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. First, and foremost, these two molecules have to collide, thereby organizing the system. A larger proportion of the collisions that occur between reactants now have enough energy to overcome the activation energy for the reaction. Molecules that have a kinetic energy equal to or higher than the threshold energy will react. The average internal energy is the energy that your reactant molecule have.
. In order for two molecules to react, they must collide. On the other hand, molecules that don't have enough kinetic energy will not react. Both of these factors raise the free energy of the system by lowering the entropy. 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. Aqueous solutions of hydrogen peroxide are stable until we add a small quantity of the I - ion, a piece of platinum metal, a few drops of blood, or a freshly cut slice of turnip, at which point the hydrogen peroxide rapidly decomposes. The Arrhenius equation can also be used to calculate what happens to the rate of a reaction when a catalyst lowers the activation energy.
The threshold energy is the energy that these molecules must have in order for a reaction to take place. In 1889, Svante Arrhenius showed that the relationship between temperature and the rate constant for a reaction obeyed the following equation. The rate of a reaction depends on the temperature at which it is run. We start by taking the natural logarithm of both sides of the equation. 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. 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. In this equation, k is the rate constant for the reaction, Z is a proportionality constant that varies from one reaction to another, E a is the activation energy for the reaction, R is the ideal gas constant in joules per mole kelvin, and T is the temperature in kelvin.
E a measures the change in the potential energy of a pair of molecules that is required to begin the process of converting a pair of reactant molecules into a pair of product molecules. The difference between the threshold energy and whatever internal energy molecules have is called the activation energy. If they don't collide with enough energy, a reaction doesn't take place and they remain as reactant molecules. Four criteria must be satisfied in order for something to be classified as catalyst. The molecules also carry more kinetic energy. As a rule, the rate of a reaction doubles for every 10 oC increase in the temperature of the system.
The only way to explain the relationship between temperature and the rate of a reaction is to assume that the rate constant depends on the temperature at which the reaction is run. The Arrhenius equation can be used to determine the activation energy for a reaction. 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. Because H 2O 2 and I - are both involved in the first step in this reaction, and the first step in this reaction is the rate-limiting step, the overall rate of reaction is first-order in both reagents. Chemical reactions are all about collisions between molecules. Catalysts increase the rates of reactions by providing a new mechanism that has a smaller activation energy, as shown in the figure below. To illustrate how a catalyst can decrease the activation energy for a reaction by providing another pathway for the reaction, let's look at the mechanism for the decomposition of hydrogen peroxide catalyzed by the I - ion.
In other words, the activation energy is what you need to supply to the molecules that don't have enough kinetic energy to reach the threshold energy. It can occur in two steps, both of which are easier and therefore faster. As the temperature increases, the molecules move faster and therefore collide more frequently. The first criterion provides the basis for defining a catalyst as something that increases the rate of a reaction. As the temperature of the system increases, the number of molecules that carry enough energy to react when they collide also increases.
However, this is not the whole story. The fourth criterion results from the fact that catalysts speed up the rates of the forward and reverse reactions equally, so the equilibrium constant for the reaction remains the same. In the presence of this ion, the decomposition of H 2O 2 doesn't have to occur in a single step. The minimum energy that molecules need to have in order for a reaction to take place is called the threshold energy. We then rearrange this equation to fit the equation for a straight line. Now, to get these unreactive molecules to actually react, you need to provide them with more kinetic energy.
The rate of reaction therefore increases with temperature. The second reflects the fact that anything consumed in the reaction is a reactant, not a catalyst. Not only do they have to collide, but they must do so with enough energy to allow for the formation of the products. As a result, the rate of reaction increases. The third criterion is a consequence of the second; because catalysts are not consumed in the reaction, they can catalyze the reaction over and over again.