MP Board · Class 12 · Chemistry · Chemical KineticsDiscuss the concept of Activation Energy and Collision Theory of chemical reactions in detail. Explain how activation energy affects the rate of a reaction and how it is determined graphically using the Arrhenius equation.

Introduction to Collision Theory

• Proposed by Max Trautz and William Lewis, the collision theory is based on kinetic molecular theory of gases.
• According to this theory, reactant molecules are assumed to be hard spheres, and a chemical reaction occurs only when reactant molecules collide with each other.
• However, not all collisions result in product formation; only a fraction of total collisions are effective.

Criteria for Effective Collisions

• Threshold Energy: Colliding molecules must possess a minimum amount of energy, known as threshold energy, to break existing bonds and form new ones.
• Activation Energy ($E_a$): The extra amount of energy that normal reactant molecules must absorb so that their energy equals threshold energy is called activation energy. Mathematically, $\text{Activation Energy} = \text{Threshold Energy} - \text{Average Energy of Reactants}$.
• Proper Orientation: Molecules must collide with proper spatial orientation so that old bonds break correctly and new bonds form successfully.
• These two conditions are mathematically incorporated in the Arrhenius equation factor: Rate $= P \cdot Z \cdot e^{-E_a/RT}$, where $P$ is steric factor and $Z$ is collision frequency.

The Arrhenius Equation and Graphical Determination

• Svante Arrhenius quantitatively related the rate constant ($k$) of a reaction with temperature ($T$) and activation energy ($E_a$): $$k = A e^{-E_a/RT}$$ where $A$ is the Arrhenius factor (frequency factor) and $R$ is the universal gas constant.
• Taking natural logarithm ($\ln$) on both sides: $$\ln k = \ln A - \frac{E_a}{RT}$|
• Converting to common logarithm (base 10): $$\log k = \log A - \frac{E_a}{2.303 R T}$$
• Comparing this equation with the equation of a straight line ($y = mx + c$):
  • $y = \log k$
  • $x = \frac{1}{T}$
  • Slope ($m$) = $-\frac{E_a}{2.303 R}$
  • Intercept ($c$) = $\log A$
• Graphical Method: When a graph is plotted between $\log k$ on the y-axis and $\frac{1}{T}$ on the x-axis, a straight line with a negative slope is obtained.
• By measuring the slope of this line ($m$), the activation energy ($E_a$) can be calculated easily using the relation: $E_a = -2.303 \times R \times \text{slope}$.