Chemical Kinetics

This chapter studies the speed (rate) of reactions. Unlike Equilibrium (which tells us how far), Kinetics tells us how fast. The math here involves basic integration and logarithmic plots. Pay close attention to the Units of Rate Constant ($k$).

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⚠️ Prerequisites

Stoichiometry: Relating moles of reactants to products.
Logarithms: Converting $\ln$ to $\log_{10}$ and plotting log graphs.
Straight Line Graphs: $y = mx + c$ (Slope and Intercept identification).

🧠 Study Approach

Graph Literacy: Many questions are graph-based. If you see a plot of $\ln k$ vs $1/T$, know instantly that the slope is $-E_a/R$. If you see Concentration vs Time is linear, it's Zero Order.

Study Sequence

1. Rate of Reaction

Average Rate vs Instantaneous Rate.
Expressing rate in terms of reactants (disappearance) and products (appearance). Dividing by stoichiometric coefficients is key!

2. Rate Law & Order (CRITICAL)

Rate Law (experimental) vs Law of Mass Action (theoretical).
Order of Reaction: Sum of powers in rate law. Can be 0, fraction, or integer.
Molecularity: Theoretical collision count (Always integer, max 3).

3. Integrated Rate Equations (Zero & First)

Zero Order: $[A] = [A]_0 - kt$. Linear decrease.
First Order: $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]}$. Exponential decrease.
Half-Life ($t_{1/2}$): Formula derivation for 0 and 1st order.

4. Pseudo First Order Reactions

Reactions that appear higher order but behave as first order because one reactant is in large excess (e.g., Hydrolysis of Ester in excess water).

5. Temperature Dependence (Arrhenius)

Effect of T on k. Rule of thumb: rate doubles for $10^\circ$ rise.
Formula: $\log \frac{k_2}{k_1} = \frac{E_a}{2.303R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)$.
Concept of Activation Energy ($E_a$).

6. Collision Theory

Threshold Energy vs Activation Energy.
Orientation Factor ($P$): Why effective collisions are needed for reaction. $Rate = P Z_{AB} e^{-E_a/RT}$.

🎯 How to Practice

Graph Identification: Draw plots of $[R]$ vs $t$ (Zero Order) and $\ln[R]$ vs $t$ (First Order). Memorize the slopes: $-k$ for zero order, $-k$ for $\ln$, and $\frac{-k}{2.303}$ for $\log$.

Unit Analysis: Identify the order of reaction just by looking at the unit of $k$.
$mol \ L^{-1} s^{-1} \to$ Zero.
$s^{-1} \to$ First.
$L \ mol^{-1} s^{-1} \to$ Second.

Numerical Drill: Solve 5 problems using the Integrated Rate Equation for First Order reactions. This is the most frequently asked numerical.

📝 Quick Revision Formulas

Rate of Reaction ($aA \to bB$) $$Rate = -\frac{1}{a}\frac{d[A]}{dt} = +\frac{1}{b}\frac{d[B]}{dt}$$

First Order Kinetics $$k = \frac{2.303}{t} \log \frac{[A]_0}{[A]}$$ $$t_{1/2} = \frac{0.693}{k}$$

Arrhenius Equation $$k = A e^{-E_a/RT}$$ $$\log \frac{k_2}{k_1} = \frac{E_a}{2.303R} \left[\frac{T_2 - T_1}{T_1 T_2}\right]$$

Unit of k $$mol^{1-n} L^{n-1} s^{-1}$$

(Where n is the order)

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Lesson Plan: Chemical Kinetics (Class 12)