Quick Revision Notes: Chemical Kinetics

Class 12 - Chemistry (MP Board)

### Concept 1: Rate of a Chemical Reaction

Chemical Kinetics is the branch of chemistry that deals with the study of reaction rates and their mechanisms.

• Rate of Reaction (अभिक्रिया की दर): Change in concentration of a reactant or product in unit time.
• Average Rate ($r_{avg}$): Measured over a long time interval. $$r_{avg} = -\frac{\Delta [R]}{\Delta t} = +\frac{\Delta [P]}{\Delta t}$$
• Instantaneous Rate ($r_{inst}$): Measured at a specific instant of time. $$r_{inst} = -\frac{d[R]}{dt} = +\frac{d[P]}{dt}$$
• Units of Rate of Reaction: $\text{mol L}^{-1}\text{s}^{-1}$ (or $\text{atm s}^{-1}$ for gases).

### Concept 2: Rate Law and Rate Constant

• Rate Law (वेग नियम): Expression which relates the rate of a reaction to the concentration terms of the reactants. For a reaction: $aA + bB \rightarrow cC + dD$ $$\text{Rate} = k[A]^x[B]^y$$ (where $x$ and $y$ may or may not be equal to stoichiometric coefficients $a$ and $b$)
• Rate Constant ($k$): It is the rate of the reaction when the concentration of each reactant is unity. It is also known as specific reaction rate.
• Units of Rate Constant ($k$): General formula for units of $k$: $\text{mol}^{(1-n)} \text{L}^{(n-1)} \text{s}^{-1}$ (where $n$ is the order of the reaction).

### Concept 3: Order and Molecularity of a Reaction

### Concept 4: Integrated Rate Equations

1. Zero Order Reactions (शून्य कोटि की अभिक्रिया)

Rate is independent of the concentration of reactants.

• Rate Law: $\text{Rate} = k[R]^0 = k$
• Integrated Rate Equation: $$k = \frac{[R]_0 - [R]}{t} \implies [R] = -kt + [R]_0$$
• Half-life Period ($t_{1/2}$): Time in which concentration of reactant is reduced to half of its initial concentration. $$t_{1/2} = \frac{[R]_0}{2k}$$

2. First Order Reactions (प्रथम कोटि की अभिक्रिया)

Rate is directly proportional to the first power of the concentration of reactant.

• Rate Law: $\text{Rate} = k[R]$
• Integrated Rate Equation: $$k = \frac{2.303}{t} \log \frac{[R]_0}{[R]}$$ (where $[R]_0$ = initial concentration, $[R]$ = concentration at time $t$)
• Half-life Period ($t_{1/2}$): $$t_{1/2} = \frac{0.693}{k}$$ (Note: $t_{1/2}$ for a first-order reaction is independent of initial concentration).

### Concept 5: Temperature Dependence of Rate Constant

• Arrhenius Equation (आर्हिनियस समीकरण): Relates rate constant with temperature. $$k = A \cdot e^{-E_a / RT}$$

  • $k$ = Rate constant
  • $A$ = Arrhenius factor / Frequency factor
  • $E_a$ = Activation energy (सक्रियण ऊर्जा)
  • $R$ = Gas constant ($8.314 \text{ J K}^{-1}\text{mol}^{-1}$)
  • $T$ = Temperature in Kelvin

• Linear Form of Arrhenius Equation (at two different temperatures $T_1$ and $T_2$): $$\log \frac{k_2}{k_1} = \frac{E_a}{2.303 R} \left( \frac{T_2 - T_1}{T_1 T_2} \right)$$ $$\log \frac{k_2}{k_1} = \frac{E_a}{2.303 R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right)$$

• Temperature Coefficient: The ratio of rate constants at two temperatures differing by $10^\circ\text{C}$ is usually between 2 and 3. $$\text{Temperature Coefficient} = \frac{k_{(T+10)}}{k_T} \approx 2 \text{ to } 3$$

### Concept 6: Collision Theory of Chemical Reactions

• Formula for Collision Rate: $$\text{Rate} = Z_{AB} \cdot e^{-E_a / RT}$$
  • $Z_{AB}$ = Collision frequency of reactants $A$ and $B$.
  • $e^{-E_a / RT}$ = Fraction of molecules with energy equal to or greater than $E_a$ (Threshold energy).
• Effective Collisions: For a reaction to occur, collisions must have proper orientation along with sufficient energy ($E \ge E_a$).
• Threshold Energy ($E_{th}$): Minimum energy required by reactants to undergo effective collisions. $$\text{Threshold Energy} = \text{Activation Energy } (E_a) + \text{Initial Potential Energy of Reactants}$$