Reaction Rates and Rate Laws

This page delves deeper into the quantitative aspects of reaction rates and introduces rate laws. It explains how reaction rates are measured and how they change over time.

The relationship between concentration and rate is explored, introducing the concept of initial rates and instantaneous rates. The page emphasizes that reaction rates typically decrease over time as reactant concentrations diminish.

Vocabulary: Instantaneous rate is the slope of a line tangent to the concentration-time curve at any given point.

Rate laws are introduced as mathematical expressions relating reaction rates to reactant concentrations. The general form of a rate law is presented:

rate = k$A$^a$B$^b

Where:

• k is the rate constant
• $A$ and $B$ are reactant concentrations
• a and b are reaction orders

Highlight: The overall order of a reaction is the sum of the individual orders with respect to each reactant.

The page stresses that stoichiometric ratios in balanced equations do not necessarily correspond to the exponents in rate laws. Methods for determining rate laws experimentally are outlined.

Example: To determine a rate law, one can compare reaction rates under conditions where one reactant concentration is held constant while the other is varied.

Reaction Mechanisms and Introduction to Equilibrium

This page introduces reaction mechanisms and transitions into the concept of chemical equilibrium. It explains how complex reactions can occur through multiple elementary steps.

Definition: A reaction mechanism is the sequence of events describing the actual process by which reactants are converted into products.

The molecularity of process in reaction mechanisms is discussed, explaining how it relates to the number of molecules involved in an elementary step.

Vocabulary: Molecularity refers to the number of molecules participating in an elementary reaction step, such as unimolecular or bimolecular processes.

The page then shifts focus to chemical equilibrium, explaining that many reactions are reversible and reach a state of balance rather than going to completion.

Highlight: Chemical equilibrium occurs when the forward and reverse reactions proceed at the same rate, resulting in constant concentrations of reactants and products.

The dynamic nature of equilibrium is emphasized, noting that reactions continue to occur even when the system appears macroscopically static.

The equilibrium constant $Kc$ is introduced, along with its mathematical expression:

Kc = $C$^c$D$^d / $A$^a$B$^b

For the reaction: aA + bB ⇌ cC + dD

Example: For the reaction SnO₂$s$ + 2CO$g$ ⇌ Sn$s$ + 2CO₂$g$, the equilibrium constant expression is Kc = $CO₂$² / $CO$², excluding solid species.

Analyzing Equilibrium Systems

This page focuses on recognizing equilibrium conditions and analyzing equilibrium systems using the equilibrium constant $K$ and reaction quotient $Q$.

Methods for identifying when a system has reached equilibrium are discussed:

• In graphical representations, equilibrium is indicated by zero slopes for all species' concentrations.
• In tabular data, equilibrium is recognized when concentration ratios remain constant over time.

The significance of the equilibrium constant's magnitude is explained:

Highlight: If K >> 1, the reaction favors products; if K << 1, the reaction favors reactants.

The reaction quotient $Q$ is introduced as a tool for determining the direction of a reaction relative to equilibrium:

Definition: The reaction quotient $Q$ has the same form as the equilibrium constant $K$ but uses instantaneous concentrations to determine if a system is at equilibrium.

Steps for using the reaction quotient to analyze equilibrium systems are outlined:

1. Calculate molarities if not given
2. Calculate the reaction quotient $Q$
3. Compare Q to K
4. Determine the direction in which the reaction will proceed

Example: If Q < K, the reaction will proceed forward to form more products; if Q > K, the reaction will proceed backward to form more reactants.

The page concludes with guidance on predicting which species will have the highest concentration at equilibrium based on stoichiometry and initial conditions.

Page 4: Equilibrium Constants and Reaction Quotient

This section focuses on quantitative aspects of chemical equilibrium, including equilibrium constants and reaction quotients.

Definition: The reaction quotient $Q$ measures the ratio of product to reactant concentrations at any point during a reaction.

Example: For the reaction 2H₂S + CH₄ ⇌ CS₂ + 4H₂, equilibrium calculations determine concentration changes.

Highlight: Temperature is the only factor that can change the equilibrium constant $K$.

Kinetics and Equilibrium: Fundamentals of Reaction Rates

This page introduces the core concepts of chemical kinetics and equilibrium. It explores the factors that influence reaction rates and the principles of collision theory. The enduring understandings highlight how concentration, pressure, and environmental factors affect reaction rates.

Factors affecting reaction rates are explained in detail:

1. Physical state: More homogeneous mixtures lead to faster reactions due to increased collisions.
2. Concentration: Higher concentrations increase the likelihood of molecular collisions.
3. Temperature: Elevated temperatures increase kinetic energy, resulting in more frequent and energetic collisions.
4. Surface area: Greater surface area enhances the probability of collisions.

The concept of activation energy is introduced, emphasizing its role in activation energy barriers restriction to chemical reactions.

Definition: Activation energy $Ea$ is the minimum amount of energy required for a reaction to occur.

Reaction coordinate diagrams are explained, illustrating the energy changes during a reaction, including the formation of the activated complex.

Highlight: The top vertex of a reaction coordinate diagram represents the formation of the activated complex, a crucial intermediate in chemical reactions.

Maxwell-Boltzmann distributions are presented to show how temperature affects the distribution of molecular energies and, consequently, reaction rates.

Example: As temperature increases, the Maxwell-Boltzmann distribution curve flattens and broadens, indicating that more molecules have sufficient energy to overcome the activation energy barrier.