Why does an activation barrier form

The minimum energy necessary to form a product during a collision between reactants is called the activation energy E a. The kinetic energy of reactant molecules plays an important role in a reaction because the energy necessary to form a product is provided by a collision of a reactant molecule with another reactant molecule.

In single-reactant reactions, activation energy may be provided by a collision of the reactant molecule with the wall of the reaction vessel or with molecules of an inert contaminant. If the activation energy is much larger than the average kinetic energy of the molecules, the reaction will occur slowly: Only a few fast-moving molecules will have enough energy to react.

If the activation energy is much smaller than the average kinetic energy of the molecules, the fraction of molecules possessing the necessary kinetic energy will be large; most collisions between molecules will result in reaction, and the reaction will occur rapidly. Figure 3 shows the energy relationships for the general reaction of a molecule of A with a molecule of B to form molecules of C and D :.

The figure shows that the energy of the transition state is higher than that of the reactants A and B by an amount equal to E a , the activation energy. Thus, the sum of the kinetic energies of A and B must be equal to or greater than E a to reach the transition state. After the transition state has been reached, and as C and D begin to form, the system loses energy until its total energy is lower than that of the initial mixture.

This lost energy is transferred to other molecules, giving them enough energy to reach the transition state. The forward reaction that between molecules A and B therefore tends to take place readily once the reaction has started.

We can use the Arrhenius equation to relate the activation energy and the rate constant, k , of a given reaction:. In this equation, R is the ideal gas constant, which has a value 8. Both postulates of the collision theory of reaction rates are accommodated in the Arrhenius equation. The frequency factor A is related to the rate at which collisions having the correct orientation occur.

At one extreme, the system does not contain enough energy for collisions to overcome the activation barrier. In such cases, no reaction occurs. At the other extreme, the system has so much energy that every collision with the correct orientation can overcome the activation barrier, causing the reaction to proceed.

In such cases, the reaction is nearly instantaneous. The Arrhenius equation describes quantitatively much of what we have already discussed about reaction rates. For two reactions at the same temperature, the reaction with the higher activation energy has the lower rate constant and the slower rate. Alternatively, the reaction with the smaller E a has a larger fraction of molecules with enough energy to react.

An increase in temperature has the same effect as a decrease in activation energy. The rate constant is also directly proportional to the frequency factor, A. Hence a change in conditions or reactants that increases the number of collisions with a favorable orientation for reaction results in an increase in A and, consequently, an increase in k. A convenient approach to determining E a for a reaction involves the measurement of k at different temperatures and using of an alternate version of the Arrhenius equation that takes the form of linear equation:.

The intercept gives the value of ln A. Determination of E a The variation of the rate constant with temperature for the decomposition of HI g to H 2 g and I 2 g is given here. What is the activation energy for the reaction? In many situations, it is possible to obtain a reasonable estimate of the activation energy without going through the entire process of constructing the Arrhenius plot. The Arrhenius equation:. Not all of the molecules have the same kinetic energy, as shown in the figure below.

This is important because the kinetic energy molecules carry when they collide is the principal source of the energy that must be invested in a reaction to get it started.

But, before the reactants can be converted into products, the free energy of the system must overcome the activation energy for the reaction, as shown in the figure below. The vertical axis in this diagram represents the free energy of a pair of molecules as a chlorine atom is transferred from one to the other. The horizontal axis represents the the sequence of infinitesimally small changes that must occur to convert the reactants into the products of this reaction.

To understand why reactions have an activation energy, consider what has to happen in order for ClNO 2 to react with NO. First, and foremost, these two molecules have to collide, thereby organizing the system. Not only do they have to be brought together, they have to be held in exactly the right orientation relative to each other to ensure that reaction can occur. Both of these factors raise the free energy of the system by lowering the entropy. As the temperature of the system increases, the number of molecules that carry enough energy to react when they collide also increases.

The rate of reaction therefore increases with temperature. As a rule, the rate of a reaction doubles for every 10 o C increase in the temperature of the system. Purists might note that the symbol used to represent the difference between the free energies of the products and the reactants in the above figure is G o , not G o. A small capital "G" is used to remind us that this diagram plots the free energy of a pair of molecules as they react, not the free energy of a system that contains many pairs of molecules undergoing collision.

If we averaged the results of this calculation over the entire array of molecules in the system, we would get the change in the free energy of the system, G o. Purists might also note that the symbol used to represent the activation energy is written with a capital " E ". This is unfortunate, because it leads students to believe the activation energy is the change in the internal energy of the system, which is not quite true.

In general, using the integrated form of the first order rate law we find that:. First order reaction : For a first order reaction the half-life depends only on the rate constant:.

Thus, the half-life of a first order reaction remains constant throughout the reaction, even though the concentration of the reactant is decreasing. Since the concentration of A is decreasing throughout the reaction, the half-life increases as the reaction progresses. That is, it takes less time for the concentration to drop from 1M to 0. Let's try a simple problem: A first order reaction has a rate constant of 1. What is the half life of the reaction? What is the rate constant?

What percentage of N 2 O 5 will remain after one day? The Activation Energy E a - is the energy level that the reactant molecules must overcome before a reaction can occur. In order to calculate the activation energy we need an equation that relates the rate constant of a reaction with the temperature energy of the system.