NEET Chemistry - Chapter 9

Chemical Kinetics

Fresh NEET kinetics notes on rate of reaction, order, molecularity, integrated rate laws, half-life, activation energy, and Arrhenius relation.

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Concept Block

1. Rate of Reaction: Average Rate, Instantaneous Rate, and Rate Expression

The rate of a reaction measures how quickly concentrations change. For $aA+bB\to cC+dD$ :

\text{Rate}=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=+\frac{1}{c}\frac{d[C]}{dt}=+\frac{1}{d}\frac{d[D]}{dt}

The minus signs appear for reactants (being consumed) and plus for products (being formed). Division by stoichiometric coefficients makes the rate expression consistent regardless of which species you track.

Average rate = $\Delta[X]/\Delta t$ over a time interval. Instantaneous rate = slope of the $[X]$ -vs- $t$ tangent at one moment.

NEET quick check: For

2N_2O_5\to4NO_2+O_2

, if

-d[N_2O_5]/dt = 0.01

M/s, then

d[NO_2]/dt = 0.02

M/s and

d[O_2]/dt = 0.005

M/s. Always apply stoichiometric factors.

Concept Block

2. Rate Law, Order of Reaction, and Molecularity — Key Distinctions

The rate law is determined experimentally: $\text{rate}=k[A]^m[B]^n$ . The exponents $m$ and $n$ are the orders with respect to each reactant — they need NOT equal stoichiometric coefficients.

Concept	Order	Molecularity
Determined by	Experiment (kinetic data)	Mechanism (elementary step)
Values	0, 1, 2, fractions, negative	1, 2, or 3 only (whole numbers)
Applies to	Overall reaction	Only elementary steps

Overall order = $m+n$ . Units of rate constant $k$ : $\text{(concentration)}^{1-(m+n)}\times\text{time}^{-1}$ .

Zero order: $k$ in M s $^{-1}$
First order: $k$ in s $^{-1}$
Second order: $k$ in M $^{-1}$ s $^{-1}$

NEET trap: A bimolecular reaction (molecularity 2) can be first order overall if one reactant is in large excess (pseudo-first-order kinetics). Example: hydrolysis of an ester in excess water.

Concept Block

3. Integrated Rate Laws for Zero, First, and Second Order

Integrating the differential rate law gives concentration as a function of time. The form of the integrated law and its linear plot uniquely identify reaction order.

Order	Integrated Law	Linear Plot	Half-Life $t_{1/2}$
Zero	$[A]=[A_0]-kt$	$[A]$ vs $t$ (slope $= -k$ )	$t_{1/2}=[A_0]/2k$ (depends on $[A_0]$ )
First	$\ln[A]=\ln[A_0]-kt$	$\ln[A]$ vs $t$ (slope $= -k$ )	$t_{1/2}=0.693/k$ (independent of $[A_0]$ )
Second	$1/[A]=1/[A_0]+kt$	$1/[A]$ vs $t$ (slope $= k$ )	$t_{1/2}=1/(k[A_0])$ (depends on $[A_0]$ )

First-order key formula (NEET most asked):

k=\frac{2.303}{t}\log\frac{[A_0]}{[A]},\quad t_{1/2}=\frac{0.693}{k}

t_{1/2}=10

min, then

k=0.0693

min

^{-1}

. After 20 min (2 half-lives), concentration drops to

[A_0]/4

Concept Block

4. Half-Life, Radioactive Decay, and Reaction Time Calculations

The concept of half-life is most important for first-order reactions because $t_{1/2}$ is constant — independent of initial concentration. This is why radioactive decay is always first-order.

\text{Amount remaining after }n\text{ half-lives}=\frac{N_0}{2^n}

\text{Time for fraction to remain}=\frac{2.303}{k}\log\frac{N_0}{N}

Example: If $t_{1/2} = 20$ min and initial concentration = 100 M, after 60 min (3 half-lives): concentration = $100/2^3 = 12.5$ M.

NEET tip: For zero-order,

t_{1/2}=[A_0]/2k

— so doubling initial concentration doubles the half-life. For second-order,

t_{1/2}=1/(k[A_0])

— so doubling initial concentration halves the half-life. These relationships are frequently tested.

Concept Block

5. Activation Energy, Arrhenius Equation, and Catalysis

Temperature affects reaction rate because higher temperature means more molecules have kinetic energy exceeding the activation energy ( $E_a$ ) threshold needed to break old bonds and form new ones.

k=Ae^{-E_a/RT}\quad(\text{Arrhenius equation})

\ln k=\ln A-\frac{E_a}{RT}

\log\frac{k_2}{k_1}=\frac{E_a}{2.303R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)

$A$ = pre-exponential (frequency) factor; $R=8.314$ J mol $^{-1}$ K $^{-1}$ ; plot $\ln k$ vs $1/T$ gives slope $=-E_a/R$ .

Catalysis: Catalysts provide an alternative reaction pathway with lower activation energy, increasing rate without changing equilibrium position or $\Delta H$ .

Type	Catalyst & reactants	Example
Homogeneous	Same phase	NO $_2$ catalyses SO $_2$ →SO $_3$ (gas phase)
Heterogeneous	Different phases	Fe in Haber process; Pt in H $_2$ SO $_4$ manufacture
Enzyme (biocatalyst)	Enzyme + substrate	Zymase for glucose → ethanol

NEET trap: A catalyst speeds up both forward and reverse reactions equally, so equilibrium position is unchanged. It only reduces time to reach equilibrium, not the value of

K_{eq}

Practice Tests

5 Chapter Tests of 25 Questions Each

Each test is original, NEET-aligned, and answer-backed. Use them as sectional revision instead of a single long mock so your weak subtopics become easier to identify quickly.

Test 1: Rate Basics

Average rate, instantaneous rate, and graph interpretation.

Test 2: Order and Molecularity

Rate law, order, molecularity, and units of rate constant.

Test 3: Integrated Laws

Zero, first, and second order equations and plots.

Test 4: Half-Life and Arrhenius

Half-life, activation energy, catalysts, and temperature dependence.

Test 5: Mixed NEET Drill

Integrated kinetics practice across all major chapter ideas.

Open Practice Tests

Finished this topic?

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Move straight from chapter-wise questions into a subject test, then loop back into weaker areas instead of ending the session here.

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