# Rate equation for an elementary reaction

Yesterday, I had a debate with a friend of mine over the determination of the rate of elementary reactions. He said:

Rate equation of elementary reaction can be directly given by just raising the reactants concentration terms to the respective coefficients of the balanced chemical equation whose rate is to be determined.

and he also gave the example of this reaction

$$\ce{2NO (g) + O2 (g) -> 2NO2 (g)}$$

whose rate is

$$\ce{[NO]^2[O2]}.$$

Questions:

• Can I write the rate equation of an elementary reaction by just simply looking at the stoichiometric coefficients in the balanced equation and raising them over the concentration of reactants?

• Are there any examples of elementary reaction where the exponential powers on the concentration terms in the rate equation comes different than the stoichiometric coefficients of that reaction?

• Yes you can write the rate equation of an elementary reaction like that. The problem is, you often don't know if the reaction is really elementary. – Ivan Neretin Oct 9 '17 at 4:47
• There's a reaction of decomposition of ammonia on Pt at high temperature. It goes like this 2NH3 --> N2 + 3H2. The order of this reaction is zero. Does that mean the reaction is not elementary? – Serotonin Oct 9 '17 at 4:50
• Yes, pretty much so. – Ivan Neretin Oct 9 '17 at 5:43
• Your NO oxidation is blatantly multistep. – Mithoron Oct 9 '17 at 11:45
• @Mithoron Yep! I just realised this – Serotonin Oct 9 '17 at 13:41

Even if it is an elementary step, the order might not be given by the stoichiometry. The observed order of a component $C$ will correspond to the amount of $C$ that is participating in the rate-determining step. E.g. SN1 has only one component taking part in the rate determining step, thus first order, SN2 has two components and is thus second order (and first order with respect to each single component).

So here is the problem. Say you are looking at an E2 reaction. The reaction is second order, as there is a base and a starting material that gets deprotonated.

However, just by looking at the stoichiometry: $$\text{Propylchlorid} + \text{Base} \rightarrow \text{Propene} + \text{Base}\cdot\text{HCl}$$ you will not know if it is an E1 (first order), if the chlorid dissociates first, or E2 where the base directly participates in the rate determining step.

To make it even worse, two equivalents of base could participate in the rate determining step. Therefore, the stoichiometry has nothing to do with the rate order.

You can imagine it like this:

If I take a look at your shoes, I see two shoe laces and you have two hands. But given this information, it would be wrong to consider that to bind you shoes, you take only one hand, as there is one hand per shoe lace. Instead, you probably took both hands to bind your shoes, as it is much easier this way. Binding your shoes is kinetics, shoe lace/hand is stoichiometry, and they are completely orthogonal.

The reaction order with respect to a reactant species cannot be determined from the chemical equation alone. You would have to be given more information. In real life, orders of chemical reactions are found experimentally.