Arrhenius Equation
Temperature dependence of the reaction rate constant.
Formula
Variables
Example
Reaction rates roughly double for every 10 °C rise — the Arrhenius temperature effect.
How it works
The Arrhenius equation connects a reaction’s rate constant to temperature by showing that only a fraction of molecules have enough energy to overcome the activation barrier. As temperature increases, the high-energy tail of the molecular energy distribution grows, so successful collisions become much more frequent and k rises exponentially. The factor A bundles collision frequency and orientation effects, while E_a determines how sensitive the reaction is to temperature.
When to use it
Use this when you need to predict or compare how fast a chemical reaction will be at different temperatures, especially for kinetics, catalysts, and activation-energy calculations. It is also useful for finding E_a from experimental rate constants measured at multiple temperatures.
Worked example, step by step
A reaction has A = 2.5 × 10^12 s^-1 and E_a = 75.0 kJ mol^-1. Find k at T = 350 K. Step 1: Write the equation: k = A e^(-E_a/RT) Step 2: Convert E_a to J mol^-1: 75.0 kJ mol^-1 = 7.50 × 10^4 J mol^-1 Step 3: Substitute values with R = 8.314 J mol^-1 K^-1: k = (2.5 × 10^12) e^[-(7.50 × 10^4)/(8.314 × 350)] Step 4: Calculate the exponent: (7.50 × 10^4)/(8.314 × 350) ≈ 25.77 So k = (2.5 × 10^12) e^-25.77 Step 5: Evaluate the exponential: e^-25.77 ≈ 6.4 × 10^-12 Step 6: Multiply: k ≈ (2.5 × 10^12)(6.4 × 10^-12) ≈ 16 s^-1 Final answer: k ≈ 1.6 × 10^1 s^-1
Common mistakes to avoid
- Using E_a in kJ mol^-1 without converting to J mol^-1 when R is in J mol^-1 K^-1
- Forgetting that temperature must be in kelvin, not °C
- Treating A as the same as k or assuming it is always equal to the collision frequency
Did You Know?
The Arrhenius equation explains why food spoils faster in warmth — reactions speed up sharply with temperature.
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