Chemical Kinetics: Reaction Rates and Mechanisms

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Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the speed, or rate, at which chemical reactions occur and the factors that affect these rates. Understanding reaction rates is essential for controlling chemical processes in industrial, environmental, and biological contexts.

Reaction Rates

Average Reaction Rate

The reaction rate is a measure of how quickly reactants are converted into products in a chemical reaction. It is typically expressed as the change in concentration of a reactant or product per unit time.

Average rate is calculated over a finite time interval.
For a reactant A, the average rate is given by:

The negative sign indicates the concentration of reactant decreases over time.

Graph showing the change in number of molecules of A and B over time

Example: The graph above shows the decrease in A molecules and the increase in B molecules as the reaction proceeds.

Stoichiometry and Reaction Rate

Reaction rates can be related to the stoichiometry of the reaction. For a general reaction:

The rate can be expressed as:

Rate equations for reactant and product

This ensures that the rate is consistent regardless of which species is monitored.

Experimental Determination of Reaction Rate

Reaction rates are often determined by measuring the concentration of a reactant or product at various times. The data can be tabulated as shown below:

Time (s)	[Br2] (M)	Rate (M/s)
0.0	0.0120	4.20 × 10−3
50.0	0.0101	3.52 × 10−3
100.0	0.00846	2.96 × 10−3
150.0	0.00710	2.49 × 10−3
200.0	0.00596	2.09 × 10−3
250.0	0.00500	1.75 × 10−3
300.0	0.00420	1.48 × 10−3
350.0	0.00353	1.23 × 10−3
400.0	0.00296	1.04 × 10−3

Table of reaction rates and concentrations

Example: The table above shows how the concentration of Br2 and the reaction rate change over time.

Instantaneous Rate

The instantaneous rate is the rate at a specific moment in time, found by taking the slope of the tangent to the concentration vs. time curve at that point.

Graph showing instantaneous rate as the slope of a tangent

Initial rate is the instantaneous rate at t = 0.

Rate Laws and Reaction Order

The Rate Law

The rate law expresses the relationship between the reaction rate and the concentrations of reactants. For a general reaction:

k is the rate constant.
x and y are the reaction orders with respect to A and B, determined experimentally.
The sum x + y is the overall reaction order.

Example: If rate = k[Br2]1[HCOOH]0 = k[Br2], the reaction is first order in Br2, zeroth order in HCOOH, and first order overall.

Experimental Determination of the Rate Law

To determine the rate law, initial rates are measured for different starting concentrations of reactants. The effect of changing each reactant's concentration on the rate is analyzed to deduce the order with respect to each reactant.

Table of experiments with varying concentrations and rates

Key Points:

Reaction order is determined from experimental data, not from the stoichiometry of the balanced equation.
Reaction order is defined in terms of reactant concentrations.

Integrated Rate Laws

Zeroth-Order Reactions

For a zeroth-order reaction, the rate is independent of the concentration of the reactant:

The integrated rate law is:

A plot of [A] vs. t yields a straight line with slope -k.

First-Order Reactions

For a first-order reaction, the rate depends linearly on the concentration of one reactant:

The integrated rate law is:

A plot of ln[A] vs. t yields a straight line with slope -k.

Graphs for first-order reactions: [A] vs t and ln[A] vs t

Half-life (t1/2): The time required for the concentration of a reactant to decrease to half its initial value. For a first-order reaction:

Graph showing half-life for a first-order reaction

Second-Order Reactions

For a second-order reaction (rate depends on the square of one reactant):

The integrated rate law is:

A plot of 1/[A] vs. t yields a straight line with slope k.

Graphs for second-order reactions: [A] vs t and 1/[A] vs t

Reaction Rates and Temperature

Collision Theory

According to collision theory, chemical reactions occur when molecules collide with sufficient energy and proper orientation. The rate of reaction increases with the frequency of effective collisions.

Activation energy (Ea) is the minimum energy required for a reaction to occur.
The steric factor (p) accounts for the fraction of collisions with the correct orientation.

Molecular collisions and orientation Potential energy diagram showing activation energy

The Arrhenius Equation

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

Or, in logarithmic form:

Arrhenius equation in logarithmic form

Where:

A is the frequency factor
Ea is the activation energy
R is the gas constant (8.314 J/K·mol)
T is the temperature in Kelvin

Reaction Mechanisms

Elementary Reactions and Molecularity

A reaction mechanism is a sequence of elementary steps that describes the pathway from reactants to products. Each elementary step involves a specific number of molecules, called the molecularity:

Unimolecular: One molecule decomposes or rearranges.
Bimolecular: Two molecules collide.
Termolecular: Three molecules collide (rare).

Example of a reaction mechanism with intermediates

Reaction intermediates are species produced in one step and consumed in another; they do not appear in the overall balanced equation.

Rate-Determining Step

In a multistep mechanism, the rate-determining step is the slowest step, which controls the overall reaction rate and determines the observed rate law.

Catalysis

Introduction to Catalysis

A catalyst is a substance that increases the rate of a chemical reaction without being consumed. Catalysts work by lowering the activation energy required for the reaction.

Potential energy diagrams with and without a catalyst

Homogeneous and Heterogeneous Catalysis

Homogeneous catalysis: Catalyst and reactants are in the same phase (usually liquid).
Heterogeneous catalysis: Catalyst and reactants are in different phases (e.g., solid catalyst with gaseous or liquid reactants).

Homogeneous catalysis example Heterogeneous catalysis example

Enzymes: Biological Catalysts

Enzymes are highly specific biological catalysts that increase the rate of biochemical reactions, often by factors of 106 to 1018. Enzyme catalysis is usually homogeneous, as both enzyme and substrate are in aqueous solution.