# What Is Activation Energy? Definition and Examples

In chemistry and physics, activation energy is the minimum amount of energy needed to start a chemical reaction. Reactants often get activation energy from heat, but sometimes energy comes from light or energy released by other chemical reactions. For spontaneous reactions, the ambient temperature supplies enough energy to achieve the activation energy.

Swedish scientist Svante Arrhenius proposed the concept of activation energy in 1889. Activation energy is indicated by the symbol Ea and has units of joules (J), kilojoules per mole (kJ/mol), or kilocalories per mole (kcal/mol). An enzyme or catalyst lowers the activation energy. (Jerry Crimson Mann, CC 3.0)

### Effect of Enzymes and Catalysts

A catalyst lowers the activation energy of a chemical reaction. Enzymes are examples of catalysts. Catalysts are not consumed by the chemical reaction and don’t change the reaction’s equilibrium constant. Typically, they work by modifying the transition state of the reaction. Basically, they give a reaction another way to proceed. Like taking a shortcut between two places, the actual distance between them doesn’t change, just the route.

Inhibitors, in contrast, increase the activation energy of a chemical reaction. This decreases the rate of the reaction.

### Activation Energy and Rate of Reaction

Activation energy is related to reaction rate. The higher the activation energy is, the slower the reaction proceeds because fewer reactants have enough energy to overcome the energy barrier at any given time. If the activation energy is high enough, a reaction won’t proceed at all unless energy is supplied. For example, burning wood releases a lot of energy, but a wood table doesn’t suddenly burst into flames. The combustion of wood requires activation energy, which may be supplied by a lighter.

The Arrhenius equation describes the relationship between reaction rate, activation energy, and temperature.

k = Ae-Ea/(RT)

Here, k is the reaction rate coefficient, A is the frequency factor for the reaction, e is the irrational number (approximately equal to 2.718), Ea is the activation energy, R is the universal gas constant, and T is the absolute temperature (Kelvin).

The Arrhenius equation shows that reaction rate changes with temperature. In most cases, chemical reactions proceed more quickly as temperature increases (up to a point). In some cases, reaction rate decreases as temperature increases. Solving for activation energy can give a negative value.

### Is Negative Activation Energy Possible?

The activation energy for an elementary reaction is zero or positive. However, a reaction mechanism consisting of several steps may have a negative activation energy. Further, the Arrhenius equation allows for negative activation energy values in cases where the rate of reaction decreases as temperature increases. Elementary reactions with negative activation energies are barrierless reactions. In these cases, increasing temperature lessens the probability that reactants combine because they have too much energy. You can think of it like throwing two sticky balls at one another. At low speeds, they stick, but if they move too fast, they bounce off each other.

### Activation Energy and Gibbs Energy

The Eyring equation is another relation describing the rate of reaction. However, the equation uses Gibbs energy of the transition state rather than activation energy. The Gibbs energy of the transition state accounts for the enthalpy and entropy of a reaction. While activation energy and Gibbs energy are related, they aren’t interchangeable in chemical equations.

### How to Find Activation Energy

Use the Arrhenius equation to find activation energy. One method involves rewriting the Arrhenius equation and recording the change in reaction rate as temperature changes:

log K = log A – Ea/2.303RT

log (k2/​k1​​) = Ea / 2.303R(1/T1​​−1/T2​​)

For example: The rate constant of a first order reaction increases from 3×10-2 to 8×10-2 as temperature increases from 310K to 330K. Calculate the activation energy (Ea).

log(8×10-2 / 3×10-2) = Ea/2.303R (1/310 – 1/330)
log 2.66 = Ea/2.303R (1.95503 x 10-4)
0.4249 Ea/2.303×8.314 x (1.95503 x 10-4)
0.4249 = Ea/19.147 x (1.95503 x 10-4)
0.4249 = 1.02106 x 10-5 x Ea
Ea = 41613.62 J/mol or 41.614 kJ/mol

You can graph ln k (natural logarithm of the rate constant) versus 1/T and use the slope of the resulting line to find activation energy:

m = – Ea/R

Here m is the slope of the line, Ea is the activation energy, and R is the ideal gas constant of 8.314 J/mol-K. Remember to convert any temperature measurements taken in Celsius or Fahrenheit to Kelvin before calculating 1/T and plotting the graph.

In a plot of the energy of the reaction versus the reaction coordinate, the difference between the energy of the reactants and the energy of the products is ΔH, while the excess energy (the part of the curve above that of the products) is the activation energy.

### References

• Atkins, Peter; de Paula, Julio (2006). Atkins’ Physical Chemistry (8th ed.). W.H.Freeman. ISBN 0-7167-8759-8.
• Espenson, James (1995). Chemical Kinetics and Reaction Mechanisms. McGraw-Hill. ISBN 0070202605.
• Laidler, Keith J.; Meiser, John H. (1982). Physical Chemistry. Benjamin/Cummings. ISBN 0-8053-5682-7.
• Mozurkewich, Michael; Benson, Sidney (1984). “Negative activation energies and curved Arrhenius plots. 1. Theory of reactions over potential wells”. J. Phys. Chem88 (25): 6429–6435. doi:10.1021/j150669a073
• Wang, Jenqdaw; Raj, Rishi (1990). “Estimate of the Activation Energies for Boundary Diffusion from Rate-Controlled Sintering of Pure Alumina, and Alumina Doped with Zirconia or Titania”. Journal of the American Ceramic Society73 (5): 1172. doi:10.1111/j.1151-2916.1990.tb05175.x