0.15 Reaction rates  (Page 6/10)

From , we can see that the data in fit the equation

It is very important to note that the form of and the appearance of are both the same as the equations and graphs for the temperature dependence of theequilibrium constant for an endothermic reaction. This suggests a model to account for the temperature dependence of the rateconstant, based on the energetics of the reaction. In particular, it appears that the reaction rate is related to the amount ofenergy required for the reaction to occur. We will develop this further in the next section.

Collision model for reaction rates

At this point, we have only observed the dependence of reaction rates on concentration of reactants and ontemperature, and we have fit these data to equations called rate laws. Although this is very convenient, it does not provide usinsight into why a particular reaction has a specific rate law or why the temperature dependence should obey . Nor does it provide any physical insights into the order of the reaction or the meaning of theconstants $a$ and $b$ in .

We begin by asking why the reaction rate should depend on the concentration of the reactants. To answerthis, we consider a simple reaction between two molecules in which atoms are transferred between the molecules during the reaction.For example, a reaction important in the decomposition of ozone $O_3$ by aerosols is $$O_3\left(g\right)+\mathrm{Cl}\left(g\right)\to O_2\left(g\right)+\mathrm{Cl}O\left(g\right)$$ What must happen for a reaction to occur between an $O_3$ molecule and a $\mathrm{Cl}$ atom? Obviously, for these two particles to react, they must come intoclose proximity to one another so that an $O$ atom can be transferred from one to the other. In general, two molecules cannottrade atoms to produce new product molecules unless they are close enough together for the atoms of the two molecules to interact.This requires a collision between molecules.

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 an $O_3$ 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 $\mathrm{Cl}$ atom to be near that specific point is also proportional to the concentrationof $\mathrm{Cl}$ atoms. Therefore, the probability for an $O_3$ molecule and a $\mathrm{Cl}$ atom to be in close proximity to the same specific point at the same time isproportional to the $\left[O_3\right]$ times $\left[\mathrm{Cl}\right]$ .

It is important to remember that not all collisions between $O_3$ molecules and $\mathrm{Cl}$ atoms will result in a reaction. There are other factors to consider includinghow the molecules approach one another. The atoms may not be positioned properly to exchange between molecules, in which casethe molecules will simply bounce off of one another without reacting. For example, if the $\mathrm{Cl}$ atom approaches the center $O$ atom of the $O_3$ 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.