Temperature Dependence of Reaction Rates and Arrhenius Activation Energy: Acid-Catalyzed Iodination of Acetone

The Arrhenius equation represents an empirical idealization assuming temperature-independent activation energy over modest thermal spans (ΔT ≤ 30 K). Over broader thermal intervals, transition state theory reveals that the pre-exponential factor possesses intrinsic temperature dependence (A = (e·k_B·T / h)·exp(ΔS‡ / R)), causing minor curvature (dE_a/dT = R = 8.314 J·mol⁻¹·K⁻¹). At temperatures exceeding 50 °C, experimental error is exacerbated by volatile acetone evaporation (vapor pressure > 68 kPa) and competitive acid-catalyzed aldol condensation of acetone into diacetone alcohol and mesityl oxide, which slightly perturbs ketone activity. At temperatures below 15 °C, water condensation on optical cuvette windows and prolonged reaction times (> 4 minutes) enhance atmospheric oxygen oxidation of iodide back to triiodide, distorting the zero-order depletion endpoint. The physical simulation engine numerically integrates the multi-step kinetic differential equations governing the acid-catalyzed iodination of acetone across the experimental domain from 20.0 °C (293.15 K) to 45.0 °C (318.15 K). The true phenomenological Arrhenius parameters embedded within the model are activation energy E_a = 84.14 kJ·mol⁻¹ (84,140 J·mol⁻¹) and pre-exponential frequency factor A = 1.541094 × 10¹⁰ L·mol⁻¹·s⁻¹. Fixed baseline experimental concentrations: [acetone]₀ = 1.000 M, [H⁺]₀ = 0.500 M, and limiting molecular iodine [I₂]₀ = 0.00100 M (1.00 mM). Under these pseudo-zero-order conditions, the constant consumption rate is r₀ = −d[I₂]/dt = k(T)·[acetone]₀·[H⁺]₀ = 0.500·k(T). The optical decolorization time to baseline extinction (A ≤ 0.005 at 465 nm) satisfies Δt = [I₂]₀ / r₀ = 0.00200 / k(T). For bath temperatures spanning 20.0 °C, 25.0 °C, 30.0 °C, 35.0 °C, 40.0 °C, and 45.0 °C, the simulated second-order rate constants evaluate to 1.569 × 10⁻⁵, 2.800 × 10⁻⁵, 4.901 × 10⁻⁵, 8.425 × 10⁻⁵, 1.423 × 10⁻⁴, and 2.365 × 10⁻⁴ L·mol⁻¹·s⁻¹, generating stopwatch decolorization intervals of 127.44 s, 71.43 s, 40.81 s, 23.74 s, 14.05 s, and 8.46 s, respectively. Linear regression of ln(k) against reciprocal absolute temperature (1000/T in K⁻¹) yields an ideal slope m = −E_a / (1000·R) = −10.120 K and intercept ln(A) = 23.458 with R² ≥ 0.9999, isolating the activation energy with an analytical accuracy within 0.025% of the theoretical value.