Chapter 3: Chemical Kinetics
Key Topics: Rate of Reaction, Order & Molecularity, Integrated Rate Equations, Half-Life, Arrhenius Equation, and Collision Theory.
1. Rate of Reaction & Stoichiometry
Chemical Kinetics is the branch of chemistry concerned with the rates of chemical reactions and their mechanisms.
Rate Expression for General Reaction:
For a general chemical reaction $aA + bB \rightarrow cC + dD$:
$$\text{Rate} = -\frac{1}{a} \frac{d[A]}{dt} = -\frac{1}{b} \frac{d[B]}{dt} = +\frac{1}{c} \frac{d[C]}{dt} = +\frac{1}{d} \frac{d[D]}{dt}$$
Rate Law & Order of Reaction:
$$\text{Rate} = k [A]^x [B]^y$$
$$\text{Overall Order of Reaction} = n = x + y$$
2. Order vs Molecularity
| Property | Order of Reaction | Molecularity of Reaction |
|---|---|---|
| Definition | Sum of powers of concentrations in the rate law expression. | Number of reacting species colliding simultaneously in an elementary step. |
| Determination | Experimental quantity. | Theoretical concept. |
| Values Allowed | Can be zero, fractional, or integer. | Must be a positive whole integer ($1, 2, 3$). Cannot be zero or fractional. |
| Applicability | Applicable to elementary as well as complex reactions. | Applicable only to elementary reactions. |
3. Integrated Rate Law Equations
Zero-Order Reaction ($n = 0$):
Differential Rate Law:
$$\frac{d[A]}{dt} = -k$$
Integrated Rate Equation:
$$k = \frac{[A]_0 - [A]}{t}$$
Half-Life ($t_{1/2}$):
$$t_{1/2} = \frac{[A]_0}{2k}$$
Units of Rate Constant ($k$):
$$\text{mol L}^{-1} \text{s}^{-1}$$
First-Order Reaction ($n = 1$):
Differential Rate Law:
$$\frac{d[A]}{dt} = -k[A]$$
Integrated Rate Equation:
$$k = \frac{2.303}{t} \log_{10} \frac{[A]_0}{[A]}$$
Half-Life ($t_{1/2}$):
$$t_{1/2} = \frac{0.693}{k}$$
Units of Rate Constant ($k$):
$$\text{s}^{-1}$$
4. Temperature Dependence & Arrhenius Equation
Arrhenius Equation:
$$k = A e^{-\frac{E_a}{RT}}$$
Where:
$$A = \text{Frequency Factor / Pre-exponential Factor}$$
$$E_a = \text{Activation Energy}$$
$$R = \text{Gas Constant } (8.314 \text{ J K}^{-1} \text{mol}^{-1})$$
$$T = \text{Absolute Temperature in Kelvin}$$
Logarithmic Form of Arrhenius Equation:
$$\ln k = \ln A - \frac{E_a}{RT}$$
$$\log_{10} k = \log_{10} A - \frac{E_a}{2.303 R T}$$
Rate Constants at Two Different Temperatures ($T_1$ and $T_2$):
$$\log_{10} \left( \frac{k_2}{k_1} \right) = \frac{E_a}{2.303 R} \left[ \frac{T_2 - T_1}{T_1 T_2} \right]$$
5. Collision Theory
Rate Equation based on Collision Theory:
$$\text{Rate} = P \cdot Z_{AB} \cdot e^{-\frac{E_a}{RT}}$$
Where:
$$Z_{AB} = \text{Collision frequency of reactants } A \text{ and } B$$
$$P = \text{Steric or Probability Factor}$$