Exhaustive Guide: Rate of Reaction & Order | Chemical Kinetics | ChemCA

Chemical Kinetics: Rate, Order & Molecularity

Module 1 | CBSE Class 12 Chemistry | Kinetics Chapter

1. Introduction to Chemical Kinetics

While Thermodynamics tells us whether a reaction is feasible (spontaneous) and Chemical Equilibrium tells us the extent to which a reaction will proceed, neither tells us how fast the reaction occurs.

Chemical Kinetics: The branch of chemistry that deals with the study of reaction rates, the factors affecting them, and the mechanisms by which reactions proceed. The word kinetics is derived from the Greek word 'kinesis' meaning movement.

2. Rate of a Chemical Reaction

The rate of a reaction can be defined as the change in concentration of a reactant or product per unit time.

Rate of disappearance of R = Decrease in concentration of R / Time taken = -Δ[R] / Δt
Rate of appearance of P = Increase in concentration of P / Time taken = +Δ[P] / Δt

Why the negative sign? Concentration of reactants always decreases with time, so Δ[R] is a negative quantity. Since the rate of reaction is always a positive quantity, we multiply it by -1 to make it positive.

Units of Rate: mol L^-1 s^-1 (or mol L^-1 min^-1). For gaseous reactions, it is expressed as atm s^-1.

2.1 Average vs. Instantaneous Rate

Average Rate (r_av): It is the rate of reaction measured over a long time interval (Δt). It does not give the true rate at a particular moment because the rate changes constantly as concentration changes.

Instantaneous Rate (r_inst): The rate of reaction at any particular instant of time. Mathematically, it is obtained when Δt approaches zero (dt). It is calculated by drawing a tangent to the concentration-time curve at that specific time.

r_inst = - d[R] / dt = + d[P] / dt

2.2 Expressing Rate in Terms of Stoichiometry

Consider a general reaction where stoichiometric coefficients are not equal:
aA + bB → cC + dD

To ensure that the calculated rate of the reaction is unique regardless of which species we are monitoring, we divide the rate of disappearance/appearance by their respective stoichiometric coefficients.

Rate of Reaction = - (1/a) d[A]/dt = - (1/b) d[B]/dt = + (1/c) d[C]/dt = + (1/d) d[D]/dt

NCERT Example: For the reaction 5Br^-(aq) + BrO₃^-(aq) + 6H⁺(aq) → 3Br₂(aq) + 3H₂O(l)
Rate = - (1/5) d[Br^-]/dt = - d[BrO₃^-]/dt = - (1/6) d[H⁺]/dt = + (1/3) d[Br₂]/dt

3. Rate Law and Rate Constant

The rate of a reaction depends upon the concentration of reactants. The representation of the rate of reaction in terms of the concentration of the reactants is known as the Rate Law.

For a general reaction: aA + bB → cC + dD

Rate Law Expression: Rate = k [A]^x [B]^y

Where:
k = Rate constant (or specific reaction rate).
x and y = Exponents that indicate how sensitive the rate is to the concentration of A and B. (Note: x and y may or may not be equal to the stoichiometric coefficients 'a' and 'b').

Key Fact: The rate law cannot be predicted theoretically by merely looking at the balanced chemical equation. It must be determined experimentally.

Rate Constant (k)

If [A] = [B] = 1 mol L^-1, then Rate = k.

Definition: The rate constant is the rate of the reaction when the concentration of each reactant is taken as unity. The value of 'k' depends on the nature of the reactant and temperature, but is independent of concentration. A larger value of 'k' indicates a faster reaction.

4. Order of a Reaction

Order of a Reaction: The sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction.

If Rate = k [A]^x [B]^y
Overall order of reaction (n) = x + y

Order with respect to A is 'x'.
Order with respect to B is 'y'.

Crucial Characteristics of Order:

It is an experimentally determined quantity.
It can be 0, 1, 2, 3, or even a fraction.
A zero-order reaction means that the rate of reaction is completely independent of the concentration of reactants.

4.1 Units of Rate Constant (k) for Different Orders

Finding the order from the unit of 'k' is a high-yield board exam question. You can derive the unit of 'k' for an $n^{th}$ order reaction using a general formula.

Unit of k = (mol L^-1)^{1 - n} s^-1

Reaction Order (n)	Calculation: (mol L^-1)^{1 - n} s^-1	Unit of Rate Constant (k)
Zero Order (n=0)	(mol L^-1)^{1 - 0} s^-1	mol L^-1 s^-1
First Order (n=1)	(mol L^-1)^{1 - 1} s^-1	s^-1
Second Order (n=2)	(mol L^-1)^{1 - 2} s^-1	mol^-1 L s^-1

5. Molecularity of a Reaction

Before understanding molecularity, we must classify reactions into two types:

Elementary Reactions: Reactions that take place in a single step.
Complex Reactions: Reactions that occur in a sequence of two or more elementary steps. In a complex reaction, the slowest step is the Rate Determining Step (RDS).

Molecularity: The number of reacting species (atoms, ions, or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction, is called the molecularity of a reaction.

Unimolecular (1): One reacting species. Example: Decomposition of ammonium nitrite.
NH₄NO₂ → N₂ + 2H₂O
Bimolecular (2): Simultaneous collision of two species. Example: Dissociation of HI.
2HI → H₂ + I₂
Trimolecular (3): Simultaneous collision of three species. Example:
2NO + O₂ → 2NO₂

NCERT Note: The probability of more than three molecules colliding simultaneously and effectively is very small. Hence, molecularity greater than 3 is rarely observed. For complex reactions, molecularity has no meaning overall; it is only defined for each individual step.

5.1 Differences between Order and Molecularity (V. Imp.)

Order of Reaction	Molecularity of Reaction
It is the sum of the powers of concentration terms in the rate law.	It is the number of reacting species colliding simultaneously in an elementary step.
It is determined strictly by experiment.	It is a theoretical concept derived from the reaction mechanism.
It can be zero, fractional, or an integer.	It is always a whole number (1, 2, 3...). It can never be zero or fractional.
Applicable to both elementary and complex reactions.	Applicable only to elementary reactions. Meaningless for complex reactions.

6. NCERT Solved Examples (Step-by-Step)

NCERT Example 4.3: Calculate the overall order of a reaction which has the rate expression:
(a) Rate = k [A]^1/2 [B]^3/2
(b) Rate = k [A]^3/2 [B]^-1

Solution:
The overall order of a reaction is the sum of the powers of the concentration terms in the rate law.
(a) Order (n) = 1/2 + 3/2 = 4/2 = 2 (Second order).
(b) Order (n) = 3/2 + (-1) = 3/2 - 2/2 = 1/2 (Half order).

NCERT Example 4.4: Identify the reaction order from each of the following rate constants:
(i) k = 2.3 × 10^-5 L mol^-1 s^-1
(ii) k = 3 × 10^-4 s^-1

Solution:
We identify the order by looking purely at the units of the rate constant 'k'.
(i) The unit is L mol^-1 s^-1 (which is the same as mol^-1 L s^-1). This corresponds to a Second Order reaction.
(ii) The unit is s^-1. This corresponds to a First Order reaction.

7. Previous Year Questions (PYQs) & Exhaustive Question Bank

Part A: Conceptual (1-2 Marks)

[CBSE 2018, 2020]

Q1. Define the term "Rate constant" (k) of a reaction. How does it differ from the rate of a reaction?

Answer: The rate constant (k) is defined as the rate of the chemical reaction when the concentration of all reactants is unity (1 mol L^-1).
Difference: The rate of reaction depends upon the concentration of reactants and changes as the reaction proceeds. The rate constant (k) is independent of the initial concentration of reactants and depends only on the temperature.

[CBSE 2017, 2021]

Q2. Why is molecularity applicable only for elementary reactions and not for complex reactions?

Answer: A complex reaction proceeds through a series of multiple steps. It is highly improbable for a large number of molecules (e.g., 5 or 6) to collide simultaneously and effectively to form products in a single step. Therefore, molecularity is defined for each individual elementary step separately, and the overall molecularity of a complex reaction has no significance.

Part B: Assertion-Reason Type (1 Mark)

[CBSE Sample Paper 2024]

Q3. Assertion (A): The order of a reaction can be zero or fractional.
Reason (R): Order of a reaction cannot be determined from the balanced chemical equation.

Answer: Both Assertion and Reason are correct, but Reason is NOT the correct explanation for Assertion.
The order can be zero or fractional because it is an experimental quantity based on how the rate depends on concentration. While it is true it cannot be deduced from a balanced equation, that fact doesn't explain *why* it can be fractional.

Part C: Application Based (2-3 Marks)

[CBSE 2015, 2019]

Q4. For a reaction A + B → Products, the rate law is given by: Rate = k[A]¹[B]².
(i) What is the order of the reaction?
(ii) If the concentration of B is doubled, keeping [A] constant, how will the rate be affected?
(iii) What will be the effect on the rate if the volume of the vessel is reduced to half?

Answer:
(i) Overall order = 1 + 2 = 3 (Third order).
(ii) Rate₁ = k[A][B]². If [B] is doubled to 2B: Rate₂ = k[A][2B]² = 4k[A][B]². The rate will increase by a factor of 4 times.
(iii) If volume is reduced to half, the concentration (mol/Volume) of both A and B will double.
New Rate = k[2A]¹[2B]² = k × 2 × 4 [A][B]² = 8 times the original rate.

[CBSE 2016]

Q5. For the reaction: 2N₂O₅ → 4NO₂ + O₂, the rate of formation of NO₂ is 2.8 × 10^-3 M s^-1. Calculate the rate of disappearance of N₂O₅.

Answer:
From the stoichiometry of the reaction, we can write the rate relationship:
Rate = - (1/2) d[N₂O₅]/dt = + (1/4) d[NO₂]/dt

We are given the rate of formation of NO₂: d[NO₂]/dt = 2.8 × 10^-3 M s^-1.
Substituting this into the equation:
- (1/2) d[N₂O₅]/dt = (1/4) × (2.8 × 10^-3)
- d[N₂O₅]/dt = 2 × (0.7 × 10^-3) = 1.4 × 10^-3 M s^-1.
Hence, the rate of disappearance of N₂O₅ is 1.4 × 10^-3 M s^-1.

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Exhaustive Guide: Rate of Reaction & Order | Chemical Kinetics