THE JOURNAL OF
PHYSICAL CHEMISTRY (Registered in U. S. Patent Office)
VOLUME61
(0Copyright, 1960, by the American Chemical Society)
JULY 25, 1960
NUMBER7
THEORETICAL PATHWAYS FOR THE REDUCTION OF Nz MOLECULES I N 8QUEOUS RIEDIA: THERMODYXAMICS OF N2Hn1 BY NORMAN BAUER Chemistry Department, Utah State Universaty, Logan, Utah Received A p r i l 1 , 1969
From an estimate that the hypothetical gaseous anion Kz-would lose its electron with the liberation of a t least 63 kca1.l mole, from the assumption that its free energy of hydration would equal that of 0 2 - , and from thermodynamic data on hydrazine and oxygen, it has been deduced that the as yet unobserved free radical NzH should be moderately stable and should require at least 32 kcal./mole of free energy for the removal of its H atom. Estimates of electron affinities, of proton and of H-atom dissociation free energies for free radicals, molecules or anions of the type NzH, ( n = 1 to 3) were also obtained; and these quantities proved to be consistent with the known reduction potential of the NI, NzHkq+couple. The results suggest that, under special conditions favorable for the stabilization of the anions Sz.,- and N2Hn,-, the reduction of NI to NzH4,, may be able to proceed through free radical intermediates by a succession of electron, water, proton captures.
I. Introduction The extraordinary stability of the N2 molecule, reflected in its dissociation energy of 225 kcal./ mole, indicates the difficulty of producing nitrogenous compounds from elementary nitrogen. Nevertheless, the fact that either nitric acid or ammonia in dilute aqueous solution is thermodynamically stable under ordinary conditions intrigues us with the possibility of oxidizing or reducing aqueous Yz. Furthermore the challenging fact of biological Nz-fixation tells us that the rate of some such process is not impracticably slow. The crucial mechanisms of the first several steps in this fixation are unknown. 2--4 I n the present study we attempt to deduce thermodynamic limitations on conceivable free radical mechanisms of biological N2-fixation from theoretical estimates of electron affinities involved in a series of one-electron transfers which would yield NzHnin an aqueous system. The conception followed here is somewhat parallel to Gorin’s (1) Paper I11 of the series “Physical-chemical Studies of Biological Nitrogen Fixation,” supported by a grant from the Herman Frasch Foundation. Ref. (4) is paper 11. (2) (a) W. D. McElroy and B. Glass, eds., “A Symposium on Sitrogen Metabolism. Function of Metallo-Flavoproteins,” The Johns Hopkins Press, Baltimore, 1950; (b) M. K. Bach, B i o c h i m . el B i o p h y s . Acta, 26, 104 (1957). (3) J. E. Csrnahan and J. E. Castle, J . Bncteriol., IS, 121 (1958). ’ (4) N. Bauer and R. G. Mortimer, Baochim. et Biophya. Acto, 40, 170 (1960).
idea5 that the formation of the anion OZaq-is the first and slowest step in oxidations by hydrated molecular oxygen. The results below are only tentative (cf. Sec. V), but the combination of principles used should eventually yield definite answers. 11. “Electron A5nity” of Gaseous Nz.-The properties of Nz and of nitrogen compounds imply that a large investment of energy would be required to creabe or stabilize the anion Nz-, if indeed it can exist. We shall bry to estimate an upper limit for the hypothetical electron affinity of Nz, AN,) defined as the energy change for reaction 4,below. This requires an upper limit for B N ~ the - , dissociation energy of N2s- according to (l),which we shall assume is given by DNO = 150 kcal./mole for the isoelectronic nitric oxide.6 It seems to be a reasonable working hypothesis that DN$-should be no greater than DNO because the nuclear or core charges in NZ- are smaller than in NO, hence are less capable of keeping the outer electrons in the “binding region” defined by Berlin.’ The upper limit of AN, the electron affinity of atomic nitrogen, ( 5 ) M. H. Gorin, Ann. N . Y . Acad. Sci., 40, 123 (1940). (6) G. Herzberg, “Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules,” D. Van Nostrand, Inc., New York. T i .Y., 1083, p. 558; A . G. Gaydon, “Dissociation Energies and Spectra of Diatomic Molecvles.” John Wiley and Sons, Inc., h-ew York, N. Y., 1947. pp. 164-165; G. G . C16utier and H. I . Schiff, J . Ckem. Phys., 91, 793 (1959). (7) T. Berlin, J. Chem. Phgs., 19, 208 (1951).
833
NORMAN BAUER
834
Vol. 64
in eq. 3 is set by the theory of Rohrlich8 since a higher value is not compatible with other estimatesg or with the failure to observe N- in mass spectra. Accordingly, we have
102.1 kcal./mole for the standard free energy of removal of an electron frorn Hgl, in contact with water vapor, instead of 104.5 kcal.,'mole for removal from dry liquid Hgl. The electron affinity of 02,used to get N2,--+Pj, S,- ; D N 5~ 150 kcal./mole (l) AF0(8), is still subject to contro~ersy.~' K, + S e --+- s?p ; -Dsz = -225 (2) We are inclined to use A = 20 kcal./mole Kg+ K g + eg- ; A N 5 12 (3) in the present study not because its absoX2,-+- 11;2g + eg- ; r l 5~ 63;~ i.e., - A x 2 2 63 (4) lute value is necessarily the correct one but because, being deduced from related Equation 4, in harmony with general expectations, thermochemical data, it is more apt to be consistmeans that gaseous N2- would be exceedingly un- ent with the electrode potential E0oz-,o2used for stable. AFo(s)than an electron affinity for O2 deduced from 111. Possible Stabilization of Nz- and the N,, spectroscopic arguments involving as yet unconNfaq- Electrode Potential.-An anion unstable in firmed excited states. This choice seems to be the gaseous state is not unprecedented in chemical justified by the result that if the alternative value reactions; and FajanslO has stressed the role of of Ao, is used below, the unreasonably large value cations or dipoles in stabilizing negative groups of 93.5 kcal./mole for -AFoh,O,- is obtained. To such as 02-. In the case of Nz- we wish to see convert Ao, to AFo(s),the Sackur equation was used if the forces of hydration may be sufficient to give for the standard entropy of an electron gas, XE2,9,8 = this anion sufficient stability in aqueous systems 3.6 e.u. Then, by ignoring the undoubtedly very for its existence at least as a fleeting intermediate small difference in vibrational and rotatioiial enbetween K, and its protonated counterpart, K2H. tropy between O2and 0 2 - , we have at 298°K. 02, e,(pt)--+ Gaq; AFoahs,red = +G.7 kcal./mole (5)
+
+
em(Hg, 1 % ) -
+e,(rt) -
; ; ;
LIFO
= -0.5 LFo = -102.1 AFa = -40,- TSo,-,, = +18.9
(6)
(7 -+0tg e,(8) 02,+0&q; AFOh,o*- = -77.0 i9) This is conceivable because most known hydration In this and following calculations we retain all energies of simple anions exceed the 63 kcal./ numbers to the nearest 0.1 kcal./niole even though mole required t o stabilize Nz-. the absolute values in most cases are far from that We shall estimate the standard free energy of reliable. In that way cert,ain small differences or hydration of gaseous N a - , A F o h , x 2 - , by making the trends in relative quant'ities may be correctly calreasonable assumption t,hat it equals AFOh,ol-, culated a t a later stage. Also, a number of small ie., is ident,ical to that of the quite similar 0,- ion. terms (e.g., AF0(6,) are included for clarityof thought Such an assumption should not be off by more than and for showing how to make better predictions as a few kcal./mole, in view of the fact that AFoh values improved data become available. for t'he halidesll (C1- = -84, Br- = -78, I- = The above value of A F o h , o p - = -77.0 kcal.,/mole -70 kcal./mole) differ by so little in spite of large is quite reasonable when compared to those of the differences in size and polarizability. halide ions quoted above, considering that 0 2 - in Using the standard oxidation pot,ential12 for aqueous systems should resemble the halide-like 02aq-+ 02, + em(pt)- of E:eT98= +0.56 v., one cx-. Thus we can use A F o h , N 2 - = -77.0 and may deduce AFOh.0,- by following the reasoning of -~4N1 2 63 kcal./mole in equations analogous to T,at,imer, Pitzer and Slansky,ll and of Latinier,l2 (5)-@) to calculate - A F o 2 89.7 kcal./mole for em(Pt)-. Ac:Iccording to eq. 5-9 beloI+*. We shall use EO,;:,^,, the electrode process Naaq- N2, for the absolute oxidatioll potent,iall~,~3 cording to t'he above method of absolute electrode = -0.56 of t'he standard calomel electrode, where E:ef,98,x= potentials, this means that the standard oxidation potential of the couple NZaq-,Nz is E"re1,ox 2 +4.16 -0.2676 v. for its potential relative to the hydrogen v., relat'ive to H2,Hag+. Such a la,rge Eorel,ox value We use +0.02 v* for the transfer suggests that hydration alone is not sufficient to of an electron from Hg to Pt met'als (volta poten- give an adequate stability for playing a role in tia1)13-15; i.e.1 E o r e l , o x ( P t ) = E'abs, ox(Pt) +Os272 T'. chemical reactions; but that jy2aqmay becolne at' 298°K. In accordance with Brewer16 we use moderately stable when situated near addi18) F. Rohrlich, J . Chem. Phys.. SO, 1608 (1959). positive charges. (9) H. 6, a '. Massey, "Negat.ive Ions." Cambridge Univcrsity tional IV. Stabilities of N2HEI,-TypeMolecules, RadiPress, Cambridge, 2nd Ed., 1950, p . 3, p . 20. cals and Anions.-We expect that molecules of the (10) K. Fajans, Chimia, 13, 354 (1959). (11) u. &I. Latimer, K. S. Pitzer and C . AI. Slansky, J . Chem. t8ypeN*H,, and their corresponding anions, would Phys., 'I, 108 (1939). be produced from NZaq- by proton capt'ure and (12) W.hI. Latimer, "Oxidation Potentials. The Oxidation States subsequent furt'her reduction by electrons or Hof the Elements and Their Potentials in Aqueous Solutions," Prenticeeg
-
02,-
--+em(ar.
+
-+
Hall, Inc., New York, N. Y., 2nd Ed., 1952. (13) R . E. Wood in "Electrochemical Constants." U. S. h'ational Bureau of Standards Circular 524, U. S . Department of Commerce, Ang. 14, 1953. (14) 0. Klein and E. Lange, Z. Elektrochem.. 44, 558 (1938). (15) B. E. Conway. "Electrochemical Data," Elsevier Pub]. Co., h'ew York, N. Y., 1951. 13. 31.
+
(16) L. Brewer in "The Chemistry and Metallurgy of Miscellaneous Materials: Thermodynamics," L. L. Quill, ed., hfcGrav--Hill Book Co., New York, K. Y., 1950, p . 156. (17) R. S. Mulliken, Phgs. Rev., 115, 1225 (1959); H. 0. Pritchard, Chem. R e m . , 62, 529 (1953). Note t h a t Mulliken does not take into account the recent upward revision of D N in ~ criticizing Pritchard'r application of the "Mulliken Rule."
THERMODYNAMICS OF N2H,
July, 1960
ntoms. In the following we will make an estimate of H-atom dissociation energies and other trends of behavior iii the series NzH, NzH2,N2H3,NzH4. This is, as far as we know, the first attempt to evaluate the stability of the free radical N2H. Concerning diimide (or "diazene"), l8 N2H2, the molecule has been ~ b s e r v e d ' ~in mass spectra and it has been postulated18 as an intermediate in the oxidation of aqueous hydrazine; while Paulingz0has speculated about the structure of N2H2. Diimide also has been postulated as the first intermediate in a reduction mechanism of N2-fixation.21 The salt NaN2H3is known and the radical ("hydrazy1,"18 or H 3 N 2 , "hydrogen pernitride") has also been postulated18 as an intermediate in hydrazine oxidation. However, the free energies of formation or of bond dissociation have not been established for the above three NzH,; and even the thermodynamics of NzH4 requires further analysis. -
+
2KzH4,, --+ S2HBsq- N2H,,,+ T2Hj,, + --+Ha, X2Hlaq +
+
; ;
835
certain free energies of proton dissociation, of hydration and of electron capture, derived below, (b) Free Energy of Proton Dissociation from NzH4.--We can estimate this quantity from Pleskov'sZ6 potentiometric studies of NaK2H3 in liquid hydrazine. He found K Z g = 8 2 X 10-25 for ~ N z H ~+~ N2H3soiv~ I ~ . + N ~ H S ~ ~which I ~ +is, close to that for the corresponding reaction in water according to an application of the well-known Born theory of hydration energies. According to this theory, the free energy of proton dissociation from NZH4 should be only about 0.0065 X 175 = 1.2 kcal./mole more favorable in water than in liquid hydrazine owing to the similarity of dielectric constant ratios ( E - l)/ E for water (0.9875)and hydrazine (0.9810) if we assume the total solvation energy of NzHbf and NzH3- to be 175 kcal./mole (analogous to Kf and Br-) and neglect presumably small entropy differences. Then we can make the estimate
AFo
AFO
=
33.6
- 1.2
=
+32.4 kcal./mole
= f10.9
(17) (18)
--+ XZH3sq- f Ha,+ ; AFOP,N,H, = $43.3 (19) (a) Free Energy of H-Atom Dissociation from (c) Free Energies of N2H,- Anion Hydration.NzH4.-Latimer12 has estimated an upper limit of We postulate that AFOh of N2H,- will increase slowly 0.6 v. for the standard reduction potential of the with increasing number of H-atoms because of the NzH3, N2H5+ couple from the experiments of polarity of the N2. . .H bond and the asymmetry Cuy and Bray.22 The following equations 10-16 of the N2H4 molecule ( ~ N * H , = 1.8 d.). Let us then give an upper limit for the dissociation free estimate the maximum polar effect per added Henergy of H from N2H4, using data for AFo(ll) and atom as an average of 3.6!4 = 0.9 kcal.,lmole, AF0(18) from standard reference work^.^^^^^ For where 3.6 represents the known AFO of mixing N2H4 and HzO. Accordingly, for K2HgAF"(14), an estimate probably reliable to 0.1 kcal./ mole was made from the known standard free energy NzHa,-; AFoh = - 7 i . 0 - 0.9 = - i 7 . 9 kcal./iiiole. of condensation of hydrazine (-2.4 k~al./mole)*~For the other anions in the series the mlues of and from the known heat of solution of hydrazine a F o h are: X:2H2- = -78.8; N2H3- = -79.7. and mater.24using the method of Hildebrand and The uncertainties in the above iiicrements teiid Scott25 which required the thermal expaiisivity of to cancel in applications below-. such as in eq. aqueous It was assumed that 20-28. - AF0(15, = 3AFo(14)/4 because the free energies of hy(d) Electron Affinities of Gaseous N2H,.--We dration of N2H,. gas must be almost entirely at- seek to place an upper limit on the electron affinity , this will determine the lower tributable to dipole interactions along N. . . H of NZH, A x j , ~for limit of the N,.. .H bond dissociation free energy. bonds. Then we have h lower limit for the difference LWO,,I < 13.8 kcal./mole A A K ~ , I \= ~ ~AN*H H - AN?may be aFo = -10.9 evaluated from the following eviAForel = 0.0 dence and combined ivith the AFo,,l = 48.6 previously derived AN* to give AFO = -6.0 the limit for A N ~ H . In this part AFO = +4.5 (d), A E o h refers to energy of hyAFo < 50.0 dration. not to a difference in In order to deduce the corresponding quantities electrode potentials. Uri2' has deduced the value -136 kcal.,'mole for x2H3, N2H2and N2H we shall need estimates of for the sum (AEoh,Ho2- -AHo*), which is in t'hermo(18) J. 17. Cahn and R . E . Powell, J. A m . Chem. SOC.,76, 2568 chemical accord with the H. . .02dissociat,ionenergy (1964), of 36 kcal./mole and the H. , .02H dissociation (19) S . K , Fon
