Second-Order and Zero-Order Reactions

This page covers second-order and zero-order reactions, providing their differential and integrated rate laws. For second-order integrated rate law, the equation is 1/[A] = kt + 1/[A]₀, which is important to memorize.

Vocabulary: Zero-order reactions have a rate that is independent of concentration, expressed as Rate = k[A]⁰ or simply Rate = k.

The page then transitions to reaction mechanisms, defining them as series of elementary steps by which a chemical reaction occurs. An example of an overall reaction (NO₂ + CO → NO + CO₂) is given, along with its experimentally determined rate law.

Definition: An intermediate is a substance formed and subsequently used up during a reaction mechanism.

Highlight: Elementary steps are reactions within a mechanism whose rate law can be written directly from its molecularity, which is the number of species that must collide to produce the reaction indicated by that step.

Elementary Steps and Rate-Determining Steps

This page elaborates on elementary steps and their corresponding rate laws. It provides a table showing various elementary steps and their rate expressions, ranging from unimolecular to termolecular reactions.

The concept of rate-determining steps is introduced, explaining that it is the slowest step in a reaction mechanism and determines the overall rate of the reaction.

Highlight: For a mechanism to be valid, the sum of elementary steps must give the overall balanced equation for the reaction, and the experimental rate law must agree with the rate-determining step.

An example of a valid mechanism is provided for the reaction NO₂ + CO → NO + CO₂, demonstrating how the rate law is determined by the slow, rate-determining step.

Example: The page presents a problem asking to identify the rate-determining step in the reaction 2H₂ + 2NO → N₂ + 2H₂O, given the rate law R = k[NO]²[H₂].

Multi-step Reactions and Energy Diagrams

This final page discusses complex rate laws and multi-step energy diagrams. It explains that sometimes rate laws may appear not to match the mechanism, but they actually do.

Example: The H₂ + Br₂ → 2HBr reaction is used to illustrate how a seemingly mismatched rate law can be reconciled with the reaction mechanism.

The page concludes with a detailed explanation of multi-step reaction energy diagrams. These diagrams visually represent:

• Intermediates
• Number of steps
• Activation energy (Ea) for each step
• Overall activation energy
• Enthalpy change (ΔH) for each step
• Overall enthalpy change
• Activated complexes
• Rate-determining step (identified by the highest Ea)

Highlight: The rate-determining step in a multi-step reaction is characterized by the longest activation energy barrier on the energy diagram.

Vocabulary: Activated complexes are high-energy, unstable arrangements of atoms formed during a reaction, represented as peaks on the energy diagram.

This comprehensive overview provides students with a solid foundation in understanding complex reaction kinetics and mechanisms.

Integrated Rate Laws and First-Order Reactions

This page introduces the concept of integrated rate laws and focuses on first-order reactions. Integrated rate laws show the relationship between concentration and time for chemical reactions. For first-order reactions, the rate law is Rate = k[A], where k is the rate constant and [A] is the concentration of reactant A.

The integrated form of the first-order rate law is ln[A] = -kt + ln[A]₀, where [A]₀ is the initial concentration. This equation produces a linear graph of ln[A] versus time, with a negative slope equal to -k.

Definition: Half-life is the time it takes for half of the original concentration to react.

Example: A problem is presented where the half-life of a reaction is 20.0 minutes. The rate constant is calculated to be 0.347 min⁻¹ using the formula k = 0.693 / t₁/₂.

Highlight: The linear relationship between ln[A] and time is a key characteristic of first-order reactions, distinguishing them from other orders.