Arrhenius Equation
k = Ae^(-Ea/RT)
The Arrhenius equation shows how rate constant k depends on temperature and activation energy. It explains why reactions speed up with temperature.
Variables
Rate constant at temperature T
Pre-exponential factor related to collision frequency
Energy barrier in J/mol
8.314 J/(mol·K)
Absolute temperature in Kelvin
Example Calculation
Scenario
A reaction has Ea = 75.0 kJ/mol and A = 4.0 x 10^13 s^-1. Calculate k at 300 K.
Given Data
Calculation
k = Ae^(-Ea/RT) = (4.0 x 10^13)e^(-75000/(8.314)(300)) = (4.0 x 10^13)e^(-30.1)
Result
k = 3.4 x 10^0 s^-1 = 3.4 s^-1
Interpretation
At 300 K, the rate constant is 3.4 s^-1. Increasing temperature will increase k exponentially because more molecules have enough energy to overcome the activation barrier.
When to Use This Formula
- ✓Calculating rate constant at different temperatures
- ✓Finding activation energy from rate data
- ✓Understanding temperature dependence of reactions
- ✓Comparing two temperatures (two-point form)
Common Mistakes
- ✗Using Ea in kJ without converting to J
- ✗Forgetting that T must be in Kelvin
- ✗Using the wrong R value
- ✗Not using the two-point form when comparing temperatures
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Common questions about this formula
ln(k2/k1) = (Ea/R)(1/T1 - 1/T2). This is useful for finding Ea from rate constants at two temperatures, or predicting k at a new temperature.
Activation energy is the minimum energy required for reactants to form products. It represents the energy barrier of the transition state. Catalysts lower Ea, speeding up the reaction.