Chemical Kinetics: Rate of Reaction & Mechanisms

Chemical Kinetics deals with the speed (rate) of chemical reactions, the factors affecting them, and their mechanisms. It is a high-weightage topic for JEE and NEET, blending concepts with numericals.

1. Rate of Reaction

The rate of reaction is defined as the change in concentration of a reactant or product per unit time. For a general reaction $aA + bB \to cC + dD$, the rate is expressed as:

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

2. Integrated Rate Equations

Understanding the distinction between Zero Order and First Order kinetics is crucial for solving numerical problems efficiently.

Zero Order Reaction

$$ [R] = [R]_0 - kt $$

$$ t_{1/2} = \frac{[R]_0}{2k} $$

First Order Reaction

$$ k = \frac{2.303}{t} \log \frac{[R]_0}{[R]} $$

$$ t_{1/2} = \frac{0.693}{k} $$

Exam Cheat Sheet: Units of Rate Constant (k)

General Formula: $ (mol)^{1-n} (L)^{n-1} s^{-1} $ where $n$ is the order.

Zero Order ($n=0$): $mol \cdot L^{-1} \cdot s^{-1}$
First Order ($n=1$): $s^{-1}$ (Independent of concentration)
Second Order ($n=2$): $mol^{-1} \cdot L \cdot s^{-1}$

Chemical kinetics class 12 notes and formula chart

Figure: Overview of Rate of Reaction and Stoichiometric Relations

3. Temperature Dependence (Arrhenius Equation)

The rate of reaction increases with temperature. The quantitative relationship between rate constant ($k$) and temperature ($T$) is given by the Arrhenius equation:

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

Key Concepts

Activation Energy ($E_a$): The minimum extra energy required by reactant molecules to form the activated complex.
Temperature Coefficient: For most reactions, rate constant doubles for every $10^\circ$ rise in temperature.