Order and Molecularity: Determining Order From Data
Two terms that are routinely confused, and four methods for finding the one that actually has to be measured.
The distinction
| Molecularity | Order | |
|---|---|---|
| Applies to | A single elementary step | The overall reaction |
| Determined by | The mechanism | Experiment |
| Possible values | 1, 2, rarely 3 | Any value, including fractional, zero or negative |
| Can it be zero? | No | Yes |
A fractional order is direct evidence of a complex mechanism, since no elementary step can have one. Encountering one in data therefore tells you immediately that several steps are involved.
Four methods for determining order
1. Integrated rate law method
Test which plot is linear.
| Order | Linear plot | Half-life depends on |
|---|---|---|
| Zero | [A] against t | Initial concentration, directly |
| First | ln[A] against t | Nothing — it is constant |
| Second | 1/[A] against t | Inversely on initial concentration |
Whichever plot gives a straight line identifies the order, and the slope gives the rate constant. This is the most reliable method when concentration-time data are available.
2. Half-life method
The dependence of half-life on initial concentration is diagnostic, as the table shows. A constant half-life regardless of starting concentration is the signature of first-order behaviour, and it is the quickest test available.
3. Initial rates method
Measure the initial rate at several starting concentrations and see how it scales. Doubling a concentration and observing the rate double indicates first order in that species; quadrupling indicates second order; no change indicates zero order.
Its advantage is that only initial rates are used, so complications from product accumulation or side reactions are avoided.
4. Isolation method
Where several reactants are involved, use a large excess of all but one. Their concentrations then barely change, so the observed order is that with respect to the remaining species alone. Repeating for each reactant gives the full rate law.
The order obtained under these conditions is called pseudo-order, and the classic example is a hydrolysis in water where water is in vast excess and the reaction appears first order despite involving two species.
Deducing a mechanism from a rate law
A proposed mechanism must predict the observed rate law. The standard procedure is to apply the steady-state approximation to intermediates and derive the rate law it implies, then compare.
Agreement does not prove a mechanism — other mechanisms may predict the same law — but disagreement disproves it. Stating that asymmetry is the mark of a careful answer, since mechanisms are never proved by kinetics alone.
Frequently asked questions
Why can order be fractional but molecularity cannot?
Because molecularity counts actual molecules colliding in one step, which must be a whole number. Order is an empirical exponent describing overall behaviour and carries no such constraint.
What does a zero-order reaction mean physically?
That the rate does not depend on the concentration of that species — typically because a surface or an enzyme is saturated, so adding more reactant cannot increase the rate.
What does a negative order indicate?
That a species inhibits the reaction, usually by binding to a catalyst or by reversing an earlier step. It is always a sign of a complex mechanism.
Can kinetics prove a mechanism?
No. It can rule mechanisms out, and a mechanism that fails to predict the observed rate law is wrong. Consistency is necessary but not sufficient.
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