Chapter 14: Chemical Kinetics – Study Notes

Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the study of the rate (speed) at which chemical reactions occur. It is essential for understanding processes such as explosions, medication effectiveness, rusting, and erosion. The reaction rate is the speed at which chemical reactions take place, measured as the change in concentration of reactants or products per unit time.

• Key topics: Factors affecting reaction rate, rate laws (zero, first, second order), activation energy, reaction mechanisms, and catalysis.

Factors Affecting Reaction Rate

Physical State of Reactants

The physical state influences how frequently and effectively reactant molecules collide. Homogeneous reactions (all gases or liquids) are typically faster than heterogeneous reactions (involving solids).

• More frequent collisions in gases and liquids lead to faster reactions.

• Solids react more slowly due to limited surface area for collisions.

Reactant Concentration

Increasing the concentration of reactants generally increases the reaction rate because more molecules are available to collide and react.

• More particles mean more collisions, increasing the chance for effective collisions.

• Increasing surface area (e.g., using a powder instead of a solid chunk) also increases reaction rate.

Reaction Temperature

Raising the temperature increases the kinetic energy of molecules, leading to more frequent and energetic collisions. This typically increases the reaction rate.

• Higher temperature means more motion and more collisions.

• More molecules have enough energy to overcome the activation energy barrier.

Presence of a Catalyst

Catalysts increase reaction rates without being consumed in the reaction. They do not appear in the overall balanced equation but provide alternative pathways with lower activation energy.

• Catalysts are crucial in biological (enzymes) and industrial processes.

Measuring Reaction Rates

Definition of Reaction Rate

Reaction rate is the change in concentration of a reactant or product over a time period:

$\text{Rate} = \frac{\Delta [\text{A}]}{\Delta t}$

• $\Delta$ symbolizes "change in"

• $[\text{A}]$ is the molar concentration of compound A

• $t$ is time

Rates are always reported as positive values, representing the amount of product formed or reactant consumed per unit time.

Average and Instantaneous Rate

• Average rate: Change in concentration over a finite time interval.

• Instantaneous rate: Rate at a specific moment, found by the slope of the tangent to the concentration vs. time curve.

Reaction Rates and Stoichiometry

Rates can be measured using either reactant disappearance or product appearance. For reactions with different stoichiometric coefficients, the rate is adjusted accordingly:

For $2O_3(g) \rightarrow 3O_2(g)$:

$\text{Rate} = -\frac{1}{2} \frac{\Delta [O_3]}{\Delta t} = \frac{1}{3} \frac{\Delta [O_2]}{\Delta t}$

Rate Laws and Rate Constants

Rate Laws

Rate laws are mathematical expressions that relate reaction rate to the concentration of reactants, determined experimentally:

$\text{Rate} = k[A]^x[B]^y$

• $k$ = rate constant (specific to each reaction and temperature)

• $x, y$ = reaction orders with respect to each reactant

The overall reaction order is the sum of the exponents.

Order ≠ Stoichiometry

The reaction order must be determined experimentally and does not necessarily match the stoichiometric coefficients in the balanced equation.

Units of the Rate Constant, $k$

• Zero order: $M\ s^{-1}$

• First order: $s^{-1}$

• Second order: $M^{-1}\ s^{-1}$

Method of Initial Rates

To determine the rate law, compare rates from experiments where one reactant's concentration changes while others are held constant. The ratio of rates gives the order with respect to each reactant.

Example Table: Rate Data for Ammonium and Nitrite Ions

Experiment Number	Initial [NH4+]	Initial [NO2-]	Observed Initial Rate (M/s)
1	0.100	0.200	5.4 × 10-7
2	0.200	0.200	1.1 × 10-6
3	0.300	0.200	1.6 × 10-6
4	0.100	0.100	2.7 × 10-7
5	0.100	0.300	8.1 × 10-7
6	0.100	0.400	1.1 × 10-6

From the data, the rate law is:

$\text{Rate} = 2.7 \times 10^{-4}\ M^{-1}s^{-1} [NH_4^+][NO_2^-]$

Integrated Rate Laws

First-Order Reactions

For a first-order reaction ($A \rightarrow$ products):

$\text{Rate} = k[A]$

Integrated form:

$\ln [A] = -kt + \ln [A]_0$

• Plot of $\ln [A]$ vs. $t$ is linear with slope $-k$.

Second-Order Reactions

For a second-order reaction ($A \rightarrow$ products):

$\text{Rate} = k[A]^2$

Integrated form:

$\frac{1}{[A]} = kt + \frac{1}{[A]_0}$

• Plot of $1/[A]$ vs. $t$ is linear with slope $k$.

Zero-Order Reactions

For a zero-order reaction:

$\text{Rate} = k$

Integrated form:

$[A] = -kt + [A]_0$

• Plot of $[A]$ vs. $t$ is linear with slope $-k$.

Half-Life of a Reaction

First-Order Reaction

The half-life ($t_{1/2}$) is the time required for half of the reactant to be consumed:

$t_{1/2} = \frac{0.693}{k}$

Second-Order Reaction

For a second-order reaction:

$t_{1/2} = \frac{1}{k[A]_0}$

*Half-life depends on the initial concentration for second-order reactions.*

Temperature and Rate: Activation Energy and the Arrhenius Equation

Effect of Temperature

As temperature increases, the rate constant $k$ increases, and thus the reaction rate increases. The rate constant approximately doubles for every 10°C rise in temperature.

Activation Energy ($E_a$)

The minimum energy required for a reaction to occur is called the activation energy. The Arrhenius equation relates the rate constant to temperature and activation energy:

$k = A e^{-E_a/(RT)}$

• $A$ = frequency factor

• $E_a$ = activation energy

• $R$ = gas constant

• $T$ = temperature in Kelvin

Collision Model and Orientation Factor

Collision Model

Reactions occur when molecules collide with sufficient energy and proper orientation. Not all collisions result in a reaction; only those with enough energy (≥ $E_a$) and correct alignment are effective.

Orientation Factor

Even if molecules collide, they must be oriented correctly for bonds to break and form. The probability of correct orientation is called the orientation factor.

Transition State (Activated Complex)

The transition state (or activated complex) is the highest energy arrangement of atoms during a reaction. The energy required to reach this state is the activation energy ($E_a$).

Reaction Coordinate Diagrams

These diagrams plot energy versus reaction progress, showing reactants, products, and the transition state. The height of the energy barrier corresponds to $E_a$.

Reassessing Effect of Temperature

At higher temperatures, a greater fraction of molecules have enough energy to overcome the activation energy barrier, increasing the reaction rate.

Summary Table: Key Equations in Chemical Kinetics

Order	Rate Law	Integrated Rate Law	Half-Life
Zero	$\text{Rate} = k$	$[A] = -kt + [A]_0$	$t_{1/2} = \frac{[A]_0}{2k}$
First	$\text{Rate} = k[A]$	$\ln [A] = -kt + \ln [A]_0$	$t_{1/2} = \frac{0.693}{k}$
Second	$\text{Rate} = k[A]^2$	$\frac{1}{[A]} = kt + \frac{1}{[A]_0}$	$t_{1/2} = \frac{1}{k[A]_0}$

Additional info: These notes are based on LSU Chemistry lecture slides and cover all foundational aspects of chemical kinetics relevant to a General Chemistry course.