order of reaction

[clarisse]

for the hypothetical reaction

aA+bB+cC→ products

it is found experimentally that the reaction rate can be expressed as:

Reaction rate = k[A]^α*^β*[C]^γ

(k=rate constant)

the order of a reaction with respect to a given reactant is the power of that reactant's concentration in the rate equation. For the hypothetical reaction just mentioned,

order of reaction with respect to A = α

order of reaction with respect to B = β

order of reaction with respect to C = γ

 

hmm, i've been researching and reading and all that but still i don't quite get how do u actually get α, β and γ... could anyone plzz try to explain it to me? thanx!!

[woelen]

Suppose you have a two-compound reaction:

 

A + B --> products

 

A reaction only occurs if a molecule of A and a molecule of B meet at the same place.

 

Now it is a matter of statistics. Because we have tremendous amounts of molecules of A and B, one can use with good approximation that the chance p(A) that a molecule of type A is at a certain place is proportional to [A], hence p(A)=k1*[A]. A similar thing holds for B, p(B)=k2*. Under the assumption that motion of molecules of type A and type B is not influenced by other molecules in the mix, one can state that the chance that both a molecule A and a molecule B are at the same place equals p(A)*p(B), hence it can be written as k1*k2*[A]*

 

Now suppose we have a reaction of the type 2A + B --> products, and the reaction is a true 3-molecule type, which only occurs if 2 molecules of type A and one molecule of type B are at the same place. Again under the assumption of statistical independence, the chance that 2 molecules of type A are at the same place is p(A)*p(A), the chance that all three molecules are at the same place equals p(A)*p(A)*p(B).

 

You see, now you get a power of [A], in my example this is power 2. With equal reasoning you can see that in general you get powers of the concentrations.

 

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

 

Now suppose we take the reaction A + B --> products. This of course also can be written as 2A + 2B ---> 2*products. If you apply the same reasoning, then you would get another result. And here comes the great pitfall. In general, the stoichiometric reaction equations do not predict the rate of reaction, you really have to understand the reaction mechanism and you have to measure in a real practical setup the order of a reaction.

 

Let's take my example 2A + B --> products.

 

Suppose this reaction proceeds as follows:

 

step 1) A + B --> AB (e.g. formation of a complex)

step 2) AB + A --> products

 

Step 1 has a rate d[AB]/dt = k1*[A]*

Step 2 has a rate d[products]/dt = k2*[AB]*[A]

 

Now you see that the real reaction dynamics require solving a set of non-linear differential equations. Now suppose that k1 is very large. This means that step 1 appears to run instantaneously. Suppose that k2 is not that large. Also suppose that [A] is in large excess to .

 

What happens here is that on mixing A and B you at once get AB and the large remaining amount of A. If [A] >> , then the reaction still appears to be first order in its dynamics. The speed of reaction seems to be proportional to [A]*. If [A] is just a little larger than things become even more complicated.

 

In general, reactions, where more than two molecules need to meet each other, are quite rare already. Reactions, where more than four molecules need to meet each other, I do not know an example of that. Almost all reaction take intermediate steps, such as in my example with 2A+B.