<p>The present work investigates the thermal stability and degradation kinetics of TA in aqueous–ethanolic mixtures (50–100% ethanol) at 90 °C over a wide pH range (2.0–12.0) using a validated stability-indicating HPLC method. TA exhibited apparent first-order degradation kinetics under all conditions studied. The rate–pH profile showed a marked increase in degradation rate with increasing pH, consistent with enhanced ionization/reactivity of TA in alkaline media. Solvent composition significantly modulated stability: degradation was minimal in 100% ethanol and maximal in 50% ethanol, underscoring the important roles of solvent polarity and viscosity in controlling degradation. Temperature effects (60–90 °C) were further evaluated at pH 9.0 in 0.1 M NaOH and in 50% ethanol, and thermodynamic parameters (Ea, A, ΔH‡, ΔS‡) were obtained from Arrhenius analysis, indicating faster degradation in alkali than in the aqueous–ethanolic system. To integrate experimental kinetics with theoretical descriptors, QSPR/ML models were developed to relate log<sub>10</sub> (<i>k</i><sub>obs</sub>) to pH, pH<sup>2</sup>, ethanol fraction, dielectric constant (ε), and ln (viscosity). Cross-validated model performance was excellent for linear and regularized approaches (RMSE ≈ 0.058 log units for LM/GLMNET/SVR), while random forest performed less well (RMSE ≈ 0.090). Holdout validation confirmed strong predictive performance (RMSE 0.041–0.055; R2 0.974–0.985), with SVR yielding the lowest error. Variable-influence analyses identified pH as the dominant driver of degradation rate, with a negative pH<sup>2</sup> term capturing curvature; mixture descriptors contributed secondary effects and were highly collinear. An Eyring-style regression of ln (<i>k</i>/T) versus 1/T at pH 9.0 showed a significant medium effect, with 50% ethanol decreasing ln (<i>k</i>/T) by 0.939 (<i>p</i> &lt; 0.005), corresponding to ~2.6-fold lower <i>k</i>/T compared with NaOH at a given temperature.</p>

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Thermal degradation kinetics of tolfenamic acid in liquid media: a combined experimental and QSPR–machine learning study

  • Muhammad Nabeel,
  • Sofia Ahmed,
  • Muhammad Ali Sheraz,
  • Reem Altaf,
  • Umair Ilyas,
  • Zubair Anwar,
  • Ayesha Awan,
  • Sadia Hafeez Kazi,
  • Muneeba Usmani,
  • Raahim Ali

摘要

The present work investigates the thermal stability and degradation kinetics of TA in aqueous–ethanolic mixtures (50–100% ethanol) at 90 °C over a wide pH range (2.0–12.0) using a validated stability-indicating HPLC method. TA exhibited apparent first-order degradation kinetics under all conditions studied. The rate–pH profile showed a marked increase in degradation rate with increasing pH, consistent with enhanced ionization/reactivity of TA in alkaline media. Solvent composition significantly modulated stability: degradation was minimal in 100% ethanol and maximal in 50% ethanol, underscoring the important roles of solvent polarity and viscosity in controlling degradation. Temperature effects (60–90 °C) were further evaluated at pH 9.0 in 0.1 M NaOH and in 50% ethanol, and thermodynamic parameters (Ea, A, ΔH‡, ΔS‡) were obtained from Arrhenius analysis, indicating faster degradation in alkali than in the aqueous–ethanolic system. To integrate experimental kinetics with theoretical descriptors, QSPR/ML models were developed to relate log10 (kobs) to pH, pH2, ethanol fraction, dielectric constant (ε), and ln (viscosity). Cross-validated model performance was excellent for linear and regularized approaches (RMSE ≈ 0.058 log units for LM/GLMNET/SVR), while random forest performed less well (RMSE ≈ 0.090). Holdout validation confirmed strong predictive performance (RMSE 0.041–0.055; R2 0.974–0.985), with SVR yielding the lowest error. Variable-influence analyses identified pH as the dominant driver of degradation rate, with a negative pH2 term capturing curvature; mixture descriptors contributed secondary effects and were highly collinear. An Eyring-style regression of ln (k/T) versus 1/T at pH 9.0 showed a significant medium effect, with 50% ethanol decreasing ln (k/T) by 0.939 (p < 0.005), corresponding to ~2.6-fold lower k/T compared with NaOH at a given temperature.