Order and Molecularity of Reaction

Master the concepts of order of reaction and molecularity with clear distinctions, examples, and JEE problem-solving strategies

11 min read

Order and Molecularity of Reaction

Real-Life Connection: Why Drug Dosage Matters

Ever noticed how medicine labels specify “Take one tablet every 8 hours” or “Take two tablets once daily”? This is directly related to reaction order!

The way your body metabolizes drugs follows specific kinetic orders:

  • Alcohol metabolism: Zero-order (constant amount processed per hour, regardless of blood alcohol level)
  • Most drugs: First-order (rate depends on drug concentration)
  • Some enzyme-limited processes: Second-order

Understanding order and molecularity helps pharmaceutical scientists determine:

  • Optimal dosing intervals
  • Safe maximum doses
  • How long drugs remain effective

Two Fundamental Concepts

Order of Reaction

Experimental, mathematical - determined from rate law

Molecularity of Reaction

Theoretical, mechanistic - determined from reaction mechanism

Critical difference: Order is found experimentally; molecularity is deduced from mechanism.

Order of Reaction

Definition

The order of reaction is the sum of powers of concentration terms in the rate law expression.

For a reaction:

$$aA + bB \rightarrow \text{Products}$$

Rate law:

$$\boxed{\text{Rate} = k[A]^m[B]^n}$$

Order = m + n

where:

  • m = order with respect to A
  • n = order with respect to B
  • (m + n) = overall order of reaction

Key Points

  1. Order is experimentally determined (not from balanced equation!)
  2. Can be zero, integer, or fractional
  3. Can be positive or negative (rare)
  4. Independent of stoichiometric coefficients

Types of Order

1. Zero Order Reaction

$$\text{Rate} = k[A]^0 = k$$

Characteristics:

  • Rate is independent of concentration
  • Rate = constant throughout
  • Units of k: mol L⁻¹ s⁻¹

Graph:

[A] vs time: Straight line with negative slope
Rate vs [A]: Horizontal line

Examples:

  1. Photochemical reactions:

    $$H_2 + Cl_2 \xrightarrow{hv} 2HCl$$

    Rate depends on light intensity, not concentration.

  2. Enzyme catalyzed reactions at high substrate concentration: All enzyme sites saturated, adding more substrate doesn’t increase rate.

  3. Surface catalyzed reactions:

    $$2NH_3 \xrightarrow{Pt} N_2 + 3H_2$$

    When surface is fully covered, rate is constant.

  4. Alcohol metabolism in body: Liver processes ~7-10g alcohol/hour regardless of blood alcohol level.

2. First Order Reaction

$$\text{Rate} = k[A]^1 = k[A]$$

Characteristics:

  • Rate directly proportional to concentration
  • Units of k: s⁻¹ or time⁻¹
  • Half-life independent of initial concentration

Graph:

[A] vs time: Exponential decay
ln[A] vs time: Straight line (negative slope = -k)

Examples:

  1. Radioactive decay:

    $$^{14}C \rightarrow ^{14}N + \beta^-$$

  2. Decomposition of N₂O₅:

    $$2N_2O_5 \rightarrow 4NO_2 + O_2$$ $$\text{Rate} = k[N_2O_5]$$

  3. Hydrolysis of ester (acid catalyzed):

    $$CH_3COOC_2H_5 + H_2O \xrightarrow{H^+} CH_3COOH + C_2H_5OH$$

    (Water in excess)

  4. Drug elimination from body (most pharmaceuticals)

3. Second Order Reaction

$$\text{Rate} = k[A]^2$$

or

$$\text{Rate} = k[A][B]$$

Characteristics:

  • Rate proportional to square of one concentration or product of two
  • Units of k: L mol⁻¹ s⁻¹ or M⁻¹ s⁻¹
  • Half-life inversely proportional to initial concentration

Graph:

1/[A] vs time: Straight line (slope = k)

Examples:

  1. NO₂ decomposition:

    $$2NO_2 \rightarrow 2NO + O_2$$ $$\text{Rate} = k[NO_2]^2$$

  2. Alkaline hydrolysis of ester:

    $$CH_3COOC_2H_5 + NaOH \rightarrow CH_3COONa + C_2H_5OH$$ $$\text{Rate} = k[CH_3COOC_2H_5][NaOH]$$

  3. Dimerization reactions:

    $$2C_4H_6 \rightarrow C_8H_{12}$$

4. Fractional Order Reaction

Order can be non-integer (0.5, 1.5, 2.5, etc.)

Examples:

  1. Acetaldehyde decomposition:

    $$CH_3CHO \rightarrow CH_4 + CO$$ $$\text{Rate} = k[CH_3CHO]^{3/2}$$

    Order = 1.5

  2. Chlorine + Chloroform:

    $$CHCl_3 + Cl_2 \rightarrow CCl_4 + HCl$$ $$\text{Rate} = k[CHCl_3][Cl_2]^{1/2}$$

    Order = 1.5

Reason: Complex mechanisms with multiple elementary steps.

Pseudo Order Reactions

When one reactant is in large excess, reaction appears to be of lower order.

Example: Acid hydrolysis of ester

$$CH_3COOC_2H_5 + H_2O \xrightarrow{H^+} CH_3COOH + C_2H_5OH$$

True rate law:

$$\text{Rate} = k[CH_3COOC_2H_5][H_2O]$$

(Second order)

Since [H₂O] » [ester], [H₂O] remains nearly constant:

$$\text{Rate} = k[CH_3COOC_2H_5][H_2O] = k'[CH_3COOC_2H_5]$$

where k’ = k[H₂O] = pseudo first order rate constant

Appears to be first order → Pseudo first order reaction

Molecularity of Reaction

Definition

The molecularity is the number of reacting species (atoms, ions, or molecules) that must collide simultaneously in an elementary step to form products.

$$\boxed{\text{Molecularity} = \text{Number of molecules in elementary step}}$$

Key Characteristics

  1. Always a whole number (1, 2, 3, …)
  2. Never zero or fractional
  3. Never greater than 3 (trimolecular is rare)
  4. Defined only for elementary reactions
  5. Theoretical concept based on mechanism

Types of Molecularity

1. Unimolecular Reactions

One molecule participates in elementary step.

Examples:

  1. Radioactive decay:

    $$^{238}U \rightarrow ^{234}Th + ^4He$$

    Molecularity = 1

  2. Isomerization:

    $$\text{Cyclopropane} \rightarrow \text{Propene}$$

    Molecularity = 1

  3. Decomposition:

    $$N_2O_5 \rightarrow NO_2 + NO_3$$

    (Elementary step) Molecularity = 1

2. Bimolecular Reactions

Two molecules collide in elementary step.

Examples:

  1. NO + O₃ reaction:

    $$NO + O_3 \rightarrow NO_2 + O_2$$

    Molecularity = 2

  2. H₂ + I₂ reaction: (Elementary step)

    $$H_2 + I_2 \rightarrow 2HI$$

    Molecularity = 2

  3. Alkaline hydrolysis:

    $$CH_3COOC_2H_5 + OH^- \rightarrow CH_3COO^- + C_2H_5OH$$

    Molecularity = 2

Most common molecularity - bimolecular collisions are frequent.

3. Trimolecular (Termolecular) Reactions

Three molecules collide simultaneously.

Examples:

  1. NO + O₂ reaction:

    $$2NO + O_2 \rightarrow 2NO_2$$

    (If this is elementary step) Molecularity = 3

  2. NO + Cl₂ reaction:

    $$2NO + Cl_2 \rightarrow 2NOCl$$

Very rare! - Probability of 3 molecules colliding simultaneously with proper orientation and energy is extremely low.

Why Molecularity > 3 is Not Observed?

Statistical probability of 4 or more molecules colliding simultaneously with:

  • Correct orientation
  • Sufficient energy
  • At the same instant

is virtually zero.

Therefore, complex reactions proceed through multiple elementary steps, each with molecularity ≤ 3.

Order vs Molecularity: The Critical Differences

AspectOrderMolecularity
DefinitionSum of powers in rate lawNumber of molecules in elementary step
DeterminationExperimentalTheoretical (from mechanism)
Value0, integer, fractionalOnly positive integer (1, 2, 3)
ApplicabilityAny reaction (overall or elementary)Only elementary reactions
Complex reactionsMay differ from stoichiometryEach step has its own molecularity
NatureMathematical conceptPhysical concept
Can be zero?YesNo
Can be fractional?YesNo

Example Demonstrating Difference

Reaction:

$$2N_2O_5 \rightarrow 4NO_2 + O_2$$

Experimentally determined rate law:

$$\text{Rate} = k[N_2O_5]$$

Order = 1 (first order)

But stoichiometry shows 2 moles of N₂O₅!

Why? Because this is NOT an elementary reaction. It proceeds through multiple steps.

One possible elementary step:

$$N_2O_5 \rightarrow NO_2 + NO_3$$

Molecularity = 1 (unimolecular)

Lesson: Never assume order from balanced equation stoichiometry!

Memory Tricks

“ORDER-M” for remembering differences:

Obtained experimentally vs Mechanistic (theoretical) Rate law based vs Molecule count based Decimals allowed vs Must be integer Even for complex reactions vs Elementary steps only Rarely > 3 in practice vs Max is 3

“MOM” for molecularity:

Molecules count Only integers (1, 2, 3) Mechanism needed

“EXPO” for order:

EXperimental Powers in rate law Often differs from stoichiometry

Common JEE Mistakes

Mistake 1: Assuming Order = Stoichiometric Coefficient

Wrong: For

$$2A \rightarrow \text{Products}$$

, order must be 2

Correct: Order is determined experimentally, independent of stoichiometry!

Mistake 2: Fractional Molecularity

Wrong: “Reaction has molecularity = 1.5”

Correct: Molecularity is always integer (1, 2, or 3). If someone says fractional molecularity, they’re confusing it with order.

Mistake 3: Molecularity for Overall Reaction

Wrong: For

$$2NO + O_2 \rightarrow 2NO_2$$

, “molecularity = 3”

Careful: Only if this is an elementary step. If it’s overall reaction with mechanism, molecularity is defined for individual steps, not overall reaction.

Mistake 4: Order from Balanced Equation

Wrong: For

$$H_2 + I_2 \rightarrow 2HI$$

, assuming order = 1 + 1 = 2

Correct: Must determine experimentally! (Though in this case it happens to be second order)

Practice Problems

Level 1: JEE Main Foundation

Problem 1: For the reaction

$$A + 2B \rightarrow C$$

, the rate law is

$$\text{Rate} = k[A][B]$$

. What is: (a) Order with respect to A? (b) Order with respect to B? (c) Overall order?

Solution: (a) Order w.r.t. A = 1 (b) Order w.r.t. B = 1 (not 2!) (c) Overall order = 1 + 1 = 2

Note: Stoichiometric coefficient of B is 2, but order w.r.t. B is 1.

Level 2: JEE Main/Advanced

Problem 2: For a reaction

$$2A + B \rightarrow C + D$$

, the following data is obtained:

Experiment[A] (M)[B] (M)Initial Rate (M/s)
10.10.12 × 10⁻³
20.20.18 × 10⁻³
30.10.24 × 10⁻³

Determine: (a) Order with respect to A (b) Order with respect to B (c) Rate law (d) Rate constant with units

Solution:

(a) Compare experiments 1 and 2 ([B] constant):

$$\frac{r_2}{r_1} = \frac{k[0.2]^m[0.1]^n}{k[0.1]^m[0.1]^n} = \frac{8 \times 10^{-3}}{2 \times 10^{-3}}$$ $$2^m = 4 \implies m = 2$$

Order w.r.t. A = 2

(b) Compare experiments 1 and 3 ([A] constant):

$$\frac{r_3}{r_1} = \frac{k[0.1]^m[0.2]^n}{k[0.1]^m[0.1]^n} = \frac{4 \times 10^{-3}}{2 \times 10^{-3}}$$ $$2^n = 2 \implies n = 1$$

Order w.r.t. B = 1

(c) Rate law:

$$\text{Rate} = k[A]^2[B]$$

(d) From experiment 1:

$$2 \times 10^{-3} = k(0.1)^2(0.1)$$ $$k = \frac{2 \times 10^{-3}}{0.001} = 2 \text{ M}^{-2}\text{s}^{-1}$$

Units: L² mol⁻² s⁻¹ or M⁻² s⁻¹

Level 3: JEE Advanced

Problem 3: The decomposition of H₂O₂ follows the mechanism:

Step 1:

$$H_2O_2 + I^- \xrightarrow{slow} H_2O + IO^-$$

Step 2:

$$H_2O_2 + IO^- \xrightarrow{fast} H_2O + O_2 + I^-$$

Overall:

$$2H_2O_2 \rightarrow 2H_2O + O_2$$

Determine: (a) Rate law (b) Order of reaction (c) Molecularity of each step (d) Role of I⁻

Solution:

(a) Rate-determining step (RDS) is Step 1 (slow):

$$\text{Rate} = k[H_2O_2][I^-]$$

(b) Order = 1 + 1 = 2 (second order)

  • First order in H₂O₂
  • First order in I⁻

(c) Molecularity:

  • Step 1: 2 molecules collide → Molecularity = 2 (bimolecular)
  • Step 2: 2 molecules collide → Molecularity = 2 (bimolecular)

(d) Role of I⁻: I⁻ is a catalyst (consumed in step 1, regenerated in step 2)

Problem 4: A reaction has order 0 with respect to A and order 2 with respect to B. If [A] is doubled and [B] is tripled, by what factor does the rate increase?

Solution:

Rate law:

$$\text{Rate} = k[A]^0[B]^2 = k[B]^2$$

Initial rate:

$$r_1 = k[B]^2$$

New rate:

$$r_2 = k(3[B])^2 = 9k[B]^2$$ $$\frac{r_2}{r_1} = \frac{9k[B]^2}{k[B]^2} = 9$$

Answer: Rate increases by factor of 9

(Doubling [A] has no effect since order w.r.t. A is zero)

Determining Order Experimentally

Method 1: Initial Rate Method

Vary initial concentrations and measure initial rates.

Procedure:

  1. Keep all concentrations constant except one
  2. Measure how rate changes
  3. Determine order for that reactant
  4. Repeat for other reactants

(Illustrated in Problem 2 above)

Method 2: Graphical Method

Plot different graphs and see which is linear:

OrderLinear plotSlope
0[A] vs t-k
1ln[A] vs t-k
21/[A] vs t+k

Method 3: Half-Life Method

Compare half-lives at different initial concentrations:

  • Zero order: t₁/₂ ∝ [A]₀
  • First order: t₁/₂ independent of [A]₀
  • Second order: t₁/₂ ∝ 1/[A]₀

See: Half-Life

Units of Rate Constant

The units of k depend on overall order:

$$\boxed{\text{Units of } k = (\text{mol L}^{-1})^{1-n} \times \text{time}^{-1}}$$

where n = overall order

Order (n)Units of k
0mol L⁻¹ s⁻¹
1s⁻¹
2L mol⁻¹ s⁻¹
3L² mol⁻² s⁻¹

Memory trick: As order increases, k units get more complex (more L and mol⁻¹ terms)

Complex Reactions and Mechanisms

Most reactions are NOT elementary - they proceed through multiple steps.

Example: NO₂ + CO Reaction

Overall:

$$NO_2 + CO \rightarrow NO + CO_2$$

Experimentally:

$$\text{Rate} = k[NO_2]^2$$

Order = 2 (depends only on [NO₂]!)

Why? Proposed mechanism:

Step 1 (slow):

$$2NO_2 \rightarrow NO_3 + NO$$

(RDS) Step 2 (fast):

$$NO_3 + CO \rightarrow NO_2 + CO_2$$

Rate = rate of slow step = k[NO₂]²

This explains why CO doesn’t appear in rate law even though it’s a reactant!

Molecularity:

  • Step 1: Bimolecular (2)
  • Step 2: Bimolecular (2)

Overall order: 2 (determined experimentally)

Connection to Other Topics

  • Order is determined from rate law expression
  • See: Rate Law
  • Half-life dependence on [A]₀ varies with order
  • See: Half-Life
  • Catalysts change mechanism (and thus molecularity of steps)
  • Don’t change overall stoichiometry or order
  • See: Catalysis

JEE Previous Year Questions

JEE Main 2021: For the reaction

$$2A + B \rightarrow A_2B$$

, if the rate law is Rate = k[A][B]², what is the order?

Answer: 1 + 2 = 3 (third order)

JEE Advanced 2018: Which statement is correct? (a) Order and molecularity are always equal (b) Molecularity can be fractional (c) Order is always an integer (d) Molecularity is defined for elementary reactions only

Answer: (d)

Explanation: (a) Wrong - order ≠ molecularity for complex reactions (b) Wrong - molecularity is always integer (c) Wrong - order can be fractional (d) Correct - molecularity is meaningful only for elementary steps

Quick Revision Table

PropertyOrderMolecularity
How determined?ExperimentalTheoretical
Can be zero?✓✗
Can be fraction?✓✗
Max value?No limit3 (practical)
For complex reaction?✓ (overall)✗ (only steps)
From rate law?✓✗
From mechanism?✗✓

Summary

Order and molecularity are two fundamental but distinct concepts in chemical kinetics:

  1. Order is experimental and mathematical
  2. Molecularity is theoretical and mechanistic
  3. For elementary reactions, order = molecularity
  4. For complex reactions, order ≠ stoichiometry
  5. Always determine order experimentally
  6. Never assume order from balanced equation

Mastering this distinction is crucial for JEE success and understanding reaction mechanisms!

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