Activation Energy & Arrhenius Equation Calculator
Calculate activation energy (Eₐ) from rate constants at two temperatures using the Arrhenius equation, or find the rate constant at any temperature.
Arrhenius Equation and Reaction Rates Guide
The Arrhenius Equation
k = Ae^(−Ea/RT). Where k = rate constant, A = pre-exponential factor (frequency of collisions with correct orientation), Ea = activation energy (J/mol), R = gas constant (8.314 J/mol·K), T = absolute temperature (K). Taking logarithms: ln k = ln A − Ea/(RT). For two temperatures: ln(k₂/k₁) = −(Ea/R) × (1/T₂ − 1/T₁). This two-point form allows Ea calculation from experimental rate constants without knowing A. A plot of ln k vs 1/T gives a straight line with gradient = −Ea/R.
Effect of Temperature on Rate
A common approximation: rate doubles for every 10°C rise in temperature. This arises because at room temperature, many reactions have activation energies in the range 50-80 kJ/mol, which corresponds to a ~2-fold rate increase per 10 K. The Arrhenius equation is more precise: high Ea reactions are more sensitive to temperature change than low Ea reactions. Exothermic reactions: temperature rise increases rate but (if equilibrium) decreases yield (Le Chatelier's principle). Endothermic reactions:
Activation Energy and Catalysis
A catalyst provides an alternative reaction pathway with lower activation energy. Lower Ea means more molecules in the Maxwell-Boltzmann distribution have sufficient energy to react → faster rate at the same temperature. The catalyst is not consumed and does not change the overall ΔH — only the activation energy and therefore the rate. Heterogeneous catalysts (solid catalyst, gaseous/liquid reactants): iron catalyst in Haber process, platinum/rhodium in catalytic converters. Homogeneous catalyst
Maxwell-Boltzmann Distribution
The Maxwell-Boltzmann distribution shows the spread of kinetic energies in a population of molecules at a given temperature. Only molecules with energy ≥ Ea can react. As temperature increases: the peak of the distribution shifts right (higher average energy), the curve flattens and broadens, and the area under the curve beyond Ea (the fraction with sufficient energy) increases disproportionately. This is why the Arrhenius equation contains an exponential term — the fraction of 'reactive' molecu
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