Unit 3 Chemical Kinetics Class 12 (2025-26): Rate Laws, Arrhenius Equation & Half-Life Formulas

Thermodynamics predicts if a reaction occurs, but Chemical Kinetics determines the speed. For Class XII students tackling the 2025-26 syllabus, mastering the “time” variable in chemistry is required for solving numerical problems and interpreting rate graphs correctly.

This guide breaks down the mathematics of reaction rates, comparing Average and Instantaneous speeds while distinguishing experimental Order from theoretical Molecularity. From deriving Integrated Rate Equations for Zero and First Order reactions to calculating Activation Energy using the Arrhenius formula, these sections provide the specific tools needed for board exams.

Explore how concentration, temperature, and catalysts dictate reaction velocity through interactive visualizers designed to clarify the mechanics behind the math.

1 Defining Reaction Rate

Rate defines speed. In chemistry, it is the change in concentration of a reactant or product per unit time.

Average Rate

Measured over a finite time interval.

r_{av} = -\frac{\Delta [R]}{\Delta t} = \frac{\Delta [P]}{\Delta t}

Instantaneous Rate

Measured at a specific moment ($\Delta t \rightarrow 0$).

r_{inst} = -\frac{d[R]}{dt} = \frac{d[P]}{dt}

Stoichiometric Normalization

Rate = $ -\frac{1}{a}\frac{d[A]}{dt} = \frac{1}{c}\frac{d[C]}{dt} $

2 Factors Affecting Rate

Concentration

Higher concentration increases collision frequency.
Rate ∝ [Reactant]ⁿ

Temperature

For every 10°C rise, rate typically doubles (Temperature Coefficient $\mu \approx 2$).

Catalyst

Provides an alternate pathway with lower Activation Energy ($E_a$).

3 Module: Collision Theory & Orientation

Collision frequency ($Z$) isn’t enough. Molecules must hit with proper Orientation and Energy.
The Steric Factor ($P$) accounts for this probability.

Ineffective Collision Result: Bounce (No Reaction)

Effective Collision Result: Product AB

4 Reaction Mechanisms

Elementary vs Complex

Elementary: Occurs in a single step. Order = Molecularity.
Complex: Occurs in multiple steps. The overall rate is controlled by the slowest step.

RDS: Rate Determining Step

Just as the narrowest part of a funnel limits flow, the slowest step limits reaction speed.

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

Step 1 $ NO + NO \rightleftharpoons N_2O_2 $ (Fast)
Step 2 $ N_2O_2 + O_2 \rightarrow 2NO_2 $ (Slow/RDS)

The rate law is derived from Step 2, substituting the intermediate $N_2O_2$ using the equilibrium constant from Step 1.

5 The Units of Rate Constant (k)

The unit of $k$ depends on the order of the reaction ($n$). This is a key identifier in problems.

General Formula

Units = (mol L^-1)^1-n s^-1

Order (n)	Formula Substitution	Final Unit
Zero (0)	(mol/L)^1-0 s^-1	mol L^-1 s^-1
First (1)	(mol/L)^1-1 s^-1	s^-1
Second (2)	(mol/L)^1-2 s^-1	mol^-1 L s^-1

6 Module: Half-Life Dynamics

How does half-life change as the reaction proceeds?
Zero Order: Half-life decreases as concentration drops.
First Order: Half-life remains constant regardless of concentration.

Select a reaction order above.

7 Integrated Rate Equations

Zero Order

\( [R] = -kt + [R]_0 \)

8 Module: Graphical Fingerprints

To determine the order experimentally, chemists look for linear plots. Toggle below to see which plot yields a straight line for each order.

9 Numerical Master Key

The Two-Temperature Formula

Used when rate constants ($k_1, k_2$) are given at two different temperatures ($T_1, T_2$) to find $E_a$.

$ \log \frac{k_2}{k_1} = \frac{E_a}{2.303 R} \left[ \frac{T_2 – T_1}{T_1 T_2} \right] $

* Note: $T$ must be in Kelvin.
* $R = 8.314\ J\ K^{-1}\ mol^{-1}$.

Problem Solving Steps

Convert all Temperatures to Kelvin ($+273$).
Identify $k_1$ (lower temp) and $k_2$ (higher temp).
Calculate $\log(k_2/k_1)$. If rate doubles, this is $\log 2 = 0.301$.
Rearrange formula to solve for $E_a$.
Final unit of $E_a$ is usually $J\ mol^{-1}$ or $kJ\ mol^{-1}$.

10 Arrhenius Equation & Collision Theory

$ k = A e^{-E_a/RT} $

When plotting $\ln k$ vs $1/T$:
Slope: $-E_a/R$
Intercept: $\ln A$

Effective Collisions

Energy Barrier: Kinetic energy $\ge E_a$.
Orientation Barrier: Proper geometric alignment.

11 Catalyst & Energy

A catalyst provides an alternate pathway with a lower activation energy ($E_a’$).

Concept Buster: Myth vs Reality

Tap a card to reveal the scientific truth.

MYTH: Temperature increases rate by lowering $E_a$.

REALITY: Temperature does NOT change the Activation Energy ($E_a$). Instead, it increases the kinetic energy of the molecules, allowing a larger fraction of them to cross the existing energy barrier.

MYTH: Zero Order reactions never complete.

REALITY: Zero Order reactions DO complete in finite time ($t = [R]_0 / k$). It is First Order reactions that theoretically take infinite time to reach 100% completion.

MYTH: Molecularity can be zero or fractional.

REALITY: Molecularity represents the number of colliding species. You cannot have 0.5 molecules colliding, nor zero molecules colliding. It must be a positive integer (1, 2, or 3).

MYTH: Catalyst increases yield.

REALITY: A catalyst speeds up the approach to equilibrium but does not change the equilibrium constant ($K_c$). The final yield of products remains the same; you just get there faster.

Deep Dive FAQ

It’s not because collision frequency ($Z$) doubles; $Z$ increases only slightly ($\approx 3\%$). The main reason is the exponential increase in the fraction of molecules having energy greater than $E_a$. This “effective” population nearly doubles.

Molecularity is defined only for elementary (single-step) reactions. A complex reaction proceeds in multiple steps. We can define molecularity for each step, but not for the overall reaction. Order, however, is an experimental value for the overall reaction.

Generally, no. Molecules need excess energy to break bonds. However, in rare barrier-less reactions (like radical combinations), $E_a \approx 0$. A theoretical “negative” $E_a$ usually implies a complex mechanism where an intermediate equilibrium is sensitive to temperature.

Learning Outcomes & Conclusion

You have mastered:

Reaction Dynamics: How concentration, temperature, and orientation dictate speed.
Mechanism Analysis: Identifying the Rate Determining Step (RDS).
Integrated Laws: Calculating $k$ and $t_{1/2}$ for Zero/First order.
Arrhenius Logic: Connecting Temperature and Activation Energy graphically.

Exam Strategy: Spot the Order

In exams, if the order isn’t given, look at the units of $k$:

$s^{-1}$ → First Order
$mol\ L^{-1}\ s^{-1}$ → Zero Order
$mol^{-1}\ L\ s^{-1}$ → Second Order

Unit 3 Chemical Kinetics Class 12 (2025-26): Rate Laws, Arrhenius Equation & Half-Life Formulas