0.16 Reaction rates  (Page 6/9)

The rate of collisions depends on the concentrations of the reactants, since the more molecules there arein a confined space, the more likely they are to run into each other. To write this relationship in an equation, we can think interms of probability, and we consider the reaction above. The probability for anO ₃ molecule to be near a specific point increases with the number of O ₃ molecules, and therefore increases with the concentration of O ₃ molecules. The probability for a Cl atom to benear that specific point is also proportional to the concentration of Cl atoms.Therefore, the probability for an O ₃ molecule and a Cl atom to bein close proximity to the same specific point at the same time is proportional to the[O ₃ ] times[Cl].

It is important to remember that not all collisions betweenO ₃ molecules and Cl atoms willresult in a reaction. There are other factors to consider including how the molecules approach one another. The atoms may not bepositioned properly to exchange between molecules, in which case the molecules will simply bounce off of one another withoutreacting. For example, if the Cl atomapproaches the center O atom of theO ₃ molecule, that O atom willnot transfer. Another factor is energy associated with the reaction. Clearly, though, a collision must occur for the reactionto occur, and therefore there rate of the reaction can be no faster than the rate of collisions between the reactant molecules.

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 ofO ₃ with Cl, the rate must therefore be proportional to[O ₃ ][Cl], and we observe this in the experimental rate law in [link] . 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 [link] 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 [link] 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 [link] , showing conceptually how the energy of the reactants varies as thereaction proceeds. In [link] , 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.