Table 13.

PCET Thermochemistry for Nitrogen Reduction^a

HN2•/HNN-H	solvent	E∘(HNNH•+/0)	pKa(HNNH•+)	pKa(HNNH)	E∘(V vs H2)b	BDFE
HNN-H	gas	–	–	–	0.17	52.625
HNNH/HN•NH-H	solvent	E∘(HNNH2+/•	pKa(HNNH2+)	pKa(HNNH2•)	E∘(V vs H2)	BDFE
HN•NH-H	gas	–	–	–	−0.56	35.6334
HN•NH-H/H2NNH-H	solvent	E∘(H2NNH2•+/0)	pKa(H2NNH2•+)	pKa(H2NNH2)	E∘(V vs H2)	BDFE
H2NNH-H	gas	-	-	–	1.04	72.6334
H2NNH-H	H2O	0.69180	7.2335	–	1.12	78.5
N2(g) + 3H2(g) → 2NH3	solvent			E∘(V vs H2)		−ΔG∘/nc
N2/NH3	gas			0.05742		49.9
N2(g)/NH3	H2O			0.092179		54.9
N2(g)/NH3	MeCN			0.063179		53.5
N2(g) + 2H2(g) → N2H4	solventc			E∘(V vs H2)		−ΔG∘/nd
N2/N2H4	gas			−0.41342,e		39.1
N2(g) + H2(g) → N2H2	solventc			E∘(V vs H2)		BDFEavg
N2/N2H2	gas			−1.07f		23.9

^aPotentials for 1e⁻ reductions are in V vs SHE if in aqueous solution and V vs Cp₂Fe^+/0 if they are in organic solution. Values for E^∘(V vs H₂) are in V; −eE^∘ is the average free energy for $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{\text{H}}_{2(\text{g})}$ addition. Uncited values of E^∘(V vs H₂) were calculated from other values in the row using Scheme 2 or eq 18. BDFEs and −ΔG^∘/n values are in kcal mol⁻¹ and if uncited were calculated from E^∘(V vs H₂) using eq 18. In many cases, the citation associated with a BDFE is for the related BDE, and the tabulated value was calculated using eq 9. Values in [square brackets] have been calculated from the other values in the row using Hess’ law.

^bE^∘(V vs H₂) of HN^•NH-H in H₂O was derived from those of N₂/N₂H₄, N₂/N₂H₂, and H₂NNHH.

^cRelated values in MeCN or H₂O have been reported, but they include computational components or different numbers of protons and electrons and therefore are not included here.^179,180

^d−ΔG^∘/n values are average free energies for the overall reaction shown except to form H^•[rather than add H_2(g)]. See Section 4.

^eOther values of ΔH^∘_f of N₂H₄ exist,42 but a similar value was obtained from another thermochemical cycle in ref 179.

^fE^∘(V vs H₂) of N₂/N₂H₂ in the gas phase was derived from those of H₂NNH-H, HN^•NH-H, and N₂/N₂H₄.