Using Transition State Theory to Understand the Kinetics for the Gas-Phase Synthesis of Ammonia

By Chloe Boyd, Stephen Case, Abigail Seputro

Faculty Mentor: Leanna Giancarlo


To identify the rate-determining step and the most stable transition state for the Haber-Bosch synthesis of gas-phase ammonia, electronic structure calculations for the reactants (N2, H2, NNH2, H2NNH2, HNNH3), intermediates, and transition states were found using the program GAMESS and the basis sets 6-31G*, 6-311G**, and STO-3G (1). The basis set 6-31G* revealed N2(g) + 3H2(g) ⇌ TS1 ⇌ NNH2(g)+ 2H2(g) as the rate-determining step because it had the smallest equilibrium constant (Keq) of 4.2085*10-36. The reaction coordinate diagram showed the most stable transition state was TS4 from the step HNNH3(g) + H2(g) ⇌ TS4 ⇌ 2NH3(g), which had the smallest change in complex enthalpy (ΔHc) of -17.058 kJ/mol. Finally, comparing the resulting changes in reaction Gibbs free energy (ΔGrxn’s), enthalpies (ΔHrxn’s) and entropies (ΔSrxn’s) to values calculated from literature revealed that 6-31G* was the most accurate basis set with a ΔHrxn of -9.6639*101 kJ/mol which had an error of 5.2712*100 % compared to the literature value of -9.1800*101 kJ/mol, ΔSrxn of -6.7433*101 J/mol*K with an error of -6.5960*101 % compared to the literature value of -1.9810*102 J/mol*K, and ΔGrxn of -7.6534*104 J/mol with an error of 1.3379*102 % compared to the literature value of -3.2736*104 kJ/mol (2). Though STO-3G had lower errors of -9.8536*10-1 % and -1.4340*102 % for ΔSrxn and ΔGrxn compared to 6-311G**’s errors of -6.5945*101 % and 2.0873*102 %, it had enthalpies for the forward and reverse equilibrium reactions that were so large that Keq for step NNH2(g) + 2H2(g) ⇌ H2NNH2(g) + H2(g) could not be calculated. STO-3G assumes that all orbitals are spherical which results in its inability to describe orbitals that participate in bonding. This assumption makes the basis set unreliable when used to find the Keq‘s for each step. Both 6-31G* and 6-311G** are ideal basis sets for such an experiment because they are polarization sets created to describe electron distribution between bonds.

(1) GAMESS. Transition State Theory: Kinetics of Ammonia Production. ChemCompute. ChemCompute | ChemCompute: Free Computational Chemistry For Undergraduates (accessed Apr. 7, 2023).

(2) Engel, T.; Reid, P.; Appendix A Data Table 4.1 Thermodynamic Data for Inorganic Compounds at 198.15 K. In Physical Chemistry Thermodynamics, Statistical Thermodynamics, and Kinetics, 4th Edition; Pearson Educations, inc.: New York, 2019. pp. 630-635.


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