The Arrhenius Equation

We know that the rate constant k increases with temperature, but how exactly are they related? The answer is provided by the Arrhenius equation, one of the most powerful relationships in physical chemistry. It links the rate constant to the temperature, the activation energy, and a pre-exponential factor.

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The Arrhenius Equation

k = Ae^(−Ea/RT)

Where:

• k = rate constant (units depend on order)
• A = pre-exponential factor (Arrhenius constant), same units as k
• e = Euler's number (base of natural logarithms, ≈ 2.718)
• Ea = activation energy (J mol⁻¹ — note: joules, not kilojoules)
• R = gas constant = 8.314 J K⁻¹ mol⁻¹
• T = absolute temperature (K — must be in kelvin)

Interpreting the Equation

The exponential term e^(−Ea/RT) represents the fraction of particles with energy ≥ Ea at temperature T. This is the Boltzmann factor. As T increases, Ea/RT decreases, so e^(−Ea/RT) increases — meaning a larger fraction of particles can overcome the activation energy barrier, so k increases.

The pre-exponential factor A accounts for the frequency of collisions and the fraction with correct orientation. It is approximately constant over moderate temperature ranges.

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