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drama2

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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?

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)

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

A

..... B

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

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

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

why concentrations are multiplied in rate law?

collision theory

collision theory and rate lawcollision 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 1VESSEL 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