CHM 210 — Physical Chemistry I: Lecture Note

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LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Course code: CHM 210 Course title: Physical Chemistry I Course credit load: 2 Units Series 1: Kinetic Theory and Behaviour of Gases Series 2: Thermodynamics, Entropy, and Free Energy Series 3: Chemical Kinetics and Reaction Mechanisms Series 4: Photochemistry and Spectroscopy Fundamentals Series 5: Electrochemistry and Conductance Laws Proposed Outline Series 1 1.1 Fundamentals of kinetic theory • 1.1.1 Postulates of kinetic theory • 1.1.2 Assumptions and limitations • 1.1.3 Connection to ideal gas behaviour 1.2 Behaviour of ideal gases • 1.2.1 Gas laws (Boyle’s, Charles’, Avogadro’s, Ideal Gas Law) • 1.2.2 Derivation of molecular velocity formula • 1.2.3 Applications of kinetic theory to ideal gases 1.3 Behaviour of real gases • 1.3.1 Deviations from ideal behaviour • 1.3.2 Van der Waals equation • 1.3.3 Compressibility factor and practical implications 1.4 Applications of kinetic theory and gas behaviour • 1.4.1 Industrial and laboratory relevance • 1.4.2 Predicting physical properties of gases • 1.4.3 Link to thermodynamics and later Series Introduction In organic chemistry, reactions often proceed through short-lived species known as reactive intermediates. These intermediates, such as carbocations, free radicals, and carbenes, play a crucial role in determining the pathways and outcomes of reactions. Rearrangement reactions, where atoms or groups shift within a molecule, further illustrate the dynamic nature of chemical

LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS transformations. Understanding these concepts equips learners with the ability to explain reaction mechanisms and predict products with confidence. The aim of this Series is to introduce you to the major types of reactive intermediates, explain their formation and stability, and explore common rearrangement reactions that occur in organic chemistry. We shall commence this Series by examining the nature and types of reactive intermediates. Next, we will explore their stability and methods of formation. Following that, we will move on to rearrangement reactions, considering examples such as hydride shifts and ring expansions. Finally, we will conclude by linking these concepts to practical applications in organic synthesis and mechanism prediction. Series Learning Outcomes Upon completing this Series, you should be able to: • SLO 1.1 define the postulates of kinetic theory of gases, • SLO 1.2 explain the assumptions and limitations of kinetic theory, • SLO 1.3 apply kinetic theory to derive the molecular velocity formula, • SLO 1.4 analyse the behaviour of ideal gases using gas laws, • SLO 1.5 evaluate deviations of real gases from ideal behaviour, • SLO 1.6 demonstrate the use of the Van der Waals equation in describing real gases, • SLO 1.7 assess the practical applications of kinetic theory and gas behaviour in laboratory and industrial contexts. 1.1 Fundamentals of Kinetic Theory 1.1.1 Postulates of kinetic theory The kinetic theory of gases is a model that explains the behaviour of gases by considering them as composed of a large number of small particles (atoms or molecules) in constant random motion. The main postulates are: • Gas particles are extremely small compared to the distances between them. • They move in random straight-line motion until they collide. • Collisions between particles and with container walls are perfectly elastic, meaning no energy is lost. • The average kinetic energy of particles is directly proportional to the absolute temperature of the gas. Fill in the blank: According to kinetic theory, the average kinetic energy of gas particles is proportional to the absolute ______.

LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Figure 1.1 Postulates of kinetic theory of gases. 1.1.2 Assumptions and limitations The kinetic theory makes simplifying assumptions to explain gas behaviour. For example, it assumes that gas particles have negligible volume and no intermolecular forces. These assumptions hold true for ideal gases but not for real gases, especially at high pressures and low temperatures. The limitations of the theory become evident when gases deviate from ideal behaviour, requiring corrections such as those introduced in the Van der Waals equation. Fill in the blank: The kinetic theory assumes that gas particles exert no ______ forces on each other. Assumptions and Limitations of the Kinetic Molecular Theory • Core Assumptions: • Point Particles: Gas particles are treated as having negligible volume; the gas is mostly empty space. • No Intermolecular Forces: There are no attractive or repulsive forces between particles. • Elastic Collisions: Collisions are perfectly elastic, meaning total kinetic energy is conserved. • Constant Random Motion: Particles move in straight lines in random directions. • Limitations (Real Gas Deviations): • High Pressure: At very high pressures, the volume of the gas particles themselves becomes significant relative to the container volume. • Low Temperature: At low temperatures, gas particles move slowly, and intermolecular attractive forces can no longer be ignored, leading to potential condensation into a liquid phase.

LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Box 1.1 Assumptions and limitations of kinetic theory 1.1.3 Connection to ideal gas behaviour An ideal gas is a hypothetical gas that perfectly obeys the assumptions of kinetic theory. The behaviour of ideal gases is described by the ideal gas law: PV=nRT, where P is pressure, V is volume, n is number of moles, R is the gas constant, and T is temperature. Kinetic theory provides the molecular basis for this law, linking macroscopic properties such as pressure and temperature to microscopic particle motion. Fill in the blank: The ideal gas law is expressed as ______ = nRT. Macroscopic Property Microscopic Interpretation Pressure ($P$) The frequency and force of particle collisions against the container walls. Volume ($V$) The total space available for particles to move, representing the "empty space" between them. Temperature ($T$) The measure of the average kinetic energy of the gas particles. Amount of Gas ($n$) The total number of particles present within the container. Table 1.1 Connection between kinetic theory and ideal gas law Pilot questions 1.1 1. State two postulates of the kinetic theory of gases. 2. What does kinetic theory assume about the volume of gas particles? 3. Under what conditions do gases deviate from ideal behaviour? 4. Write the equation of the ideal gas law. 5. How does kinetic theory explain the relationship between temperature and kinetic energy? 1.2 Behaviour of Ideal Gases 1.2.1 Gas laws (Boyle’s, Charles’, Avogadro’s, Ideal Gas Law) The behaviour of ideal gases can be explained using several fundamental gas laws. Boyle’s law states that the pressure of a fixed amount of gas is inversely proportional to its volume at constant temperature. Charles’ law shows that the volume of a gas is directly proportional to its absolute temperature at constant pressure. Avogadro’s law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. These laws combine to form the ideal gas law, expressed as PV=nRT.

LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Fill in the blank: According to Boyle’s law, pressure is inversely proportional to ______ at constant temperature. Figure 1.2 Fundamental gas laws. 1.2.2 Derivation of molecular velocity formula The kinetic theory provides a molecular basis for gas laws by linking macroscopic properties to microscopic motion. The root mean square velocity (u\_rms) of gas molecules is derived from kinetic theory and is given by: urms=3RTM where R is the gas constant, T is the absolute temperature, and M is the molar mass of the gas. This formula shows that molecular velocity increases with temperature and decreases with molar mass. Fill in the blank: The root mean square velocity of gas molecules increases with ______ and decreases with molar mass. Gas Molar Mass (kg/mol) urms (m/s) Hydrogen ($H_2$) $0.002016$ $1920.12$ Oxygen ($O_2$) $0.03200$ $481.95$ Carbon Dioxide ($CO_2$) $0.04401$ $410.96$ Table 1.2 Root mean square velocity of selected gases 1.2.3 Applications of kinetic theory to ideal gases The kinetic theory explains how pressure arises from collisions of gas molecules with container walls, and how temperature reflects the average kinetic energy of molecules. These insights allow chemists to predict gas behaviour under varying conditions. For example, the theory explains why lighter gases diffuse faster than heavier ones, and why pressure increases when temperature rises at constant volume. Fill in the blank: According to kinetic theory, pressure results from collisions of gas molecules with the ______ walls.

LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Applications of Kinetic Molecular Theory • Diffusion and Effusion: Kinetic theory explains how gas particles naturally spread from areas of high concentration to low concentration (diffusion) and how they escape through tiny openings (effusion). Lighter gas particles possess higher velocities, causing them to diffuse and effuse more rapidly than heavier ones, as governed by Graham's Law. • Pressure-Temperature Relationship (Gay-Lussac’s Law): By linking temperature to the average kinetic energy of particles, the theory explains that increasing the temperature of a gas in a fixed volume causes particles to strike the container walls with more frequency and greater force, resulting in

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