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6: Recitations

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    • 6.1: Balancing Reactions, Yield, and Limiting Reagents
      This page covers balancing chemical reactions through the conservation of mass, ensuring that reactant and product masses are equal. It offers a systematic method for balancing equations with examples, such as ethylene and oxygen reactions. The page also introduces the concept of yield, detailing how much product can be obtained from initial reactants and explains limiting reagents that may affect product yield by being consumed first.
    • 6.2: Avogadro and Moles, Periodic Table, Isotopes, and Combustion
      This page covers Avogadro's number and moles, which are essential for chemical reactions and mass measurement. It highlights the periodic table's role in understanding atomic properties, including atomic mass and isotopes. Average atomic mass as a weighted average is explained, and combustion reactions are examined, with glucose as a case study for identifying limiting reagents and calculating yields based on reactant moles.
    • 6.3: Waves, Photons, and Bohr Model
      This page discusses photons as energy particles defined by their frequency or wavelength, governed by the Planck-Einstein relation. It explores the electromagnetic spectrum, highlighting that photon energy is not influenced by wave amplitude. The Bohr model explains electron transitions in hydrogen, showing how photons can excite electrons to higher energy levels.
    • 6.4: Energy, Frequency, Wavelength, and Ionization
      This page examines the Planck-Einstein relation linking energy, frequency, and wavelength of photons, detailing units such as joules, electron volts, and Hertz. It clarifies ionization, particularly hydrogen's ionization energy, showcasing how photons can eject electrons. Practical examples illustrate calculations of photon energy, electron velocities, and emission rates from light sources, providing a comprehensive understanding of these concepts in physics.
    • 6.5: Quantum Numbers
      This page describes the four quantum numbers that characterize electrons in an atom: principal (n), orbital angular momentum (l), magnetic (m), and spin (m_s). It explains their functions, such as indicating energy levels and orbital shapes, and the Pauli Exclusion Principle, which prohibits electrons from sharing identical quantum numbers, using carbon's electronic configuration as an example.
    • 6.6: Aufbau Principle, Electron Filling, Box Notation, and Photoelectron Spectroscopy
      This page covers the Aufbau principle for electron filling in subshells, including the use of quantum numbers and examples of electronic configurations for elements like bromine and carbon. It highlights Hund's rule regarding the occupancy of orbitals and introduces photoelectron spectroscopy (PES) as a technique for analyzing electronic structures, explaining how to interpret binding energy data for elemental analysis.
    • 6.7: Periodic Trends, Lewis Dot Diagrams, and Formal Charge
      This page covers periodic trends concerning atomic structure, electron behavior, atomic radius variations, and the differences in size between cations and anions. It introduces Lewis dot diagrams to represent valence electrons and bonding, providing guidelines for their construction. Additionally, it explains how to calculate formal charge to evaluate molecular stability, illustrated with the CO₂ example.
    • 6.8: Resonance, and Formal Charge (cont.)
      This page explains resonance as the delocalization of electrons in molecules represented by multiple stable resonance structures. These structures must maintain the same atomic arrangement, satisfy the octet rule, and have formal charges on electronegative atoms. Examples include ozone and carbonate (\(CO_3^{2-}\)), with resonance structures showing averaged electron distribution. Stability is determined by evaluating formal charges, with preference for the lowest charge on each atom.
    • 6.9: VSEPR and Polarity
      This page explores the Valence Shell Electron Pair Repulsion (VSEPR) theory for predicting molecular geometry from Lewis structures, detailing how to identify electron groups and assign shapes like tetrahedral and bent. It addresses molecular polarity, explaining how electronegativity differences yield dipole moments, and provides examples with CO2 and H2O to demonstrate the concepts of net dipole moments and molecular polarity.
    • 6.10: Hybridization, Atomic Orbitals, and Molecular Orbital Theory
      This page covers hybridization and atomic orbitals, focusing on their importance in bond stability and molecular geometry. It highlights beryllium's sp hybridization for equal bond formation despite full electron shells.
    • 6.11: More Molecular Orbital Theory and Intermolecular Forces
      This page covers Molecular Orbital (MO) Theory for heterogeneous dimers, focusing on the significance of atomic orbital energy levels and resulting asymmetric MO diagrams, illustrated by the cyanide ion (CN⁻) with a bond order of 3. It also explains Intermolecular Forces (IMFs), including London Dispersion Forces, dipole-dipole interactions, and hydrogen bonds, stressing their varying strengths and molecular dependencies, and concludes with examples for identifying hydrogen-bonding molecules.
    • 6.12: Band Diagrams, Semiconductors, and Doping
      This page explains band diagrams and their significance in understanding the electronic structures of semiconductors, insulators, and metals. It details the relationships between valence and conduction bands, thermal energy, and electron excitation, emphasizing the unique conductive properties of semiconductors and their applications in solar cells and LEDs.
    • 6.13: Bravais Lattices and Crystal Packing
      This page explores Bravais lattices, vital for understanding crystal structures, especially cubic lattices: simple cubic, body-centered cubic, and face-centered cubic. It explains the number of atoms per unit cell and introduces key metrics like packing density and atomic packing factor. The page also covers geometric relationships and examples for calculating atomic packing in 2D unit cells.
    • 6.14: Miller Indices and Interplanar Spacing
      This page explains Miller indices, a notation system in crystallography for identifying points, directions, and planes in crystalline materials, especially within cubic Bravais lattices. It describes how to represent points as \( (h, k, l) \), directions as \([h k l]\), and families of planes as \(\{h k l\}\). The process involves determining intercepts along lattice vectors and using reciprocals, accounting for crystal symmetry in families.
    • 6.15: X-ray Generation, Diffraction, and Bragg's Law
      This page discusses X-rays as high-energy electromagnetic radiation requiring significant energy transitions within atoms to generate characteristic types, like \(K_\alpha\) and \(K_\beta\). It covers the production of X-rays from high-energy electrons interacting with heavy elements through Bremsstrahlung and characteristic radiation.
    • 6.16: X-ray Diffraction and Selection Rules
      This page covers X-ray diffraction (XRD) as a technique for analyzing crystal structures through scattered X-rays. It discusses selection rules for Bravais lattices, including how to identify crystal planes and perform spectrum analysis. In addition, it differentiates between body-centered cubic (BCC) and face-centered cubic (FCC) structures, noting the prohibition of certain planes in BCC and providing calculations to derive interplanar spacing and lattice constants.
    • 6.17: Point Defects and Arrhenius-like Vacancy Activation
      This page covers point defects in materials, highlighting zero-dimensional imperfections in covalent and ionic solids, including self-interstitials, vacancies, and Schottky and Frenkel defects. It explains that defect creation is entropically favorable and models these using Arrhenius relationships. Additionally, it details the calculation of activation energy (\(E_V\)) through concentration ratios at varying temperatures, resulting in an activation energy value of 0.
    • 6.18: Line Defects, Mechanics and Stress-strain Curves, and Slip
      This page covers line defects in crystals, specifically dislocations that disrupt atomic structure. It highlights the energy requirements for creating and moving dislocations, leading to a meta-stable state. Stress-strain curves are discussed as tools for examining material properties, including elastic and plastic deformation, yield stress, and fracture. The page also explains slip planes and directions, underlining their importance in the yield process of crystalline materials.
    • 6.19: Glasses and Cooling Curves
      This page covers amorphous materials, particularly glasses, and their formation due to the absence of ordered crystalline structures. It distinguishes between single crystals, polycrystalline materials, and amorphous materials, emphasizing molar volume as a measure of disorder. The cooling process's significance in determining whether a material crystallizes or forms glass is highlighted through cooling curves.
    • 6.20: Glass Formers and Network Modifiers
      This page explores the chemistry and properties of silica glass, primarily made of silicon dioxide (SiO₂). It details how oxygen atoms function as bridging elements in solid silica, forming tetrahedral networks that become disordered upon melting. The introduction of network modifiers like Na₂O and Al₂O₃ disrupts the silica structure by introducing nonbridging oxygens, affecting thermal properties and efficiency.
    • 6.21: Reaction Kinetics, Rate Laws and Rate Constants
      This page covers reaction kinetics, emphasizing how reactant concentrations impact reaction rates. It defines reaction orders (zero, first, second) and discusses experimental methods for determining rates, including rate laws to illustrate the concentration-rate relationship. Additionally, it includes the calculation of rate constants and deriving integrated rate laws for various reaction orders.
    • 6.22: Equilibrium, Solubility Product, and Common Ion Effect
      This page covers the concept of equilibrium in chemical reactions, particularly dynamic equilibrium, where forward and reverse reaction rates are equal. It introduces the equilibrium constant (\(K_{eq}\)) and the reaction quotient (\(Q\)), and explains their role in determining reaction direction. Additionally, it discusses the solubility product and its application to dissolving solids, including the influence of common ions on solubility.
    • 6.23: Acids, Bases, and Dissociation
      This page elaborates on the definitions of acids and bases from Brønsted-Lowry and Lewis perspectives, detailing Brønsted-Lowry acids as proton donors and Lewis acids involving electron transfer. It emphasizes water's amphoteric nature and discusses acid (K_a) and base (K_b) dissociation constants, linking them to acid-base strength. The page includes examples of strong acids and bases and concludes with a comparison of acid strengths based on their dissociation constants.
    • 6.24: pH and pOH, pKa and pKb
      This page explains pH and pOH as logarithmic measures of acidity and basicity, with pH values less than 7 indicating acidity and those above indicating basicity. It presents the relationship \( pH + pOH = 14 \) and introduces \( pK_a \) and \( pK_b \) for comparing acid and base dissociation constants. Additionally, the page includes examples on calculating pH from concentration and vice versa.
    • 6.25: Polymers, Radical Polymerization, Condensation Polymerization, and Polymer Properties
      This page covers polymers, focusing on their structure and synthesis through radical and condensation polymerization processes. Radical polymerization uses free radicals to initiate chain reactions, whereas condensation polymerization involves monomers that release water during formation.
    • 6.26: Steady State Diffusion, Diffusion Coefficient, Fick’s Second Law
      This page covers steady-state diffusion according to Fick's first law, explaining the transfer of species from high to low concentration, defining key concepts like diffusion flux and coefficient, and noting temperature effects. It addresses diffusion mechanisms across matter phases and introduces Fick's second law, which describes how concentration profiles change over time, complete with its mathematical solution.

    This page titled 6: Recitations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Donald Sadoway (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform.