Chemistry: The Central Science

Textbook Reference: Fifteenth Edition by Brown, LeMay, Bursten, Murphy, Woodward, StoltzfusChapter: 14 - Chemical KineticsCopyright: © 2023 Pearson Education, Inc. All Rights Reserved

Chemical Kinetics Overview

The study of the rate (speed) of chemical reactions encompasses various phenomena including explosions, medications, rusting, and erosion. Understanding chemical kinetics provides insight into how fast reactions proceed and the factors influencing these rates.

Reaction Rate

Definition: The reaction rate is quantified as the change in concentration of reactants or products per unit time (M/time).Influencing Factors: Several main factors affect reaction rates:

1. Physical state of reactants:

   • Collision frequency: Effectiveness of reactant collisions is influenced by their physical state (gas, liquid, solid).

   • Homogeneous Reactions: Occur when all reactants are in the same phase, thus leading to faster reaction rates.

   • Heterogeneous Reactions: Involve reactants in different phases, usually resulting in slower reactions due to limited contact.

2. Reactant Concentrations:

   • Higher concentrations generally speed up reaction rates, as more reactant molecules lead to more collisions.

   • Increased surface area, such as using fine powder instead of larger solid pellets, contributes to faster reaction rates.

3. Reaction Temperature:

   • Increased temperatures typically increase reaction rates by giving molecules more kinetic energy, which results in more frequent and energetic collisions.

   • Higher temperature allows more molecules to overcome the activation energy barrier necessary for reactions to proceed.

4. Presence of a Catalyst:

   • Catalysts accelerate reactions without being consumed, altering the pathways and the nature of molecular collisions.

   • Important in biological processes (e.g., enzymes) and in various industrial applications to improve efficiency.

Reaction Rate Measurement

• Expression: Reaction rate is expressed as the change in concentration over a period:[ Rate = \frac{\Delta [Reactants/Products]}{\Delta t} ]

• Rates are always described as positive values and can be categorized as either average or instantaneous rates.

  • Average Rate: Measures the change over intervals (e.g., increase in product concentration or decrease in reactant concentration).

  • Instantaneous Rate: This is measured at a specific moment, often at time zero, but can be challenging to determine. It is calculated as the slope of the tangent to the concentration vs. time curve.

Reaction Rates and Stoichiometry

• Rates can be derived from either reactants or products; however, they provide the same magnitude with opposite signs.

• Average Rates and Stoichiometric Coefficients: To express rates that reflect the stoichiometric coefficients, one must adjust according to these coefficients to maintain accurate relative rates.

14.2 Rate Laws and Rate Constants: Method of Initial Rates

Rate Laws

• Rate laws are mathematical expressions that relate the reaction rate to the concentrations of reactants.

• Specific Rate Constant (k): A value that is determined experimentally; its units depend on the order of the reaction.

• Reaction Order: This is the sum of the exponents (orders) that correspond to each reactant in the rate law.

• It is supposed to be experimentally determined, as it does not necessarily equate to the stoichiometry of the reaction.

Magnitudes and Units of k

• Fast reactions typically exhibit k values of 10 or higher, whereas slow reactions have lower k values, sometimes below 10.

Method of Initial Rates

• To determine the rate law, experiments are conducted whereby the concentration of one reactant is varied while others remain constant.

• A systematic approach focuses on how varying reactant concentrations influences observed rates and their proportional relationships.

Rate Law Result

• The final rate law expresses the relationship of reaction rates to the concentrations of reactants, forming the basis for predicting reaction dynamics.

14.3 Integrated Rate Laws

Integrated rate laws provide mathematical relationships that connect rate, rate constants, and concentration over time for different types of reactions.

First-Order Reactions

• First-order reactions display characteristics governed by the concentration of a single reactant. An example involves the conversion of methyl isonitrile to acetonitrile. This reaction defines its rate law based on concentration changes over time.

• Linear Relationships: Rearrangement of the integrated rate law gives rise to linear graphs that showcase first-order kinetics. Analysis of plots reveals specific slopes that provide the value of k.

Second-Order Reactions

• These reactions depend on one reactant raised to the second power or two reactants each to the first power, requiring a rearrangement in integration to derive linear relationships.

• Confirmation: Second-order characteristics may be confirmed through evaluating decomposition reactions.

Zero-Order Reactions

• Independent of reactant concentration, these reactions display linear behavior in concentration versus time plots. They provide unique insights into reaction dynamics when reactants saturate reaction environments.

Half-Life for First-Order Reactions

• Half-life, defined as the time taken for the concentration of a reactant to reduce to half its initial value, underpins the behavior of first-order kinetics. Mathematical expressions convey how half-life remains constant regardless of initial concentration variations.

Half-Life for Second-Order Reactions

• Second-order reactions exemplify a variable half-life, demonstrating a dependency on the concentration of reactants, which may complicate predictions.

14.4 Temperature and Rate: Activation Energy and Arrhenius Equation

• Reaction rates exhibit temperature-dependent behavior, as temperature increases typically cause rate constants to double, reflecting the underlying kinetic molecular interactions.

Collision Model

• Based on the kinetic molecular theory, this model posits that successful reactions occur only when molecules collide effectively. The orientation of these molecules during collisions is crucial for achieving product formation.

Activation Energy Model

• This model identifies the minimum energy threshold necessary for reactants to undergo a transformation, directly associating reaction energy profiles with the activation energy barrier.

Transition State (Activated Complex)

• Energy state representations illustrate how reactants transition into products through a transitional complex before reforming as stable products.

Effect of Temperature on Energy Distribution

• With increased temperatures, the fraction of molecules possessing sufficient energy to overcome the activation energy barrier increases, thus accelerating reaction rates significantly.

Determining Activation Energy

• The Arrhenius equation serves as a foundational tool for computing activation energy, where graphical analyses using varying temperatures can provide insights into reaction kinetics.

14.5 Reaction Mechanisms

• Reaction mechanisms detail the stepwise progression of reactions, differentiating elementary reactions from complex multi-step processes.

Molecularity

• Defined as the number of reactant species involved in the elementary step:

  • Unimolecular: Involves one reactant.

  • Bimolecular: Involves two reactants.

  • Termolecular: Involves three reactants, though rare due to strict collision requirements.

Rate-Determining Step

• The overall reaction rate is often governed by the slowest step, known as the rate-determining step, which constrains the maximum rate of the entire process.

Requirements of a Plausible Mechanism

• Valid mechanisms must comply with observed rate laws, adhere to the conservation of mass by balancing equations, and facilitate the regeneration of intermediates, which can play significant roles in multi-step reactions.

14.6 Catalysis

• Catalysts are substances that enhance reaction speeds without undergoing permanent changes themselves.

Homogeneous Catalysts

• These catalysts are in the same phase as their reactants, often employed in solutions, facilitating more effective interactions.

Heterogeneous Catalysts

• These operate in a different phase than the reactants, commonly seen in solid-gas interactions; their surface properties significantly influence reaction dynamics.

Biological Catalysts (Enzymes)

• These are specialized catalysts found in living organisms that operate at active sites, ensuring specificity towards substrates.

Lock-and-Key Model

• This model encapsulates enzyme specificity by suggesting that the active site has a specific shape that only fits particular substrate molecules, though some flexibility in enzyme structure may be observed during substrate interactions.