Temperature Dependence: Arrhenius Equation & Collision Theory
Temperature profoundly impacts reaction rates. For most chemical reactions, a $10^\circ$ rise in temperature doubles the reaction rate. This guide breaks down the quantitative relationship provided by Svante Arrhenius.
1. The Arrhenius Equation
The mathematical relationship between the rate constant ($k$), temperature ($T$), and activation energy ($E_a$) is given by:
$A$: Frequency Factor (Pre-exponential factor), $E_a$: Activation Energy, $R$: Gas Constant
Exam Cheat Sheet: Graphical Analysis
When plotting $\ln k$ (y-axis) against $1/T$ (x-axis):
- Slope ($m$): Equal to $-E_a/R$. (Negative slope indicates rate decreases as $1/T$ increases, i.e., $T$ decreases).
- Intercept ($c$): Equal to $\ln A$.
- Concept: Higher $E_a$ leads to a steeper slope, meaning the reaction is more sensitive to temperature changes.
Figure: Boltzmann Distribution Curve showing effect of Temperature on Activation Energy
2. Collision Theory & Activation Energy
According to collision theory, not all molecular collisions result in a chemical reaction. Only those collisions are effective that possess:
Criteria for Effective Collisions
- Energy Barrier: Reacting molecules must possess energy $\ge$ Threshold Energy.
- Orientation Barrier: Molecules must collide with proper orientation to break old bonds and form new ones.
- Activation Energy ($E_a$): The extra energy required by reactant molecules to reach the threshold energy.
Threshold Energy = Average K.E. of reactants + Activation Energy
3. Maxwell-Boltzmann Distribution
This statistical distribution explains why a small temperature increase causes a large increase in rate. A $10^\circ$ rise doesn't just increase the average kinetic energy slightly; it effectively doubles the fraction of molecules having energy greater than $E_a$.
Effect of Catalyst
- A catalyst provides an alternate pathway with lower Activation Energy ($E_a'$).
- It does not change the enthalpy ($\Delta H$) or Gibbs free energy ($\Delta G$) of the reaction.
- It does not shift the equilibrium constant ($K_{eq}$), but helps attain equilibrium faster.
No comments:
Post a Comment