Chemical Kinetics: Temperature, Reaction Mechanisms, and Catalysis

Chemical Kinetics: Effect of Temperature and Reaction Mechanisms

Temperature Dependence of Reaction Rate

The rate of a chemical reaction depends not only on the concentration of reactants but also on temperature. The rate law is typically expressed as:

• Rate Law: $\text{Rate} = k[A]^m$

• Rate Constant (k): The value of k changes with temperature, and its dependence is described by the Arrhenius Equation.

The Arrhenius Equation is:

• $k = Ae^{-\frac{E_a}{RT}}$

• Where: A = Frequency factor $E_a$ = Activation energy R = Gas constant (8.314 J mol–1 K–1) T = Temperature (K)

Collision Theory

Collision theory explains why and how reactions occur, especially in the gas phase. A reaction only takes place after a collision between reactant particles. However, not all collisions result in a reaction.

• Successful Collisions: Must have sufficient energy to break bonds and proper orientation for new bonds to form.

• Frequency Factor (A): Represents the number of approaches to the activation barrier per unit time.

• Exponential Factor: Fraction of molecules with enough energy to overcome the activation barrier, depends on temperature.

Activation Energy and Potential Energy Diagrams

Activation energy ($E_a$) is the minimum energy required for a reaction to occur. It is the energy difference between reactants and the transition state (activated complex).

• High $E_a$: Slower reaction

• Low $E_a$: Faster reaction

• Transition State: High-energy, unstable arrangement of atoms between reactants and products

Arrhenius Plots

The Arrhenius equation can be rearranged to a linear form for graphical analysis:

• $\ln k = -\frac{E_a}{R}\frac{1}{T} + \ln A$

• Plotting $\ln k$ vs $1/T$ yields a straight line with slope $-E_a/R$ and y-intercept $\ln A$.

Reaction Mechanisms

Elementary Steps and Molecularity

Reactions often proceed through a series of steps called a mechanism. Each step is an elementary step, which cannot be broken down further and proceeds as written.

• Molecularity: Number of reactant particles involved in an elementary step (unimolecular, bimolecular, termolecular).

• Rate Law for Elementary Steps: Determined directly from the reactants in that step.

Elementary Step	Molecularity	Rate Law
A → products	1	Rate = k[A]
A + A → products	2	Rate = k[A]2
A + B → products	2	Rate = k[A][B]
A + A + A → products	3 (rare)	Rate = k[A]3
A + A + B → products	3 (rare)	Rate = k[A]2[B]
A + B + C → products	3 (rare)	Rate = k[A][B][C]

Rate-Determining Step

In a multi-step mechanism, the slowest step is the rate-determining step. The overall rate law for the reaction is governed by this step.

• Example: If step 1 is slow and involves NO2, the rate law is Rate = k[NO2]2.

Steady-State Approximation

When intermediates are difficult to measure, the steady-state approximation assumes their concentration remains constant during the reaction. The rate of formation equals the rate of consumption.

• Application: Used to express the rate law in terms of measurable reactants and products.

Catalysis

Role of Catalysts

A catalyst provides an alternative reaction pathway with lower activation energy, increasing the reaction rate without being consumed.

• Homogeneous Catalysts: Same phase as reactants

• Heterogeneous Catalysts: Different phase than reactants

• Enzymes: Biological catalysts that orient substrates for reaction

Summary Table: Key Equations

Equation	Description
$k = Ae^{-\frac{E_a}{RT}}$	Arrhenius equation for rate constant
$\ln k = -\frac{E_a}{R}\frac{1}{T} + \ln A$	Linearized Arrhenius equation
Rate = k[Reactant]n	General rate law
Rate = k[NO2]2	Example rate law for a bimolecular step