On a potential energy diagram, activation energy is the vertical distance between the energy level of the reactants and the highest point on the curve, called the transition state. It’s represented as the “hill” that reactants must climb over before they can turn into products. The y-axis shows energy, the x-axis shows the progress of the reaction, and activation energy is always measured from the starting energy level up to the peak.
How To Read a Potential Energy Diagram
These graphs have two axes. The y-axis represents potential energy (usually in kilojoules per mole). The x-axis represents something called the “reaction coordinate,” which is just a way of tracking how far along the reaction has progressed from reactants to products. There are no specific numbers on the x-axis. Instead, the left side represents the starting materials, and the right side represents the products, with the path between them showing how energy changes during the reaction.
The graph always has a hump or hill shape. The reactants sit at one energy level on the left. The curve rises to a peak, then falls to the energy level of the products on the right. Activation energy is the vertical arrow drawn from the reactant energy level straight up to the top of that peak. It is not the distance from the peak down to the products, and it is not the overall energy change of the reaction.
The Peak: What the Transition State Means
The very top of the hill on the graph is called the transition state (sometimes called the activated complex). It’s an unstable, momentary arrangement of atoms that exists only at the instant when reactants are converting into products. Think of it as the halfway point of a molecular collision where old bonds are breaking and new bonds are forming simultaneously. No molecule stays in this state for any measurable time. It exists only at the peak of the energy barrier, and the height of that peak above the reactants is your activation energy.
Exothermic vs. Endothermic Reactions
The shape of the graph changes depending on whether the reaction releases or absorbs energy, but the location of activation energy stays the same: always from reactants up to the peak.
In an exothermic reaction, the products sit lower on the y-axis than the reactants. The overall energy change is negative because the system releases energy to its surroundings. The hill still rises above the reactant level before dropping down to the lower product level. Activation energy is the height from the reactant line to the top of the hill, not from the product line.
In an endothermic reaction, the products sit higher on the y-axis than the reactants. The system absorbs energy, so the overall energy change is positive. The hill still rises above the reactant level to a peak before settling at the higher product level. Activation energy is again measured from the reactant energy level up to the peak. Because the products are already higher than the reactants, the peak tends to be even taller on endothermic diagrams, meaning these reactions generally require more activation energy.
Activation Energy for the Reverse Reaction
The same graph also shows the activation energy for the reverse reaction, which is the vertical distance from the product energy level up to the same peak. In an exothermic forward reaction, the products are lower in energy, so the reverse activation energy is larger. The reverse reaction has to climb a taller hill. In an endothermic forward reaction, the reverse is true: products are higher, so the reverse activation energy (from products up to the peak) is smaller than the forward activation energy.
The transition state peak doesn’t move. It’s the same point on the graph regardless of direction. What changes is where you start measuring from.
How a Catalyst Changes the Graph
When a catalyst is present, it lowers the peak of the hill. On a graph, a catalyzed reaction is often drawn as a second, shorter curve overlaid on the original. The reactant and product energy levels stay exactly the same, because a catalyst doesn’t change the overall energy released or absorbed. It only provides an alternate pathway that requires less energy to get started. The result is a smaller vertical distance between the reactant level and the new, lower peak.
Calculating Activation Energy From the Graph
On a simple potential energy diagram, you can read activation energy directly. Subtract the energy of the reactants from the energy at the peak. If the reactants sit at 50 kJ/mol and the peak is at 120 kJ/mol, the activation energy is 70 kJ/mol.
There’s a second type of graph used in more advanced chemistry courses. Instead of plotting energy vs. reaction progress, it plots the natural log of the reaction rate constant (ln k) on the y-axis against the inverse of temperature (1/T) on the x-axis. This is called an Arrhenius plot, and it produces a straight line. The slope of that line equals the negative activation energy divided by the gas constant (8.314 J/mol·K). So if you know the slope, you multiply it by negative 8.314 to get the activation energy in joules per mole.
If you only have rate constant data at two different temperatures rather than a full graph, you can use the two-point form of the Arrhenius equation. You plug in the two rate constants and two temperatures, and the formula solves for activation energy directly. But on a standard energy diagram of the kind you’ll see in introductory chemistry, no calculation is needed. The activation energy is simply the height of the hill above the reactants, read straight off the y-axis.