Carbon Isotope Effect during Oxidation of Carbon Monoxide with Nitrogen Dioxide

By use of naturally occurring C¹² and C¹³ isotopes in carbon monoxide, the effect of carbon mass on the rate of the reaction $$\mathrm{CO}+{\mathrm{NO}}_2={\mathrm{CO}}_2+\mathrm{NO}$$ has been studied in a 15–1 Vycor flask, in the temperature range 540–727°K, and at pressures between 1 and 20 mm. The rate constant for the reaction was k=12×10¹² exp (—31,600/RT) cc mole^—1 sec^—1. The ratio of rate constants k₁₂/k₁₃ was 1.022 at 540°K, 1.019 at 638°K, and 1.016 at 727°K. An activated complex was set up with normal bond distances and normal force constants, and with the reaction coordinate explicitly given in terms of internal coordinates with an interaction term such that the restoring force on an antisymmetric stretching symmetry coordinate is reduced to zero. By means of E. B. Wilson's FG matrix methods, a vibrational analysis was made of the activated complex, all vibration frequencies were determined for one species, and shifts in frequency due to isotopic substitution were computed by a perturbation method. Similarly, the ratio of effective mass of the reaction coordinate was evaluated, and calculations were checked by the Teller‐Redlich product rule. The isotope rate effect was computed by Bigeleisen's formulation of the activated complex theory. For a set of force constants well within the range of normal values and for normal bond radii, calculated isotope rate ratios at all temperatures are in excellent agreement with observed ones.