A unified kinetic and thermodynamic model of evaporation for forensic applications

Abstract

A unified kinetic and thermodynamic model was derived to predict evaporation for forensic applications, such as fire debris analysis. In this model, a reversible first-order reaction served as the foundation, with rate constants (kinetic regime) and standard vapor pressures (thermodynamic regime) as input parameters. The rate constants and standard vapor pressures for normal (n-) alkanes were fit by linear regression to the retention index, with correlation coefficients of 0.9969 and 0.9998, respectively. These regression equations were used to calculate fraction-remaining curves as a function of the retention index. From these curves, the kinetic and thermodynamic models were able to predict the total fraction remaining of the fuel, either as a bulk quantity or as a chromatogram, as well as the fractions remaining of individual compounds.To evaluate the kinetic and thermodynamic models, gasoline samples were experimentally evaporated to nominal fractions remaining of 0.7, 0.5, 0.3, and 0.1 (30%, 50%, 70% and 90% evaporated). The experimental chromatograms were compared to predicted chromatograms, with Pearson product-moment correlation coefficients of 0.9913 – 0.9068 for the kinetic model and 0.9903 – 0.8921 for the thermodynamic model. The experimental and predicted fractions remaining for individual compounds were compared for n-alkanes and alkylbenzenes spanning a wide range of retention indices and abundances. For the n-alkanes, the mean average percent error was 2.8 – 13.9% for the kinetic model and 3.2 – 20.2% for the thermodynamic model. This approach provides a unified basis for the comparison of the models, and demonstrates the accurate performance of each model.