Methods for studying reaction kinetics in gas chromatography, exemplified by using the 1-chloro-2,2-dimethylaziridine interconversion reaction

Abstract

In this paper, methods are described that are used for studying first-order reaction kinetics by gas chromatography. Basic theory is summarized and illustrated using the interconversion of 1-chloro-2,2-dimethylaziridine enantiomers as a representative example. For the determination of the kinetic and thermodynamic activation data of interconversion the following methods are reviewed: (i) classical kinetic methods where samples of batch-wise kinetic studies are analyzed by enantioselective gas chromatography, (ii) stopped-flow methods performed on one chiral column, (iii) stopped-flow methods performed on an achiral column or empty capillary coupled in series with two chiral columns, (iv) on-flow method performed on an achiral column coupled in series with two chiral columns, and (v) reaction gas chromatography, known as a dynamic gas chromatography, where the interconversion is performed on chiral column during the separation process. The determination of kinetic and thermodynamic activation data by methods (i) through (iv) is straightforward as the experimental data needed for the evaluation (particularly the concentration of reaction constituents) are accessible from the chromatograms. The evaluation of experiments from reaction chromatography method (v) is complex as the concentration bands of reaction constituents are overlapped. The following procedures have been developed to determination peak areas of reaction constituents in such complex chromatograms: (i) methods based on computer-assisted simulations of chromatograms where the kinetic activation parameters for the interconversion of enantiomers are obtained by iterative comparison of experimental and simulated chromatograms, (ii) stochastic methods based on the simulation of Gaussian distribution functions and using a time-dependent probability density function, (iii) approximation function and unified equation, (iv) computer-assisted peak deconvolution methods. Evaluation of the experimental data permits the calculation of apparent rate constants for both the interconversion of the first eluted ( k ¯ A → B app ) as well as the second eluted ( k B → A app ) enantiomer. The mean value for all the rate constants (from all the reviewed methods) was found for 1-chloro-2,2-dimethylaziridine A → B enantiomer interconversion at 100 °C: k ¯ A → B app = 21.2 × 10 − 4 s − 1 with a standard deviation σ = 10.7 × 10 −4. Evaluating data for reaction chromatography at 100 °C { k ¯ app = k A → B app = k B → A app = 13.9 × 10 − 4 s − 1 , σ = 3.0 × 10 −4 s −1} shows that differences between k A → B app and k B → A app are the same within experimental error. It was shown both theoretically and experimentally that the Arrhenius activation energy ( E a) calculated from Arrhenius plots (ln k app versus 1/ T) is proportional to the enthalpy of activation { E a = Δ H + RT}. Statistical treatment of Gibbs activation energy values gave: Δ G ¯ app = 110.5 kJ mo l − 1 , σ = 2.4 kJ mol −1, Δ G ¯ A → B app = 110.5 kJ mo l − 1 , σ = 2.2 kJ mol −1, Δ G ¯ B → A app = 110.3 kJ mo l − 1 , σ = 2.8 kJ mol −1. This shows that the apparent Gibbs energy barriers for the interconversion of 1-chloro-2,2-dimethylaziridine enantiomers are equal Δ G ¯ app = Δ G A → B app = Δ G B → A app and within the given precision of measurement independent of the experimental method used.