Where:
K = Equilibrium constant
ΔH = Standard enthalpy changes of the reaction
R = Universal gas constant
T = Absolute temperature
Using the logarithm property ln(a/b) = ln(a) − ln(b):
The enthalpy change ΔH is the difference between the forward (E₁) and backward (E₂) activation energies: ΔH = E₁ − E₂.
Integral both sides, treating Eₐ and R as constants:
Where C is the constant of integration. Let C = ln A.
This is the linear form of the Arrhenius equation.
Exponentiate both sides:
This gives the final Arrhenius equation:
Where:
k = Rate constant
A = Pre-exponential factor (or frequency factor)
Eₐ = Activation energy
R = Universal gas constant
T = Absolute temperature (in Kelvin)
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Arrhenius Equation: Derivation, Formula & Notes PDF is a fundamental concept in physical chemistry. Understanding the mechanisms, reaction conditions, and stereo-chemical outcomes is crucial for mastering organic chemistry. Our curated resources provide step-by-step visualizations to help you excel.
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What is the Arrhenius equation?
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Activation Energy represents the minimum energy barrier that reacting molecules must overcome to transform into products. A higher Ea means fewer molecules have enough energy to react at a given temperature, leading to a slower reaction rate.
According to the Arrhenius equation, the rate constant increases exponentially with temperature. This is because a small increase in temperature significantly increases the fraction of molecules with energy greater than the activation energy.
The factor 'A' (also called the frequency factor) represents the frequency of collisions between reactant molecules and the probability that they are oriented correctly for a reaction to occur.