Arrhenius Equation Calculator

k = A * exp(-Ea / (R*T)), where k is the rate constant, A is the pre-exponential (frequency) factor, Ea is activation energy in J/mol, R = 8.314 J/(mol*K), and T is temperature in Kelvin. The equation describes how reaction rates increase with temperature.

The pre-exponential factor (A) represents the frequency of collision attempts between reactant molecules, adjusted for the orientation requirement. It has the same units as the rate constant k. While A weakly depends on temperature, it is often treated as constant over moderate temperature ranges.

Taking the natural log: ln(k) = ln(A) - Ea/(R*T). Plotting ln(k) vs 1/T gives a straight line with slope = -Ea/R and intercept = ln(A). This Arrhenius plot is used experimentally to determine Ea and A from rate constant measurements at different temperatures.

The slope of the Arrhenius plot is -Ea/R. A steeper slope means higher Ea, so the reaction rate is more sensitive to temperature. A reaction with Ea = 100 kJ/mol doubles in rate every ~7 degC near 25 degC; one with Ea = 50 kJ/mol requires a larger temperature increase to double.

Transition state theory expands on Arrhenius by describing the activated complex (transition state) at the top of the energy barrier. The rate depends on both the activation energy (enthalpy barrier) and the entropy of activation (the probability of achieving the right configuration). The Eyring equation: k = (kB*T/h) * exp(-delta G_dagger/(R*T)).