Arrheniusformule

The Arrhenius formula, also known as the Arrhenius equation, is a fundamental relation in chemical kinetics that describes how the rate constant k of a reaction depends on temperature. It is commonly written as k = A exp(-Ea/(R T)), where Ea is the activation energy, A is the pre-exponential factor (frequency factor), R is the universal gas constant, and T is the absolute temperature in kelvin. The equation can be rearranged to its linear form, ln k = ln A - Ea/(R T), which yields a straight line when ln k is plotted against 1/T with slope -Ea/R and intercept ln A.

Origins and use: The Arrhenius equation was proposed by Svante Arrhenius in 1889 to explain how chemical reaction rates increase with temperature. It is an empirical relation that aligns with ideas from collision theory and transition state concepts. In practice, it is used to determine Activation energy from experimental data by constructing an Arrhenius plot (ln k versus 1/T) and extracting Ea from the slope, while the intercept provides information about A. The equation is widely applied across chemistry, biochemistry, materials science, and related fields to describe temperature dependence of reaction rates.

Limitations and variants: The Arrhenius formula approximates many reactions over moderate temperature ranges, but deviations occur when reaction mechanisms change with temperature, phase transitions occur, or diffusion controls the rate at extremes. At very low temperatures, quantum tunneling can become relevant, and at high temperatures the simple form may fail. In some cases a modified Arrhenius equation is used, allowing A or Ea to vary with temperature, or incorporating additional factors to better reflect complex kinetics.