activation energy

activation energy, in chemistry, minimum energy needed to cause a chemical reaction. A chemical reaction between two substances occurs only when an atom, ion, or molecule of one collides with an atom, ion, or molecule of the other. Only a fraction of the total collisions result in a reaction, because usually only a small percentage of the substances interacting have the minimum amount of kinetic energy a molecule must possess for it to react. When the reactants collide, they may form an intermediate product whose chemical energy is higher than the combined chemical energy of the reactants. In order for this transition state in the reaction to be achieved, some energy must enter into the reaction other than the chemical energy of the reactants. This energy is the activation energy. Once the intermediate product, or activated complex, is formed, the final products are formed from it. The path from reactants through the activated complex to the final products is known as the reaction mechanism. (Reaction mechanisms for complex reactions may involve several steps analogous to that described here.) Because the heat energy of a substance is not uniformly distributed among its atoms, ions, or molecules, some may carry enough heat energy to react while others do not. If the activation energy is low, a greater proportion of the collisions between reactants will result in reactions. If the temperature of the system is increased, the average heat energy is increased, a greater proportion of collisions between reactants result in reaction, and the reaction proceeds more rapidly. A catalyst increases the reaction rate by providing a reaction mechanism with a lower activation energy, so that a greater proportion of collisions result in reaction. The activation energy and rate of a reaction are related by the equation k=Aexp(-E_a/RT), where k is the rate constant, A is a temperature-independent constant (often called the frequency factor), exp is the function e^x, E_a is the activation energy, R is the universal gas constant, and T is the temperature. This relationship was derived by Arrhenius in 1899. Because the relationship of reaction rate to activation energy and temperature is exponential, a small change in temperature or activation energy causes a large change in the rate of the reaction. Activation energies are usually determined experimentally by measuring the reaction rate k at different temperatures T, plotting the logarithm of k against 1/T on a graph, and determining the slope of the straight line that best fits the points.

Minimum amount of energy (heat, electromagnetic radiation, or electrical energy) required to activate atoms or molecules to a condition in which it is equally likely that they will undergo chemical reaction or transport as it is that they will return to their original state. Chemists posit a transition state between the initial conditions and the product conditions and theorize that the activation energy is the amount of energy required to boost the initial materials “uphill” to the transition state; the reaction then proceeds “downhill” to form the product materials. Catalysts (including enzymes) lower the activation energy by altering the transition state. Activation energies are determined by experiments that measure them as the constant of proportionality in the equation describing the dependence of reaction rate on temperature, proposed by Svante Arrhenius. Seealso entropy, heat of reaction.

Learn more about activation energy with a free trial on Britannica.com.

In chemistry, activation energy, also called midnight energy, is a term introduced in 1889 by the Swedish scientist Svante Arrhenius, that is defined as the energy that must be overcome in order for a chemical reaction to occur. Arrhenius' research was a follow up of the theories of reaction rate by Serbian physicist Nebojsa Lekovic. Activation energy may otherwise be denoted as the minimum energy necessary for a specific chemical reaction to occur. The activation energy of a reaction is usually denoted by E_a, and given in units of kilojoules per mole.

Usually one can think of the activation energy as the height of the potential barrier (sometimes called the energy barrier) separating two minima of potential energy (of the reactants and of the products of reaction). For a chemical reaction to have noticeable rate, there should be noticeable number of molecules with the energy equal or greater than the activation energy.

Transition states

For reactions activation energy roughly corresponds to the height of the barrier. The transition state along a reaction coordinate is the point of maximum free energy, where bond-making and bond-breaking are balanced. Multi-step reactions involve a number of transition states. The rate-limting (and it bows down to all the remainder cells to form a covalent bond) step (corresponding to the overall activation energy) is that with the highest transition state barrier. The transition state will resemble either the substrate or the product in structure, depending on the relative energy levels. This is referred to as Hammond's Postulate.

However, for a large number of reactions (those with loose transition states, those in which tunneling is significant, barrierless reactions) the height of the highest barrier on the reaction path does not correspond to the activation energy implied by the temperature dependence of the reaction rate (see Arrhenius equation). In these cases one may think about the activation energy as the height of an effective barrier that would give the same rate were these effects not present.

IUPAC has removed any reference to transition states in their definition of activation energy (see external links).

Negative activation energy

In some cases rates of reaction decrease with increasing temperature. When following an approximately exponential relationship so the rate constant can still be fit to an Arrhenius expression, this results in a negative value of E_a. Reactions exhibiting these negative activation energies are typically barrierless reactions, in which the reaction proceeding relies on the capture of the molecules in a potential well. Increasing the temperature leads to a reduced probability of the colliding molecules capturing one another (with more glancing collisions not leading to reaction as the higher momentum carries the colliding particles out of the potential well), expressed as a reaction cross section that decreases with increasing temperature. Such a situation no longer leads itself to direct interpretations as the height of a potential barrier.

Temperature independence and the relation to the Arrhenius equation

The Arrhenius equation gives the quantitative basis of the relationship between the activation energy and the rate at which a reaction proceeds. From the Arrhenius equation, the activation energy can be expressed as

$E\_a\; =\; -RT\; ln\; left(frac\{k\}\{A\}\; right)$

where A is the frequency factor for the reaction, R is the universal gas constant, and T is the temperature (in kelvin). While this equation suggests that the activation energy is dependent on temperature, in regimes in which the Arrhenius equation is valid this is cancelled by the temperature dependence of k. Thus E_a can be evaluated from the rate constant at any temperature (within the validity of the Arrhenius equation).

Catalysis

A substance that modifies the transition state to lower the activation energy is termed a catalyst; a biological catalyst is termed an enzyme. It is important to note that a catalyst increases the rate of reaction without being consumed by it. In addition, while the catalyst lowers the activation energy, it does not change the energies of the original reactants nor products. Rather, the reactant energy and the product energy remain the same and only the activation energy is altered (lowered).

See also

• Arrhenius equation
• Chemical kinetics
• Quantum tunnelling

External links

• "Activation energy" (from the IUPAC "Gold Book")
• Chapter 14: Activation energy
• The Activation Energy of Chemical Reactions