1.1 Fundamentals of chemical kinetics

Introduction to Chemical Kinetics

Chemical kinetics studies how fast reactions happen and what factors control their speed. It tracks how quickly reactants are consumed and products are formed over time, which is essential for controlling reactions in fields like pharmaceuticals, chemical engineering, and materials science.

Definition of Chemical Kinetics

Chemical kinetics goes beyond asking whether a reaction occurs (that's thermodynamics) and instead asks how fast it occurs and by what pathway. A reaction might be thermodynamically favorable but incredibly slow without the right conditions.

• Studies the rates of chemical reactions and the factors that influence them
• Investigates how quickly reactants are consumed and products are formed over time
• Provides insights into reaction mechanisms, the step-by-step molecular pathways from reactants to products
• Applied across chemistry, biology, and engineering whenever reaction speed matters

Reaction Rate and Concentration Relationships

Reaction rate quantifies the change in concentration of a reactant or product per unit time. For a simple reaction where reactant A becomes product B, the rate is expressed as:

$rate = -\frac{d[A]}{dt} = \frac{d[B]}{dt}$

The negative sign in front of $\frac{d[A]}{dt}$ accounts for the fact that reactant concentration decreases over time, keeping the rate value positive.

The rate law describes how the rate depends on reactant concentrations:

$rate = k[A]^m[B]^n$

• $k$ is the rate constant, a value specific to a given reaction at a given temperature
• $m$ and $n$ are the reaction orders with respect to reactants A and B. These are determined experimentally, not from the balanced equation (unless the reaction is elementary)

Increasing reactant concentrations generally increases the reaction rate because more molecules are available to collide. In some cases, accumulation of products can slow the reaction through product inhibition or by driving a reverse reaction.

Factors Influencing Reaction Rates

Role of Activation Energy

Activation energy ($E_a$) is the minimum energy reactant molecules must have upon collision to initiate a reaction. Think of it as an energy hill that molecules need to climb before they can roll down into products.

• Higher $E_a$ means fewer molecules have enough energy to react, so the reaction is slower
• Lower $E_a$ means more molecules can clear the barrier, so the reaction is faster
• Catalysts lower $E_a$ by providing an alternative reaction pathway. They speed up the reaction without being consumed in the process

The Arrhenius equation connects the rate constant to activation energy and temperature:

$k = Ae^{-E_a/RT}$

• $A$ is the pre-exponential (frequency) factor, related to how often molecules collide with proper orientation
• $R$ is the gas constant ($8.314 \, J \, mol^{-1} K^{-1}$)
• $T$ is the absolute temperature in Kelvin

The exponential term $e^{-E_a/RT}$ is what makes temperature so powerful. Even a modest temperature increase can significantly raise $k$ because more molecules now have enough energy to overcome $E_a$.

Elementary vs. Complex Reactions

Elementary reactions occur in a single molecular event with no intermediates. They pass through one transition state, and their rate laws can be written directly from the stoichiometry.

The molecularity of an elementary reaction tells you its order:

1. Unimolecular (one molecule reacts) → first-order. Example: radioactive decay
2. Bimolecular (two molecules collide) → second-order. Example: dimerization reactions
3. Termolecular (three molecules collide simultaneously) → third-order. These are rare because three-body collisions are unlikely. Example: certain steps in ozone formation

Complex reactions consist of multiple elementary steps connected through intermediates (species that are produced in one step and consumed in a later step).

• The overall reaction order often cannot be determined just by looking at the balanced equation
• The rate-determining step is the slowest elementary step in the sequence, and it governs the overall rate of the reaction. It acts as a bottleneck
• Chemists use tools like the steady-state approximation (assuming intermediate concentrations stay roughly constant) and rate-limiting step analysis to derive rate laws for complex reactions
• Examples include enzymatic reactions and hydrocarbon combustion, both of which involve many sequential and parallel elementary steps