Order & Molecularity of a Reaction

Order of a Reaction

The order of a reaction is the sum of the powers of the concentration terms in the experimentally determined rate law. For Rate $= k[A]^x[B]^y$:

$$\text{Order} = x + y$$

Key facts about order:

• It is an experimental quantity (not from the equation).
• It can be zero, a whole number, fractional, or even negative.
• The order with respect to a particular reactant is the power of that reactant's concentration.

Examples: For Rate $= k[A]^{1/2}[B]^{3/2}$, order $= \tfrac{1}{2} + \tfrac{3}{2} = 2$. For Rate $= k[A]^{3/2}[B]^{-1}$, order $= \tfrac{3}{2} - 1 = \tfrac{1}{2}$ (half order).

Molecularity of a Reaction

Molecularity is the number of reacting species (atoms, ions or molecules) that collide simultaneously in an elementary reaction to bring about the reaction.

• Unimolecular (molecularity 1): one species, e.g. $\text{NH}_4\text{NO}_2 \rightarrow \text{N}_2 + 2\text{H}_2\text{O}$.
• Bimolecular (molecularity 2): two species collide, e.g. $2\text{HI} \rightarrow \text{H}_2 + \text{I}_2$.
• Termolecular (molecularity 3): three species collide (rare, because simultaneous three-body collisions are unlikely).

Molecularity is a theoretical concept that applies only to elementary (single-step) reactions and is always a positive whole number (1, 2 or 3) — never zero or fractional.

Complex Reactions and the Rate-Determining Step

Most real reactions occur in several elementary steps (a reaction mechanism). For such complex reactions:

• Molecularity of the overall reaction has no meaning — only individual elementary steps have a molecularity.
• The overall rate is governed by the slowest step, called the rate-determining step (RDS).

Key Point — Order vs Molecularity:

• Order is experimental, can be 0/fractional/negative, and applies to overall reactions.
• Molecularity is theoretical, always a positive integer (1-3), and applies only to elementary steps.
• For an elementary reaction, order = molecularity.

[JEE Tip] A reaction can be, say, first order overall but its mechanism may involve a bimolecular slow step followed by fast steps. Always treat order (measured) and molecularity (mechanistic) as separate ideas unless told the reaction is elementary.

Solved Examples

Example 1: Order from a rate law

For Rate $= k[A]^{1/2}[B]^{2}$, find the order with respect to A, to B, and overall.

Solution: Order in A $= \tfrac{1}{2}$; order in B $= 2$; overall $= \tfrac{1}{2} + 2 = \tfrac{5}{2}$ (2.5).

Example 2: Half order

For Rate $= k[A]^{3/2}[B]^{-1}$, find the overall order.

Solution: Overall order $= \tfrac{3}{2} + (-1) = \tfrac{1}{2}$ (half order).

Example 3: Molecularity of an elementary reaction

State the molecularity of the elementary reaction $2\text{HI} \rightarrow \text{H}_2 + \text{I}_2$.

Solution: Two HI molecules collide, so the molecularity is 2 (bimolecular).

Example 4: Why is termolecularity rare?

Why are termolecular elementary reactions uncommon?

Solution: A termolecular step needs three species to collide simultaneously with the right energy and orientation — a statistically very unlikely event — so such reactions are rare.

Example 5: Order can be zero

Can the order of a reaction be zero? Can molecularity be zero?

Solution: Order can be zero (e.g. some surface-catalysed reactions). Molecularity cannot be zero — at least one species must take part in an elementary step, so molecularity is a positive integer (1, 2 or 3).

Example 6: Elementary reaction relation

For an elementary reaction $A + B \rightarrow$ products, what are its order and molecularity?

Solution: For an elementary step, order = molecularity. Here two species react, so molecularity = 2 and the rate law is Rate $= k[A][B]$, overall order = 2.

Example 7: Order vs coefficient

For $2\text{NO} + \text{O}_2 \rightarrow 2\text{NO}_2$, experiment gives Rate $= k[\text{NO}]^2[\text{O}_2]$. State the order; does it match the coefficients here?

Solution: Order $= 2 + 1 = 3$. In this particular case the orders happen to match the coefficients, but that is not guaranteed in general — it must always be confirmed experimentally.

Example 8: Negative order meaning

What does a negative order with respect to a species imply?

Solution: A negative order means that increasing that species' concentration decreases the rate (it inhibits the reaction), e.g. a product that slows the forward reaction.

Example 9: Molecularity of a unimolecular reaction

Give the molecularity of $\text{NH}_4\text{NO}_2 \rightarrow \text{N}_2 + 2\text{H}_2\text{O}$ (elementary).

Solution: One species decomposes, so molecularity $= 1$ (unimolecular).

Example 10: Rate-determining step

In a multi-step reaction, which step controls the overall rate?

Solution: The slowest step — the rate-determining step — controls the overall rate, just as the narrowest section of a pipe limits water flow.