Arrhenius Equation

Exponential Form:

$$k = A e^{-\frac{E_a}{RT}}$$

Logarithmic Forms (Natural & Base-10):

$$\ln k = \ln A - \frac{E_a}{RT}$$

$$\log_{10} k = \log_{10} A - \frac{E_a}{2.303 RT}$$

Concept: The Arrhenius equation describes the exponential relationship between the rate constant ($$k$$) of a chemical reaction and the absolute temperature ($$T$$). It accounts for the fraction of molecules possessing energy equal to or greater than the activation energy ($$E_a$$).

Notation & Key Units: *

• $$k$$ = Rate constant of the reaction
• $$A$$ = Arrhenius pre-exponential factor / Frequency factor (same units as $$k$$) 
• $$E_a$$ = Activation energy ($$\text{J mol}^{-1}$$ or $$\text{kJ mol}^{-1}$$)
• $$R$$ = Universal gas constant ($$8.314 \text{ J K}^{-1} \text{ mol}^{-1}$$)
• $$T$$ = Absolute temperature in Kelvin ($\text{K}$)
• $$e^{-\frac{E_a}{RT}}$$ = Fraction of collisions having energy$$\ge E_a$$ (dimensionless)