Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the study of the rates at which chemical reactions occur and the factors that affect these rates. Understanding reaction rates is essential for controlling chemical processes in laboratory and industrial settings.

• Reaction rate: The speed at which a chemical reaction occurs, typically measured as the change in concentration of a reactant or product per unit time.

• Reaction rate is proportional to the frequency of collisions between reactant molecules.

Factors Affecting Reaction Rate

• Physical State of Reactants: Gases and liquids react faster than solids due to increased molecular mobility. For solids, increasing surface area (e.g., using a powder instead of a tablet) increases reaction rate.

• Reactant Concentrations: Higher concentrations generally increase reaction rate due to more frequent collisions.

• Reaction Temperature: Increasing temperature raises kinetic energy, leading to more frequent and energetic collisions, thus increasing reaction rate.

• Catalyst: Catalysts increase reaction rate without being consumed. They provide alternative reaction pathways with lower activation energy. Examples include enzymes and catalytic converters.

Review of Solutions (Chapter 13)

Definitions

• Solution: Homogeneous mixture of two or more substances in a single phase (liquid or gas), with uniform appearance and properties throughout.

• Solvent: The component present in the greatest amount; the substance that dissolves the solute.

• Solute: The component present in a smaller amount; the substance dissolved in the solvent. There can be more than one solute.

Molar concentration (M) is defined as:

Reaction Rate

Measuring Reaction Rate

Reaction rate is determined by the change in concentration of a reactant or product over a specific time period.

• means "change in" (final - initial).

• means molar concentration of substance A.

• is time.

Rate is always expressed as a positive value. Common units: M/s (moles per liter per second).

Types of rate measured:

• Average rate

• Instantaneous rate

• Initial rate

General formula:

Example: Average Rate Calculation

For the reaction , the average rate at which B appears and A disappears over a time interval is:

Example calculation:

Tabular Data: Reaction Rate Example

For the reaction :

Instantaneous Rate

The instantaneous rate is the slope of the concentration vs. time curve at a specific point. The initial rate is the instantaneous rate at .

Reactions typically slow down over time as reactant concentrations decrease.

Relative Rates and Stoichiometry

Stoichiometric Relationships

For reactions with a 1:1 mole ratio, the rates of disappearance and appearance are equal:

For reactions with different stoichiometric coefficients, rates are related by those coefficients. Example:

For , the rate of HI disappearance is twice the rate of H2 or I2 appearance.

Example: Ozone Decomposition

For :

• Rate of appearance = × Rate of disappearance

• appears 1.5 times faster than disappears.

Rate Laws and Rate Constants

Rate Laws

A rate law expresses the relationship between reaction rate and reactant concentrations. It must be determined experimentally.

General form:

• = rate constant

• , = reaction orders with respect to A and B

The overall reaction order is the sum of the exponents.

Reaction Order Examples

• First-order in A (): Doubling [A] doubles the rate.

• Second-order in A (): Doubling [A] increases rate by a factor of 4.

• Zero-order in A (): Changing [A] has no effect on rate.

Experimental Determination of Rate Laws

Rate laws are determined by varying reactant concentrations and measuring initial rates.

Rate law for this reaction: (first order in each reactant, overall second order).

Units of Rate Constant (k)

• Zero-order:

• First-order:

• Second-order:

• Third-order:

Integrated Rate Laws

First-Order Reactions

For a first-order reaction ( products):

Integrated rate law:

• A plot of vs. is linear with slope .

Half-Life for First-Order Reactions

The half-life () is the time required for the concentration of a reactant to decrease by half:

Second-Order Reactions

For a second-order reaction ( products):

Integrated rate law:

• A plot of vs. is linear with slope .

Half-life for second-order reactions is concentration-dependent:

Zero-Order Reactions

For zero-order reactions, rate is independent of reactant concentration:

Integrated rate law:

Collision Theory and Activation Energy

Collision Model

Reactions occur when molecules collide with sufficient energy and proper orientation. The minimum energy required is called activation energy (E_a).

• Higher temperature increases kinetic energy and collision frequency.

• Only a fraction of collisions have enough energy to overcome .

Arrhenius Equation

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

• = frequency factor

• = activation energy (J)

• = gas constant ()

• = temperature (K)

Linearized form:

A plot of vs. yields a straight line with slope .

Reaction Mechanisms

Elementary Steps and Molecularity

A mechanism is a sequence of elementary steps showing how reactants become products. Each step has a molecularity:

Termolecular steps are rare.

Rate-Determining Step

The slowest step in a mechanism controls the overall reaction rate and determines the rate law.

Intermediates and Transition States

• Intermediate: Formed and consumed during the reaction; not present in the overall equation.

• Transition state: High-energy, unstable state during bond breaking/forming; cannot be isolated.

Catalysis

Catalysts

Catalysts increase reaction rate by lowering activation energy and providing alternative pathways. They are not consumed in the reaction.

• Homogeneous catalyst: Same phase as reactants (e.g., dissolved in solution).

• Heterogeneous catalyst: Different phase (e.g., solid catalyst with gaseous reactants).

Example: Automotive catalytic converters use solid catalysts (Pt, Pd, Rh) to convert pollutants to less harmful substances.

Enzymes

Enzymes are biological catalysts with active sites where substrates bind. The lock-and-key model describes how substrates fit into the enzyme's active site.

Additional info: Some context and examples were expanded for clarity and completeness, including definitions, formulas, and applications relevant to General Chemistry.