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, 2021 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.
– user112830
Jul 7, 2021 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, 2021 at 16:28
• @RodrigodeAzevedo Because it works but I am unable to understand how?
– user112830
Jul 8, 2021 at 13:50
• I have mentioned it is a simple reaction meaning elementary.
– user112830
Jul 8, 2021 at 14:19

Try examining the Arrhenius Equation and see if that gives you more information about the rate constant.

In general, the rate of reaction (in terms of the reactants) is a function of how many successful collisions occur per unit time. There are also unsuccessful collisions. You can also write the rate of reaction in terms of the products. Since the products are not always 1:1 with the reactants, this wouldn't necessarily equate to the number of successful collisions.

In gas phase reactions, inert species can influence the rate of reaction. Since they aren't colliding with the reactants to form the products, the concentrations can't always be equal to the number of collisions.

• Thanks but need a more clear explanation
– user112830
Jul 8, 2021 at 4:03
• Your reasoning is not correct. The concentration terms raised to the powers of stoichiometric coefficients do not represent the total number of collisions. An inert species does not participate in the reaction but can be included in the rate law. Therefore, the concentrations raised to the stochiometric coefficient can't possibly represent the number of collisions. I think you are on the right track with the rate constant. You should read about and examine the Arrhenius Equation, I think this may give you more insight about the rate constant. Jul 8, 2021 at 4:39