinetic isotope 4 X 3314 effect from eq. 3 using ZYH = 1246 3600 3 X 3000 = 27,102and ZVH*= 4 X 3314 2 X 3000 3600 2 X 3400 = 29,656 where 2 X 3400 has been added to the second sum to conserve bonds. We then have
+
+
+
+
+ +
27,102 - 29,656 (kH/kD)2,, = antilog = 0.30 (12) 3734 The assumed structure and frequencies of the transition state, eq. 11, are by no means unique. However all plausible alternatives give rise to secondary kinetic isotope effects that are significantly less than unity. Thus, we may calculate a primary kinetic isotope effect from the relation which for cis-3,3-diphenylcyclopropane-l,2-dicarboxylic acid is
1.6/0.30 = 5.3
(14)
Analogous values for the other acids are shown in Table I. Thus, we see that a secondary solvent kinetic isotope effect masked the expected large primary kinetic isotope effect in the experimental data of Table I. Furthermore, the similarity of the primary kinetic isotope effects indicates a similar reaction mechanism for the two acid series. In the past, such comparatively large kinetic isotope effects have been associated with symmetric transition states in, which the transferring proton is bound equally strongly to both reactants.lB However, Willi and W~lfsber@~ have recently rejected this conclusion as superficial; for instance, high hydrogen-bending force constants in the transition state could produce a low experimental kinetic isotope effect even though the extent of bond making and breaking was identical. While the systems considered here axe not of the protonated ether or carbonyl type for which Willil* felt it necessary to replace the Bunton-Shiner method with an approach requiring an estimation of ratios of partition functions, it may eventually be interesting to carry out an analysis of our kinetic data using Willi’s method19 since it would yield limiting values of kH/kD that could be compared directly with experiment. (16) C. A. Bunton and V. J. Shiner, Jr., J . Am. C h . SOC.,83, 44 (1961). (16) C. A. Bunton and V. J. Shiner, Jr., dbid., 83, 3216 (1961). (17) A.V. Willi and M. Wolfsberg, C h .Ind. (London),2097 (1964). (18) A. V. Willi, Z.Naturjorsch., 19b, 461 (1964). (19) A. V. Willi, “Siiurekatalytische Reaktionen der organischen Chemie,” Verlag Vieweg, Braunschweig, West Germany, 1966, p. 91 ff.
The J o u d of Phy&
Chmtktru
In principle, one would then be able to identify the transition state as being linear or nonlinear. As our eq. 10 clearly indicates, we prefer the latter possibility.
The Catalytic Reduction of Nitric and Nitrous Oxide
by R. J. Kokes Depart& o j Chemistry, The Johm Hopkins University, Baltimore, Maryland 91818 (Received July 86, 1966)
Recently,’ it has been suggested that on supported metallic catalysts hydrogen can be activated by the metal component and migrate from particle to particle. If this be so, it would seem that the catalytic reduction of nitric oxide with hydrogen should yield the same products as observed for the reaction of hydrogen atoms with nitric oxide. Harteck2 has shown that, at low temperatures, the latter reaction proceeds via the formation of (HNO),, a solid species that decomposes rapidly to yield nitrous oxide and water when the temperature is raised above -100”. Similar overall reactions have been suggested8 involving the intermediate HNO, a well-characterized species14in the gas phase. Recently in this laboratory5 we have found that the reaction reported by Harteck also occurs between nitric oxide adsorbed on Cabosil and hydrogen atoms produced in the gas phase. On the other hand, the available data in the literaturee-10suggest that the catalytic reduction yields water and ammonia, nitrogen, or hydroxylamine. Only in a very old reference’’ WBS the formation of nitrous oxide noted. Most of (1) H. W. Kohn and M. Boudart, Science, 145, 1949 (1964); S. Khoobiar, J . Phys. C h m . , 68, 411 (1964). (2) P. Harteok, Ber., 66, 423 (1933). (3) A. R. Knight and H. E. Gunning, Can. J . Chem., 41, 763 (1963). (4) M.A. A. Clyne and B. A. Thrush, DiScussWna Faraday SOC.,33, 139 (1962). (6) R. Gonzales and R. J. Kokes, unpublished results. (6) P. Neogi and B. B. Adhikary, C h m . Abstr., 5, 1031 (1911): B. B. Akhikary, ibid., 10, 24 (1916); L. Andrussov, ibid., 21, 1872 (1927); H. Tropsch and T. Bahr, ibid., 24, 4983 (1930). (7) R. J. Ayen and M. 8. Peters, Ind. Eng. Chem. Process Design Deudop., 1, 204 (1962). (8)L. Duparo, P. Wenger, and C. Unfer, Helv. Chim. Acta, 11, 337 (1928). (9) P. Sabatier, “Catalysis in Organic Chemistry,” translated by E. E. Reid, D. Van Nostrand Co., New York, N. Y.,1922,pp. 137, 181, 186. (10)A. J. Butterworth and J. R. Partington, Trans. Faraday SOC., 26, 144 (1930). (11) S. Cooke, PTOC. Phil. SOC.(Glasgow), IS, 284 (1887).
