CHM 406 — Reaction Kinetics: Lecture Note

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LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS

LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Course code: CHM 406 Course Title: Reaction Kinetics Course Unit: (2 Units C: LH 30) List of Series: 1. Series 1: Rate Equations and Reaction Orders 2. Series 2: Integrated Rate Laws and Reaction Half-Life 3. Series 3: Collision Theory, Activation Energy, and the Arrhenius Equation 4. Series 4: Catalysis, Reaction Mechanisms, and Enzymatic Processes 5. Series 5: Photochemical Reactions and Chemical Warfare Agents Suggested Outline Part 1: Fundamentals of Rate Equations • 1.1.1 Definition of rate of reaction • 1.1.2 Expressing rate using concentration changes • 1.1.3 Relationship between balanced chemical equations and rate expressions Part 2: Orders of Reaction • 1.2.1 First-order reactions and their characteristics • 1.2.2 Second-order reactions and their characteristics • 1.2.3 Third-order reactions and their characteristics Part 3: Instantaneous and Average Rates • 1.3.1 Graphical representation of reaction rates • 1.3.2 Distinguishing instantaneous rate from average rate • 1.3.3 Practical applications of rate determination Part 4: Determining Rate Laws from Experimental Data • 1.4.1 Initial rate method • 1.4.2 Determining order with respect to each reactant • 1.4.3 Overall order of reaction and rate constant with units Introduction Chemical reactions are not only about what substances are transformed but also about how fast these transformations occur. The study of reaction rates provides valuable insights into the mechanisms of chemical change and helps chemists predict and control processes in both

LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS laboratory and industrial settings. Understanding rate equations and reaction orders is therefore a fundamental starting point in reaction kinetics, as it lays the groundwork for more advanced topics such as integrated rate laws, activation energy, and catalysis. The aim of this Series is to introduce you to the principles of rate equations and reaction orders, equipping you with the skills to express reaction rates, classify reactions by order, and determine rate laws from experimental data. We shall commence this Series by exploring the fundamentals of rate equations, including how reaction rates are expressed in terms of concentration changes. Next, we will move on to examine first, second, and third-order reactions, highlighting their distinct characteristics. Following that, we will consider instantaneous and average rates, using graphical methods to distinguish between them. Finally, we will wrap up by studying how rate laws are determined experimentally, focusing on the initial rate method and the calculation of overall order and rate constants. This progression will ensure you gain a solid foundation in the quantitative aspects of reaction kinetics. Series Learning Outcomes Upon completing this Series, you should be able to: • SLO 1.1 define the rate of a chemical reaction and express it in terms of concentration changes, • SLO 1.2 explain how coefficients in a balanced chemical equation relate to the rate expression, • SLO 1.3 describe the characteristics of first-order reactions, • SLO 1.4 describe the characteristics of second-order reactions, • SLO 1.5 describe the characteristics of third-order reactions, • SLO 1.6 distinguish between instantaneous and average rates using graphical methods, • SLO 1.7 demonstrate how to determine reaction rates from concentration–time graphs, • SLO 1.8 apply the initial rate method to determine the order of reaction with respect to each reactant, • SLO 1.9 calculate the overall order of a reaction and the rate constant with appropriate units. 1.1 Fundamentals of Rate Equations 1.1.1 Definition of rate of reaction The rate of reaction is defined as the change in concentration of a reactant or product per unit time. It provides a measure of how quickly a chemical process occurs. Rates can be expressed in terms of either the disappearance of reactants or the appearance of products. Fill in the blank: The rate of reaction is defined as the change in __________________ of a reactant or product per unit time.

LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Diagram showing concentration changes of reactants and products over time. Figure 1.1: Rate of reaction expressed as change in concentration per unit time. 1.1.2 Expressing rate using concentration changes The rate of a reaction is often expressed mathematically as: [ \text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = \frac{1}{b}\frac{d[B]}{dt} ] Here, [A] represents the concentration of reactant A, [B] represents the concentration of product B, and a and b are the stoichiometric coefficients from the balanced chemical equation. The negative sign indicates that the concentration of reactants decreases with time. Fill in the blank: The negative sign in the rate expression indicates that the concentration of __________________ decreases with time.

LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Image showing a balanced chemical equation with rate expressions derived from stoichiometric coefficients. Plate 1.1: Expressing rate using stoichiometric coefficients. 1.1.3 Relationship between balanced chemical equations and rate expressions A balanced chemical equation provides the stoichiometric relationship between reactants and products. This relationship is essential for writing correct rate expressions. For example, in the reaction: [ 2A + B \rightarrow 3C ] The rate can be expressed as: [ \text{Rate} = -\frac{1}{2}\frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{1}{3}\frac{d[C]}{dt} ] This ensures that the rate is consistent regardless of whether it is expressed in terms of reactants or products. Fill in the blank: A balanced chemical equation provides the __________________ relationship between reactants and products.

LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Box 1.1: Key points on rate expressions and balanced equations Box summarising how stoichiometric coefficients are used in rate expressions. Pilot questions 1.1 1. The rate of reaction is defined as the change in __________ per unit time. A. Pressure B. Concentration C. Temperature D. Volume 2. The negative sign in the rate expression indicates that the concentration of __________ decreases with time. A. Products B. Reactants C. Catalysts D. Enzymes 3. In the reaction (2A + B \rightarrow 3C), the rate expressed in terms of A is: A. (-\frac{d[A]}{dt}) B. (-\frac{1}{2}\frac{d[A]}{dt}) C. (\frac{d[A]}{dt}) D. (\frac{1}{2}\frac{d[A]}{dt}) 4. A balanced chemical equation provides the __________ relationship between reactants and products. A. Random B. Stoichiometric C. Empirical D. Approximate

LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS 5. Which of the following can be used to express the rate of a reaction? A. Disappearance of reactants B. Appearance of products C. Both A and B D. Neither A nor B 1.2 Orders of Reaction 1.2.1 First-order reactions and their characteristics A first-order reaction is one in which the rate depends linearly on the concentration of a single reactant. This means that if the concentration of the reactant is doubled, the rate of reaction also doubles. Mathematically, the rate law can be expressed as: [ \text{Rate} = k[A] ] where k is the rate constant and [A] is the concentration of the reactant. First-order reactions are common in processes such as radioactive decay and certain unimolecular reactions. Fill in the blank: In a first-order reaction, if the concentration of the reactant is doubled, the rate of reaction __________________. Short description: Graph showing concentration versus time for a first-order reaction. Caption: Figure 1.2: Concentration–time curve for a first-order reaction. AI prompt: “Generate a graph showing exponential decay of concentration versus time for a first-order reaction.” Search string: “first-order reaction concentration time graph OER”

LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS 1.2.2 Second-order reactions and their characteristics A second-order reaction is one in which the rate depends on the square of the concentration of a single reactant, or on the product of the concentrations of two different reactants. The rate law can be expressed as: [ \text{Rate} = k[A]^2 \quad \text{or} \quad \text{Rate} = k[A][B] ] Second-order reactions are often observed in bimolecular processes where two particles must collide for the reaction to occur. Fill in the blank: A second-order reaction may depend on the square of the concentration of one reactant or on the __________________ of two reactants. Image showing two molecules colliding to represent a bimolecular second-order reaction. Plate 1.2: Collision representation of a second-order reaction. 1.2.3 Third-order reactions and their characteristics A third-order reaction is one in which the rate depends on the cube of the concentration of a single reactant, or on a combination of concentrations that add up to three. The rate law can be expressed as: [ \text{Rate} = k[A]^3 \quad \text{or} \quad \text{Rate} = k[A]^2[B] \quad \text{or} \quad \text{Rate} = k[A][B][C] ] Third-order reactions are less common because the probability of three particles colliding simultaneously is very low. They are usually observed in complex mechanisms rather than simple reactions.

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