Intermediate Topic 444 of 1102 Kinetics & Equilibrium
Arrhenius Equation
k equals A times e to the minus Ea over RT, linking rate constant to temperature.
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In-depth explanation of Arrhenius Equation
The Arrhenius equation expresses the rate constant as k = A exp(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is 8.314 J per mol K and T is the absolute temperature. It shows that the rate constant rises exponentially as temperature increases, because a larger fraction of molecules have energy above the barrier. The pre-exponential factor represents collision frequency and orientation requirements and is nearly independent of temperature. Taking the ratio of two rate constants gives ln(k2/k1) = (Ea/R)(1/T1 - 1/T2), which allows Ea to be estimated from two measurements.
Going deeper: Arrhenius Equation
Key ideas: Working form: ln(k2/k1) = (Ea/R)(1/T1 - 1/T2). Example steps: convert to kelvin, take the ratio, multiply by R, and report Ea in kJ per mol. The exponential factor exp(-Ea/RT) is the Boltzmann fraction of collisions with enough energy, for example about 10^-9 at 50 kJ per mol and room temperature.
Common mistakes and connections: A common failure is using Celsius, or taking ln of ratios the wrong way around. Another is assuming Ea and A are fixed over very large temperature ranges, when real curvature arises, and assuming a catalyst changes only Ea but not A. The equation links to collision theory and gives the linear Arrhenius plot of ln k against 1/T.
Visualization of Arrhenius Equation
k = A exp(-Ea/RT) rises steeply with T. With Ea = 75 kJ/mol, going from 300 K to 310 K multiplies k by about 2.6. The interactive lesson shows this as a live animation or chart.
Worked example and use case
For Ea = 75 kJ per mol, raising the temperature from 300 K to 310 K increases k by a factor of about 2.6.
Frequently asked questions about Arrhenius Equation
What is Arrhenius Equation?
k equals A times e to the minus Ea over RT, linking rate constant to temperature.
Is Arrhenius Equation a beginner, intermediate or advanced topic?
Arrhenius Equation is a intermediate topic in Kinetics & Equilibrium. It builds on the vocabulary of beginner topics in this area.
What should I learn before Arrhenius Equation?
Study these earlier topics in Kinetics & Equilibrium first: Activation Energy, Transition State Theory, Activated Complex.
What comes after Arrhenius Equation?
The next topics in Kinetics & Equilibrium are Arrhenius Plot and Pre-exponential Factor.
Can I practise Arrhenius Equation with quizzes?
Yes. The interactive lesson includes a self-check question on Arrhenius Equation, and the Kinetics & Equilibrium quiz draws on every topic in this area.
Where Arrhenius Equation fits in Kinetics & Equilibrium
Arrhenius Equation is topic 25 of 91 in Kinetics & Equilibrium.