Article pubs.acs.org/JPCA
Why Are Addition Reactions to N2 Thermodynamically Unfavorable? Weston Thatcher Borden* Department of Chemistry and the Center for Advanced Scientific Computing and Modeling, University of North Texas, 1155 Union Circle, #305070, Denton, Texas 76203-5070, United States S Supporting Information *
ABSTRACT: Thermochemical data are used to show that, of the 89.9 kcal/ mol difference between the endothermicity of H2 addition to N2 (ΔH = 47.9 kcal/mol) and the exothermicity of H2 addition to acetylene (ΔH = −42.0 kcal/mol), less than half is due to a stronger π bond in N2 than in acetylene. The other major contributor to the difference of 89.9 kcal/mol between the enthalpies of hydrogenation of N2 and acetylene is that the pair of N−H bonds that are created in the addition of H2 to N2 are significantly weaker than the pair of C−H bonds that are created in the addition of H2 to acetylene. The reasons for this large difference between the strengths of the N−H bonds in E-HNNH and the C−H bonds in H2CCH2 are analyzed and discussed.
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INTRODUCTION Addition reactions to a π bond of dinitrogen (N2) are thermodynamically unfavorable. For example, based on the experimental heat of formation of E-diazene at 298.15 K,1 the addition of H2 to N2 to form E-HNNH2 is endothermic by 47.9 kcal/mol.
that are made are at least as important as the relative strengths of the N−N and C−C π bonds that are broken in causing the reaction in eq 1 to be endothermic by 47.9 kcal/mol and the reaction in eq 2 to be exothermic by 42.0 kcal/mol. The reasons why the N−H bonds formed in the reaction in eq 1 are much weaker than the C−H bonds formed in eq 2 are discussed.
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H 2+N≡N→E−HN=NH ΔH(298.15)=47.9 kcal/mol
METHODS The enthalpy changes in the reactions in eqs 1 and 2 can be written in terms of the differences between the bond dissociation enthalpies (BDEs) of the bonds that are broken and the bonds that are made. The relevant BDEs for the reaction in eq 1 are
(1)
In contrast, based on ΔfH°(298.15 K) = 54.6 kcal/mol for acetylene and ΔfH°(298.15 K) = 12.6 kcal/mol for ethylene,1 addition of H2 to the former hydrocarbon, to give the latter, is exothermic by 42.0 kcal/mol.
ΔH = BDE(H 2) + BDE(π NN) − BDE(E‐HNN−H)
H 2+HC≡CH→H 2C=CH 2 ΔH(298.15)=−42.0 kcal/mol
− BDE(H−NN•)
(2)
where the bonds that are made are shown in boldface. For the reaction in eq 2
What accounts for the nearly 90 kcal/mol difference between the enthalpies of addition of one mole of H2 to these two, isoelectronic, triply bonded molecules? The generally held belief among chemists is that a π bond in N2 is unusually strong.3 However, it seems rather unlikely that a π bond in N2 is stronger than a π bond in acetylene by 90 kcal/mol. What else could account for the huge difference between the enthalpies of the two addition reactions in eqs 1 and 2? In this paper, experimental thermochemical data1 are used to show that there is another major contributor to the difference between the enthalpies of the addition reactions in eqs 1 and 2. The relative strengths of the pairs of N−H and C−H σ bonds © XXXX American Chemical Society
(3)
ΔH = BDE(H 2) + BDE(πCC) − BDE(H 2CCH−H) − BDE(H−HCCH•)
(4)
The BDEs in eqs 3 and 4 were obtained from the experimental heats of formation at 298.15 K, given in the Received: November 21, 2016 Revised: January 5, 2017
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DOI: 10.1021/acs.jpca.6b11728 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A Active Thermochemical Tables.1,2 The BDEs were also computed at the G4 level of theory.4 The two sets of values were found to be in excellent agreement, differing by, at most, 0.6 kcal/mol. The G4 and the experimental BDEs are compared in the Supporting Information for this manuscript. Although either set of BDEs could have been used in the text of this manuscript, the experimental values were chosen.
Scheme 1. BDEs at 298.15 K of the N−H and C−H Bonds in E-HNNH, H2CNH, and H2CCH21,2
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RESULTS AND DISCUSSION This paper begins by discussing the large difference between BDE (E-HNN−H) and BDE (H2CCH−H), then turns to the much smaller difference between BDE (H−NN•) and BDE (H−HCCH•), and finally to the difference between BDE (πNN) and BDE (πCC). Using the heats of formation at 298.15 K, given in the Active Thermochemical Tables1,2 BDE(E‐HNN−H) = 63.9 kcal/mol
in Scheme 1, a C−H bond in H2CNH is 14.4 kcal/mol weaker than a C−H bond in H2CCH2. This 14.4 kcal/mol difference in C−H BDEs can be attributed to the fact that the carbon radical center in •CHNH is stabilized by the lone pair of electrons on nitrogen; whereas, there is no lone pair of electrons on the CH2 group to stabilize the •CHCH2 radical. The same type of radical stabilization in HNN • presumably contributes to making the N−H BDE in E-HNNH smaller than the N−H BDE in H2CNH. However, in this latter case, the difference between the N−H BDEs in H2CNH and E-HNNH is 24.1 kcal/mol, which is 9.7 kcal/mol more than the 14.4 kcal/mol difference between the C−H BDEs in H2CCH2 and H2CNH. Some or all of the 9.7 kcal/mol greater difference between BDE (H2CN−H) = 88.0 kcal/mol and BDE (E-HNN− H) = 63.9 kcal/mol than between BDE (H2CCH−H) = 110.5 kcal/mol and BDE (E-HNCH−H) = 96.1 kcal/mol is due to the greater ability of a nitrogen lone pair to stabilize the adjacent radical center on nitrogen in HNN• than on carbon in HNCH•. The resonance structure that represents the stabilization of a radical center by a nitrogen lone pair involves transfer of an electron from nitrogen to the radical center, and this electron transfer should be facilitated by the greater electronegativity of a radical center on nitrogen than on carbon. Experimental evidence of the greater ability of a nitrogen lone pair to stabilize an adjacent radical center on nitrogen than on carbon comes from comparison of the difference of 8.2 kcal/ mol between BDE (H3CCH2−H) = 100.9 kcal/mol and BDE (H2NCH2−H)) = 92.7 kcal/mol with the difference of 16.4 kcal/mol between BDE (H3CNH−H) = 99.5 kcal/mol and BDE (H2NNH−H) = 83.1 kcal/mol.1 An adjacent nitrogen provides a 16.4−8.2 = 8.2 kcal/mol greater resonance stabilization energy (RSE) for the nitrogen-centered H2NNH• radical than for the carbon-centered H2NCH2• radical.5 However, there is another possible contributor to the additional 9.7 kcal/mol greater effect of an adjacent nitrogen on weakening of the N−H bond in E-HNNH, compared to a C−H bond in HNCH2. On loss of a hydrogen to form the HNN• radical, the radical center rehybridizes, so that the nitrogen lone pair occupies an AO that is nominally sp hybridized and that points away from the lone pair that occupies a nominally sp2 AO on the NH group. This rehybridization decreases the overlap between the AOs containing the lone pairs of electrons and thus reduces the four-electron destabilization caused by the overlap between these doubly occupied AOs in E-HNNH.6 The effects of possible contributions from reductions in the lone-pair repulsion energies to lowering the N−H BDEs in E-HN
(5)
and BDE(H 2CCH−H) = 110.5 kcal/mol
(6)
One of the pair of N−H bonds made in the hydrogenation of N2 to E-HNNH is 46.6 kcal/mol weaker than one of the pair of C−H bonds made in the hydrogenation of acetylene to ethylene. This very large difference between the strengths of these bonds made to carbon and to nitrogen accounts for over 50% of the ca. 89.9 kcal/mol difference between the enthalpy changes in these two reactions. Why is an N−H bond in E-HNNH much weaker than a C−H bond in ethylene? Insight is provided by also considering the addition of H2 to HCN, a reaction in which a C−H bond and an N−H bond are both made. H 2+HCN→H 2C=NH ΔH(298.15)=−9.7 kcal/mol
(7)
In analogy to eqs 3 and 4, the enthalpy change in the reaction in eq 7 can be expressed as a difference between BDEs, either ΔH=BDE(H 2)+BDE(πCN) −BDE(H 2CN−H)−BDE(H−CHN•)
(8)
or ΔH =BDE(H 2)+BDE(πCN)−BDE(H−HC=NH) −BDE(E‐•HCN−H)
(9)
For the N−H bond and the C−H bond in H2CNH, the relevant BDEs at 298.15 H are1 BDE(H 2C=N−H)=88.0 kcal/mol
(10)
BDE(H−CH=NH)=96.1 kcal/mol
(11)
The N−H bond and a C−H bond in H2CNH are stronger by, respectively, 24.1 and 32.2 kcal/mol than an N−H bond in E-HNNH, and these differences make large contributions to the 57.6 kcal/mol greater exothermicity of the addition of H2 to HCN than to N2. For convenience, the BDEs of the N−H and C−H bonds in E-HNNH, H2CNH, and H2CCH2 are summarized in Scheme 1. An important clue to one of the factors that contribute to making an N−H bond in E-HNNH 46.6 kcal/ mol weaker than a C−H bond in H2CCH2 is that, as shown B
DOI: 10.1021/acs.jpca.6b11728 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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C−H and N−H BDEs from Scheme 1, and BDE (H2) = 104.2 kcal/mol.1 Unfortunately, neither the “formal” C−H and N−H σ BDEs in the radicals nor the BDEs of the π bonds, formed by loss of a hydrogen atom from each radical, can be measured separately. It is, however, possible to estimate the “formal” C−H and N− H σ BDEs in the radicals from the measured C−H and N−H σ BDEs for forming the radicals, which are given in Scheme 1. For example, using the Benson assumption,9,10 the “formal” C−H BDE in the vinyl radical is taken to be the same as the C−H BDE in H2CCH2 (BDE = 110.5 kcal/mol).11 The “formal” C−H BDE in forming HCN from CH2N• is also assumed to be 110.5 kcal/mol. Although the “formal” C−H BDEs in the H-CHCH• and H-CHN• radicals are assumed to be the same, the actual values of the C−H BDEs measured in these two radicals would, of course, differ, due to the difference between the BDEs of the C−C and C−N π bonds formed in H−CHCH • → HCCH and in H−CHN• → HCN. In the expression for BDE (•HCN−H) in Scheme 2, why is 14.4 kcal/mol added to the N−H BDE of 88.0 kcal/mol in
NH are discussed in the Supporting Information for this manuscript. Scheme 1 shows that the nominally sp2 N−H bond in H2CNH is 22.5 kcal/mol weaker than an sp2 C−H bond in H2CCH2. At first this seems very surprising, because an sp3 N−H bond in NH3 (BDE = 108.6 kcal/mol) is 3.6 kcal/mol stronger than an sp3 C−H bond in CH4 (BDE = 105.0 kcal/ mol.1 However, the relative N−H and C−H bond strengths reverse when the nitrogen and carbon are both sp2 hybridized. For example, breaking an sp2 N−H bond in •NH2 (BDE = 92.4 kcal/mol), to form the triplet state of NH, requires 18.3 kcal/ mol less enthalpy than breaking an sp2 CH bond in •CH3 (BDE = 110.7 kcal/mol), to form the triplet state of CH2.1 The much greater strength of the bond that is made in going from a triplet carbene to a carbon-centered radical than in going from a triplet nitrene to an aminyl radical7 is the reason why triplet carbenes abstract hydrogen atoms, but triplet nitrenes do not.8 As discussed previously,7 the reason why the N−H BDE of • NH2 is much lower than the C−H BDE of •CH3, is that, upon loss of a hydrogen atom from •NH2, the nitrogen rehybridizes from being nominally sp2 to being nominally sp. Consequently, in going from •NH2 to triplet NH, there is a very large increase in the 2s character of the lone pair of electrons on nitrogen, which stabilizes the lone pair and lowers the energy of triplet NH. There is also a small amount of rehybridization in going from •CH3 to triplet CH2, which increases slightly the carbon 2s character in the C−H bonds. However, unlike the case in triplet NH, there is, of course, no lone pair of electrons in triplet CH2, whose energy can be lowered by rehybridization. On replacing the CH2 groups in H2CNH and H2CCH2 by NH groups, one might expect a similar difference of ca. 22.5 kcal/mol between an N−H BDE in E-HNNH and a C−H BDE in HNCH2, assuming that the lone pair of electrons on the nitrogen in each radical formed have the same radical stabilizing effect in both the HNN• and HNCH• radicals. However, as shown in Scheme 1 the actual difference between an N−H BDE in E-HNNH and a C−H BDE in HNCH2 is 32.2 kcal/mol, which is 9.7 kcal/mol more than 22.5 kcal/ mol. As discussed above, some or all of this 9.7 kcal/mol can be attributed to the greater ability of a nitrogen lone pair to stabilize an adjacent radical center on nitrogen than on carbon. In summary, using the energy differences in Scheme 1, it is possible to account for the 46.6 kcal/mol difference between a C−H BDE in H2CCH2 and an N−H BDE in E-HNNH as the sum of two effects. They are (1) an intrinsic energy difference of 22.5 kcal/mol between sp2 C−H and N−H BDEs, based on the difference between the C−H BDE in H2CCH2 and the N−H BDE in H2CNH, and (2) resonance stabilization of the HNN• radical by the lone pair on nitrogen by RSE = −24.1 kcal/mol. However, as noted above and as discussed in the Supporting Information, a third effect− relief of the four-electron destabilization of E-HNNH, due to overlap of the lone pairs−could also make a contribution to lowering the N−H BDE in this molecule. Turning now to the BDEs of the C−H and N−H bonds in the four radicals in Scheme 1, these BDEs are the differences between the “formal” strengths of the C−H and N−H σ bonds that are broken and the strengths of the C−C, C−N, and N−N π bonds that are made. These enthalpy differences between the σ bonds that are broken and the π bonds that are made can be calculated by substituting into eqs 3, 4, 7, and 8 the experimental enthalpy of each hydrogenation reaction, the
Scheme 2. “Formal” BDEs of the N−H and C−H bonds in • HCCH2, H2CN•, E-•HCNH, and •NNHa
Subtraction of the BDEs of the π bonds that would be formed from the “formal” σ BDEs in these radicals gives the N−H and C−H BDEs that would actually be measured in these radicals.
a
H2CN−H? The mathematical reason is that, in order for the sum of the C−H and N−H BDEs for forming HCN from H2CNH to be independent of the order in which these two bonds are broken, the sums of the C−H and N−H BDEs for these two pathways must, of course, be the same. Therefore, BDE(H−HCNH) + BDE(•HCN−H) = BDE(H 2CN−H) + BDE(H−CHN•)
(12)
Substituting the values of BDE (H−HCNH) = 96.1 kcal/ mol and BDE (H2CN−H) = 88.0 kcal/mol from Scheme 1 and the value of BDE (H−CHN•) = 110.5 kcal/mol from Scheme 2, and then solving eq 12 for the “formal” BDE for • HCN−H → HCN gives BDE(•HCN−H) = 88.0 + 14.4 = 102.4 kcal/mol (13)
The physical reason for the addition of 14.4 kcal/mol to the N−H BDE of 88.0 kcal/mol in the expression for the “formal” BDE of •HCN−H is that the lone-pair of electrons on N stabilizes the •HCN−H radical by 110.5−96.1 = 14.4 kcal/ mol. However, on breaking the N−H bond in the radical, this stabilization of the unpaired electron is lost, since it is replaced C
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The Journal of Physical Chemistry A by formation of a π bond in HCN. Thus, the expression for BDE (•HCN−H) in eq 13 contains a term for −RSE = 14.4 kcal/mol. BDE (•NN−H) also contains a term for −RSE = 24.1 kcal/mol for the resonance stabilization in this radical that is lost upon N−H dissociation and formation of N2.6 The addition of 24.1 kcal/mol contributes to the fact that the formal value of BDE (•NN−H) = 112.1 kcal/mol in Scheme 2 is 48.2 kcal/mol higher than BDE (HNN−H) = 63.9 kcal/mol in Scheme 1. The remaining 24.1 kcal/mol comes from the fact that the lone pair on the adjacent nitrogen lowers BDE (HN N−H) by this amount of enthalpy, but not BDE (•NN−H). Equations 3, 4, and 8 (or 9) can now be used to obtain the BDE of a π bond in HCCH,12 NN, and HCN. The relevant ΔH values are given in eqs 1, 2, and 7; the necessary C−H and N−H BDEs are provided in Schemes 1 and 2, and BDE(H2) = 104.2 kcal/mol.1 Solving eqs 3, 4, and 8 (or 9) for the value of BDE(π) in each equation gives BDE(π NN) = 119.7 kcal/mol
(14)
BDE(πHCCH) = 74.8 kcal/mol
(15)
BDE(πHCN) = 84.6 kcal/mol
(16)
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AUTHOR INFORMATION
Corresponding Author
*(W.T.B.) E-mail:
[email protected]. ORCID
Weston Thatcher Borden: 0000-0003-4782-3381 Notes
The author declares no competing financial interest.
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ACKNOWLEDGMENTS The author is grateful to Professor Paul B. Hopkins for his many contributions to this research and to the Robert A. Welch Foundation (Grant B0027) for support
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REFERENCES
(1) Heats of formation [ΔfH°(298.15 K)] were taken from the Argonne National Laboratory’s Active Thermochemical Tables: (http://atct.anl.gov/Thermochemical%20Data/version%201.118/ index.php). These values were used to derive the enthalpies of reaction (ΔH) and bond dissociation enthalpies (BDEs) at 298.15 K that are given in this manuscript. (2) The heat of formation of Z-HNNH is 4.6 kcal/mol higher than that of E-HNNH.1 (3) For example, the sixth edition of Cotton and Wilkinson states, “The great strength of the NN bond is principally responsible for the chemical inertness of N2 and for the endothermicity of most nitrogen compounds, even though they may contain strong bonds.” Cotton, F. A.; Wilkinson, G.; Murillo, C. A.; Bochmann, M. Advanced Inorganic Chemistry, Sixth ed., John Wiley & Sons: New York, 1999; p 314. (4) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 Theory. J. Chem. Phys. 2007, 126, 084108. (5) The 6.2 kcal/mol larger difference between BDE (H2CCH− H) = 110.5 kcal/mol and BDE (E-HNCH−H) = 96.1 kcal/mol in Scheme 1 than between BDE (H3C−CH2−H) = 100.9 kcal/mol and BDE (H2N−CH2−H) = 92.7 kcal/mol is presumably due to the shorter C-N bond in HNCH• than in H2N−CH2•. The shorter C− N bond allows greater resonance stabilization of the radical center in HNCH• than in H2N-CH2• by the lone pair of electrons on nitrogen. Similarly, the 7.7 kcal/mol larger difference between BDE (H2CN−H) = 88.0 kcal/mol and BDE (E-HNN−H) = 63.9 kcal/mol in Scheme 1 than between BDE (H3C−NH−H) = 99.5 kcal/mol and BDE (H2N−NH−H) = 83.1 kcal/mol is also presumably due to the shorter N−N bond in HNN• than in H2NNH•. (6) Relief of the four-electron repulsion between the lone pairs of nonbonding electrons could contribute to lowering the N−H BDE in not only E-HNN−H but also in H2N−NH−H. (7) Kemnitz, C. R.; Karney, W. L.; Borden, W. T. Why Are Nitrenes More Stable than Carbenes? An Ab Initio Study. J. Am. Chem. Soc. 1998, 120, 3499. (8) See, for example: Borden, W. T.; Gritsan, N. P.; Hadad, C. M.; Karney, W. L.; Kemnitz, C. R.; Platz, M. S. The Interplay of Theory and Experiment in the Study of Phenylnitrene. Acc. Chem. Res. 2000, 33, 765. (9) Benson, S. W. Bond Energies. J. Chem. Educ. 1965, 42, 502. (10) Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976; pp 63−65. (11) Using the heats of formation of ethylene, ethane, and vinyl radical from reference 1, the Benson assumption gives BDE(π) = 64.6 kcal/mol in ethylene. This thermochemical value of the π BDE in ethylene values is essentially the same as the value that is obtained from the kinetics of the E−Z isomerization of ethylene-1,2-d2. Douglas, J. E.; Rabinovitch, B. S.; Looney, F. S. Kinetics of the
A π bond in N2 is 44.9 kcal/mol stronger than a π bond in acetylene and 35.1 kcal/mol stronger than a π bond in HCN. This is not really a surprising finding, since the NN bond length in N2 is about 0.10 Å shorter than the CC bond length in acetylene and about 0.06 Å shorter than the CN bond length in HCN. The shorter NN bond length in N2 is responsible for the fact that the wave function for a π bond in N2 has less diradical character than the wave function for a π bond in acetylene.13
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CONCLUSIONS The greater strength of a π bond in N2 than in acetylene does contribute to making the addition of H2 to N 2 less thermodynamically favorable than the addition of H2 to acetylene. 14 However, as discussed in the Supporting Information, 44.9 kcal/mol provides an upper limit to the greater strength of a π bond in N2 than in acetylene. Thus, the difference in π bond strengths probably contributes less than 50% of the 89.9 kcal/mol difference between the enthalpy changes in these two reactions. The remaining contribution of ≥50% comes from the difference between the strengths of the sp2 C−H and N−H bonds that are formed when acetylene and N2 are hydrogenated. Thus, contrary to popular belief,3 the thermodynamic unfavorability of addition of H2 to N2 is only partly due the strength of the N−N π bond that is broken in this reaction. The relative weakness of the sp2 N−H σ bonds in E-HNNH that are made in this reaction actually plays a slightly larger role.15
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from decreased lone-pair repulsion to weakening an N− H bond in both E-HNN−H and in H−NN• (PDF)
ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b11728. Comparison of the values of ΔH for the reactions in eqs 1 and 2 and the BDEs at 298.15 K, derived from the experimental heats of formation [ΔfH°(298.15 K)] in the Active Thermochemical Tables,1 with the values of ΔH and the BDEs, computed at the G4 level of theory2 and a discussion of the consequences of a possible contribution D
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The Journal of Physical Chemistry A Thermal Cis-Trans Isomerization of Dideuteroethylene. J. Chem. Phys. 1955, 23, 315. (12) Nicolaides, A.; Borden, W. T. Ab Initio Calculations of the Relative Strengths of the Pi Bonds in Acetylene and Ethylene and their Effect on the Relative Energies of Pi Addition Reactions. J. Am. Chem. Soc. 1991, 113, 6750. (13) Xu, L. T.; Dunning, T. H., Jr. Variations in the Nature of Triple Bonds: The N2, HCN, and HC2H Series. J. Phys. Chem. A 2016, 120, 4526. (14) The experimental enthalpies of hydrogenation, combined with the experimental BDEs in Scheme 1 and BDE(H2) = 104.2 kcal/mol, require that BDE(πNN) − BDE(H−NN•) = 7.6 kcal/mol in eq 3, and BDE(πCC) − BDE(H−HCCH•) = − 35.7 kcal/mol in eq 4. Thus, the addition of a hydrogen atom to N2 is thermodynamically unfavorable by 7.6 kcal/mol; but the addition of a hydrogen atom to acetylene is thermodynamically favorable by 35.7 kcal/mol. (15) The tendency to attribute reactivity, or the lack of it, to the strengths of the bonds that are broken in reactions is a mistake that is commonly made. For a discussion of another example, see ref 12.
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