Advanced Topic 445 of 1102 Kinetics & Equilibrium
Arrhenius Plot
A graph of ln k versus 1 over T whose slope is minus Ea over R.
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In-depth explanation of Arrhenius Plot
An Arrhenius plot graphs ln k against 1/T, and for most reactions it gives a straight line. Rearranging the Arrhenius equation gives ln k = ln A - Ea/RT, so the slope of the line is -Ea/R and the intercept is ln A. The activation energy can therefore be obtained from the slope multiplied by R, and the pre-exponential factor from the intercept. Curvature in the plot can indicate a change in mechanism within the temperature range studied, or quantum tunnelling at low temperature. Arrhenius plots are a standard way of reporting kinetic data in both chemistry and biology.
Going deeper: Arrhenius Plot
Key ideas: Plot ln k on the y axis against 1/T in K^-1 on the x axis. Slope = -Ea/R, so Ea = -slope x 8.314, and the intercept at 1/T = 0 equals ln A. Using at least four temperatures spread over 30 K or more improves accuracy. With log10 k the slope equals -Ea/(2.303 R).
Common mistakes and connections: Students mix up slope and Ea, forget the negative sign, or use T in Celsius for the axis. Extrapolating the line to 1/T = 0 is a long extrapolation, so A is less accurate than Ea. A curved plot is a signal of a changing rate-determining step or a complex mechanism. Enzyme and protein data also show curvature beyond the denaturation temperature.
Visualization of Arrhenius Plot
ln k against 1/T is a straight line with slope -Ea/R; a slope near -9000 K means Ea is about 75 kJ/mol, and the intercept gives ln A. The interactive lesson shows this as a live animation or chart.
Worked example and use case
A measured slope of -9000 K corresponds to Ea = 9000 x 8.314 = 74.8 kJ per mol.
Frequently asked questions about Arrhenius Plot
What is Arrhenius Plot?
A graph of ln k versus 1 over T whose slope is minus Ea over R.
Is Arrhenius Plot a beginner, intermediate or advanced topic?
Arrhenius Plot is a advanced topic in Kinetics & Equilibrium. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Arrhenius Plot?
Study these earlier topics in Kinetics & Equilibrium first: Transition State Theory, Activated Complex, Arrhenius Equation.
What comes after Arrhenius Plot?
The next topics in Kinetics & Equilibrium are Pre-exponential Factor and Temperature Effect on Rate.
Can I practise Arrhenius Plot with quizzes?
Yes. The interactive lesson includes a self-check question on Arrhenius Plot, and the Kinetics & Equilibrium quiz draws on every topic in this area.
Where Arrhenius Plot fits in Kinetics & Equilibrium
Arrhenius Plot is topic 26 of 91 in Kinetics & Equilibrium.