Order and Molecularity

CHERate, Order & Molecularity

Order is an experimental quantity from the rate law, while molecularity is a theoretical count from a single elementary step; confusing the two is a classic exam slip. This subtopic also covers reading order off concentration-rate data and the cap on molecularity.

Rate law and overall order

\text{rate} = k[A]^x[B]^y \qquad n = x + y

x,y

orders in

A,B

;

n

overall order, found by experiment

Order from initial-rate ratio

x = \dfrac{\log(\text{rate}_2/\text{rate}_1)}{\log([A]_2/[A]_1)}

with

[B]

held constant between the two runs

Order = sum of the powers of concentration terms in the experimentally determined rate law; it can be zero, fractional, or negative.
Molecularity = number of reacting species in a single elementary step; it is always a whole number ( $1$ , $2$ , or $3$ ) and never zero or fractional.
Order is found only by experiment and generally cannot be read off the balanced equation, since most reactions occur through multi-step mechanisms.
Molecularity is never greater than three because the simultaneous collision of four or more molecules with correct energy and orientation is virtually impossible.
Overall order equals the molecularity only for an elementary (single-step) reaction; for a multi-step reaction the slowest (rate-determining) step fixes the rate law.
Determine order from data by comparing experiments: doubling $[A]$ while $[B]$ is fixed and seeing the rate $\times 4$ means order $2$ in $A$ ( $\text{rate} \propto [A]^2$ ).
Examples: a zero-order reaction is the decomposition of $HI$ on a gold surface; a pseudo first-order reaction is acid hydrolysis of an ester in excess water.
Molecularity applies only to a single elementary step and so has no meaning for an overall complex reaction; order applies to the overall reaction.
Order is a property of the rate law (experimental), whereas molecularity is a property of the mechanism (theoretical) — keep the two ideas in separate columns when distinguishing.
Fractional or zero overall order is a clear signal that the reaction is not elementary and proceeds through a mechanism with a rate-determining step.
For an elementary unimolecular step molecularity $=1$ (e.g. a decomposition), bimolecular $=2$ (most common), termolecular $=3$ (rare).
Worked method: order in each reactant comes from the experiment pair where only that reactant's concentration changes; multiply factors to get the overall order, then solve for $k$ .

Where the marks go

Reading order straight off the stoichiometric coefficients of the balanced equation — order must come from experimental rate data.
Assigning a molecularity to an overall multi-step reaction — molecularity is defined only for a single elementary step.
Claiming order is always a whole number — it can be zero, fractional, or even negative, unlike molecularity.
Saying molecularity can be zero — it is a count of colliding species, so the minimum is one.
Forgetting to keep $[B]$ constant when extracting the order in $A$ from a data table, contaminating the ratio.

How the board asks it

Distinguishorder is experimental, molecularity is theoretical
Distinguish between the order and molecularity of a reaction, giving two points of difference. Give one example each of a reaction of fractional order and a bimolecular elementary reaction.
Numericalorder from initial-rate data
For the reaction $A + B \rightarrow$ products, doubling $[A]$ at constant $[B]$ makes the rate four times, while doubling $[B]$ at constant $[A]$ leaves the rate unchanged. Write the rate law, state the overall order, and calculate the rate constant $k$ given that the rate is $2.0 \times 10^{-3}\ \text{mol L}^{-1}\text{s}^{-1}$ when $[A] = [B] = 0.1\ \text{mol L}^{-1}$ .
Define / stateorder = sum of powers in the rate law
Define the order of a reaction. State whether the order of a reaction can be zero, fractional or negative, and state the values that the molecularity of an elementary step may take.
Give reasonsmolecularity is never greater than three
Explain why the molecularity of a reaction is never greater than three, whereas the order of a reaction may be zero or fractional.
Numericalrate-change factor from rate law
A reaction is first order in $A$ and second order in $B$ . Calculate the factor by which the rate changes when $[A]$ is halved and $[B]$ is tripled simultaneously.

Practise this topic

PreviousEffect of Concentration on Rate; Rate Expressions NextUnits of k and Determining Order from Units

Written for Sublevo. Question text quoted anywhere in these notes is the Council’s and carries its year and paper; the board’s own diagrams are not reproduced.