0.5 Reaction rates  (Page 7/10)

Therefore, we can say that, in a bimolecular reaction , where two molecules collide and react, the rate of the reaction will be proportional tothe product of the concentrations of the reactants. For the reaction of $O_3$ with $\mathrm{Cl}$ , the rate must therefore be proportional to $\left[O_3\right]\left[\mathrm{Cl}\right]$ , and we observe this in the experimental rate law in . Thus, it appears that we can understand the rate law by understanding the collisions which mustoccur for the reaction to take place.

We also need our model to account for the temperature dependence of the rate constant. As noted at the end ofthe last section , the temperature dependence of the rate constant in is the same as the temperature dependence of the equilibrium constant for anendothermic reaction. This suggests that the temperature dependence is due to an energetic factor required for the reaction to occur.However, we find experimentally that describes the rate constant temperature dependence regardless of whether the reaction isendothermic or exothermic. Therefore, whatever the energetic factor is that is required for the reaction to occur, it is not just theendothermicity of the reaction. It must be that all reactions, regardless of the overall change in energy, require energy tooccur.

A model to account for this is the concept of activation energy . For a reaction to occur, at least some bonds in the reactant molecule must be broken, so that atomscan rearrange and new bonds can be created. At the time of collision, bonds are stretched and broken as new bonds are made.Breaking these bonds and rearranging the atoms during the collision requires the input of energy. The minimum amount of energy requiredfor the reaction to occur is called the activation energy, $E_a$ . This is illustrated in , showing conceptually how the energy of the reactants varies as thereaction proceeds. In , the energy is low early in the reaction, when the molecules are stillarranged as reactants. As the molecules approach and begin to rearrange, the energy rises sharply, rising to a maximum in themiddle of the reaction. This sharp rise in energy is the activation energy, as illustrated. After the middle of the reaction has passedand the molecules are arranged more as products than reactants, the energy begins to fall again. However, the energy does not fall toits original value, so this is an endothermic reaction.

shows the analogous situation for an exothermic reaction. Again, as thereactants approach one another, the energy rises as the atoms begin to rearrange. At the middle of the collision, the energy maximizesand then falls as the product molecules form. In an exothermic reaction, the product energy is lower than the reactantenergy.

thus shows that an energy barrier must be surmounted for the reaction tooccur, regardless of whether the energy of the products is greater than ( ) or less than ( ) the energy of the reactants. This barrier accounts for the temperature dependence ofthe reaction rate. We know from the kinetic molecular theory that as temperature increases the average energy of the molecules in asample increases. Therefore, as temperature increases, the fraction of molecules with sufficient energy to surmount the reactionactivation barrier increases.