# How do the terms in a rate law relate to effectiveness and number of collisions of reactants?

In chemical kinetics, we use rate law to find the instantaneous rate of reaction.

Let us consider a simple reaction

$$\ce{aA + bB -> products}$$

where the rate law is

$$\mathrm{rate} = k[\ce{A}]^a[\ce{B}]^b$$

I think that the rate constant tells us about the effectiveness of collisions for the reaction at a particular temperature; and the concentration terms raised to the powers of stoichiometric coefficients represents the total number of collisions.

Is my reasoning correct? If not, what is the correct explanation?

• Sounds about right. Then again, reactions are rarely simple, and the actual rate law might differ from $k[A]^a[b]^b$, but that's another story. Jul 7 at 11:56
• @IvanNeretin I am not sure how concentration terms raised to the powers of stoichiometric coefficients represents the total number of collisions, could you please prove some mathematical approach to figure this out. Also, I know about the complex reaction and how it differs but I want to know the basic idea behind the rate law thus assuming it is a simple reaction. Thanks for your clarification. Jul 7 at 16:18
• Rate laws such as this only show how many reactant species are needed to produce the product according to mass balance. They tell us nothing about how the reaction actually happens. The actual mechanism for any reaction has to be determined by experiment. You can imagine that if, say, $a=b=2$ the chance of four solute species coming together at the same small instance and in the same place is so absolutely tiny, that it just does not happen. What tends to happen is that two species form an intermediate and this reacts again and so on. (There are whole books on this topic) Jul 7 at 16:28
• @RodrigodeAzevedo Because it works but I am unable to understand how? Jul 8 at 13:50