# Is there any empirical upper limit for order of reaction?

I learned from one of my teachers that empirically reaction with order greater that 3 are never found. But, I am suspicious of the truth value of his claim.

To add to my suspicion there is this paper from 1932 referring to a fourth-order reaction

It seems to me theoretically there should be no upper limit for a reaction as it is possible for 4,5,6... chemical species to come together with the right activation energy in the right direction.

However, empirically making 4 or 5 chemical species to form a transition species is very hard. So, there should be a empirical limit to order of reaction in the light of chemistry we know today.

What is this limit?

• Are you asking why he didn't provide a reference for something that is empirically not observed? – Zhe Jul 19 '17 at 17:16
• If you can't find an example of a fourth order reaction, then the empirical limit is 3... – Zhe Jul 19 '17 at 17:34
• Also, consider what you are asking. You want four separate species to come together in a transition state? – Zhe Jul 19 '17 at 17:34
• @Zhe read this. pubs.acs.org/doi/abs/10.1021/ja01350a021 – Mockingbird Jul 19 '17 at 17:37
• Can't you simply edit my question? That would be better. Better than pointing mini errors. – Mockingbird Jul 19 '17 at 17:43

The order of a reaction is an experimentally determined quantity and can be positive, negative or fractional. The order need not be related to the stoichiometric coefficients, although sometimes it is. In some reactions it is not possible to define an order. There seems to be no reason therefore why the order cannot be greater than three; the iodate-iodine reduction (Dushman) reaction $\ce{IO3^- + 5I^- + 6H^+ -> 3I2 + 3H2O}$ has the rate expression $r \approx \ce{[I^-][IO_3^-][H^+]^2 }$.

If the reaction is $aA+bB \rightarrow cC+dD$ then the rate is

$$r= - \frac{1}{a}\frac{d[A]}{dt} = \frac{1}{c}\frac{d[C]}{dt}= \cdots =k[A]^\alpha[B]^\beta[C]^\gamma \cdots$$

where the order n is $n=\alpha+\beta+\gamma$ and these need not be the same as a, b and c.

If the rate expression is not of this form then it is hard to define an order; one familiar example is the chain reaction $\ce{H2 + Br2}$ where the experimentally determined rate law for the production of HBr has the form $\displaystyle r=\frac{k_2[\ce{H_2}][\ce{Br_2}]^{1/2}}{1+k_2'[\ce{HBr}]/[\ce{Br}]}$ where an overall order cannot be defined.

The order should not be confused with molecularity which describes the number of species reacting in a postulated elementary reaction and which is always a small positive number. Effectively this means 1 or 2. A molecularity of 3 is not impossible but the chance of three reactive species colliding at the same time is vanishingly small. In practice when a molecularity of 3 is suspected it is often found that in subsequent experiments an intermediate is formed between of the two species which then reacts with the third at a slightly later time.

• In an order 4 reaction, the transition state for the rate determining step still requires that four species are coming together. Otherwise, I don't see how you would get order 4. It doesn't mean that they're all combining in a single step, but you do need to have 4. – Zhe Jul 19 '17 at 18:02
• @Zhe, I'm afraid not, the order is an experimentally determined quantity, and is not related at all to what actually happens at a molecular level. This is given by the molecularity. The order is obtained by observing the dependence of rate on the concentration of various species, hence the complicated and unexpected rate expression for $\ce{H2 + Br2}$ – porphyrin Jul 20 '17 at 7:31
• For a reaction with a well-defined mechanism, I am forced to disagree because the rate law of the reaction reflects the difference between the states that define the activation barrier. I agree that this is not in general the case because some reactions are not so easy to describe. – Zhe Jul 20 '17 at 13:50
• @Zhe, its just the difference between order and molecularity; certainly a molecularity of 4 in not possible and probably not 3 as I mention in my text. The order tells us nothing about what happens at the molecular level and this is why chemical kinetics is difficult and reaction mechanisms hard to determine, e.g. an example is the reaction $\ce{H2 + Br2}$ mentioned above. – porphyrin Jul 20 '17 at 15:10
• OK. I don't see us disagreeing on anything. There are times when order reflects the molecularity of a well-defined mechanism. – Zhe Jul 20 '17 at 16:46