# Understanding Rate Laws and Collision Theory

• drama2
In summary, the textbook explains that the rate law for elementary step reactions depends on the product of the reactant concentrations, rather than their sum, because particles must collide to react according to collision theory. This is demonstrated in the textbook with a diagram showing that the number of possible collisions quadruples when the concentration of both reactants is doubled. However, the example given in the conversation shows that the number of possible collisions increases differently depending on the type of particles and the formula for the rate law. The textbook explains that the total number of collisions depends only on the number of particles, not their types.
drama2
hi mate,

very confused by something in my textbook explaining rate law and would be very grateful if someone could clarify it for me. here goes...

text book excerpt:

text book
rate laws for elementary step

elementary step ----------------------- molecularity----------- rate law

...(1) a -> product..... unimolecular....... k[A]

...(2) 2A -> product ...... bimolecular ...... k[A]^2

...(3) A + B -> product...... bimolecular ...... k [A]

why concentrations are multiplied in rate law?

collision theory

collision theory and rate law

textbook tells us: "if particles must collide to react, the laws of probability tell us why rate depends on product of reactant concentrations not sum."

one implication of this is that in the case of bimolecular elementary step reactions (see table above) if concentrations are doubled rate of reaction goes four time faster.

this seems pretty obvious for forumla 3 (see above table) and the textbook shows a neat little diagram of how the number of possible collisions quadruples when you double the number particles in a vessel from 2 to 4 SEE DIAGRAM below (by the way ignore the full stops they are the only way i could create distance between the reactant particles the damn post kept condensing the spaces between characters)

VESSEL 1

-----------------------------
A

..... B

------------------------------

VESSEL 2

-----------------------------
A ...... B

A .... B

-----------------------------

clearly in the first instance there is only one possible collision and when u double the concentration of both reactants in the second you can draw four possible collisions between the particles thus explaining why the reaction proceeds four times quicker.

so far so good. the trouble is if you draw this same diagram for forumula (2) i.e.( four B particles in a vessel) in the table above you can draw six possible collisions in the second instance and yet judging by the formula [a]^2 there should only be a quadrupling of the rate. this disparity between n.o of possible collisions with increasing concentration and predicted rate increase gets worse with higher numbers. anyway my question is shouldn't the increase in rate for reaction (2) with increasing concentrations be higher than that for (3) and if it shouldn't why not?

if anyone could clear this up it would be great

thanks alot

john

You are neglecting changes to total number of collisions, no idea if it is your fault, or books fault.

sorry but i don't understand what you're saying. Would you mind elaborating further. i still can't wrap my head around the following example:

imagine two A particles in a vessel and in another vessel one A and one B particle.

see below
vessel 1
--------------------
A

. . . . . . . . . . A
--------------------

and
vessel 2
--------------------

A . . . . . . . . B

-------------------

clearly in both cases there is only one possible collision. now let's see what happens when you double concentration of reactants:

vessel 1
--------------------
A . . . . . . . . A

A . . . . . . . . A
---------------------

and
vessel 2
----------------------

A . . . . . . . . . B

A . . . . . . . . . B

----------------------

now in vessel one there are 6 possible collisions (6 times as many as were possible before) whilst in contrast in vessel two there are 4 possible collisions ( 4 times as many as before). according to the rate law for elementary steps the reaction rate in both cases should quadruple with a doubling in the concentration of the reactants. the explanation given is due to the quadrupling of the number of possible collisions, but in the case of the first vessel there is SIX times as many possible collisions! by that logic in this particular example the rate in vessel one should be six times faster when the concentration is doubled but the forumla is [A]^2 which means it quadruples. what's going on?

drama2 said:
now in vessel one there are 6 possible collisions (6 times as many as were possible before) whilst in contrast in vessel two there are 4 possible collisions ( 4 times as many as before).

Number of possible collisions doesn't depend on the types of objects, only on their number. Either n(n-1) or n(n-1)/2 depending on whether AB and BA are the same or not.

## 1. What is a rate law?

A rate law is an equation that describes the relationship between the rate of a chemical reaction and the concentration of reactants. It is typically expressed in the form: rate = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are the concentrations of reactants, and m and n are the reaction orders.

## 2. How do you determine the rate law of a reaction?

The rate law of a reaction can be determined experimentally by measuring the initial rates of the reaction at different concentrations of the reactants. By plotting the initial rates against the corresponding concentrations, the reaction orders can be determined and used to write the rate law equation.

## 3. What is collision theory?

Collision theory is a concept that explains how chemical reactions occur. It states that in order for a reaction to take place, the reacting particles must collide with each other with sufficient energy and in the correct orientation.

## 4. How does temperature affect the rate of a reaction?

Increasing the temperature of a reaction typically increases the rate of the reaction. This is because at higher temperatures, the reacting particles have more kinetic energy, resulting in more frequent and energetic collisions. Additionally, an increase in temperature can lower the activation energy of a reaction, making it easier for the reaction to occur.

## 5. Can the rate law of a reaction change?

Yes, the rate law of a reaction can change under certain conditions. For example, if the reaction mechanism changes, the rate law may also change. Additionally, changes in temperature or the presence of a catalyst can also alter the rate law of a reaction.

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