CHEM 142_Lecture_3_with polleverywhere

CHEM 142: The Global Impact of Chemistry for Engineering

Instructor and Copyright Information

• Instructor: Dr. Levent Inci

• Copyright: © 2020 W. W. Norton & Company

Questions to Ponder

• What exactly is light?: Explore the nature and properties of light, including its dual particle-wave nature.

• How does light interact with matter?: Discuss phenomena such as reflection, refraction, and absorption, and their significance in chemistry.

• What properties of matter determine the interaction?: Consider factors like atomic structure and bond types.

• Greenhouse gases?: Delve into the role of various gases in trapping thermal energy in the Earth's atmosphere.

• What’s so special about fossil fuels? Why can’t carbon dioxide be recycled?: Investigate the energy processes involved in fossil fuels and the challenges associated with carbon dioxide's lifecycle in environmental contexts.

Electron Wave Equations

• Erwin Schrödinger (1925):

  • Developed the foundational concept of wave functions (ψ) which mathematically describe the behavior of quantum particles, including electrons.

  • Wave functions allow us to understand how electron waves change with respect to location (x) and time (t).

  • The square of the wave function (ψ²) indicates orbital shapes, revealing the probable locations of electrons within an atom.

The Particle in a Box Model

• Boundary Conditions: Define the potential (V) of the system

  • V(x) = ∞ at boundaries (x=0 and x=L)

  • V(x) = 0 when within the confines of the box itself, which is crucial for understanding quantization in confining potentials.

• Wave Equation:

  • -\frac{h^2}{2m}\frac{d^2ψ}{dx^2} = Eψ

  • This equation forms the basis of quantum mechanics within a confined system, leading to quantized energy states.

Energy Levels

• Energy Formula:

  • E_n = \frac{n^2h^2}{8mL^2}

  • n is the quantum number defining distinct energy levels (n = 1, 2,...).

Energy Levels in Hydrogen Atom

• Key Points:

  • The energy of the electron is solely reliant on the principal quantum number (n).

  • The first energy level (n=1) is known as the ground state, the most stable configuration.

• Energy Formula:

  • E_n = -\frac{2.178 \times 10^{-18}}{n^2}

  • As n approaches infinity, ionization occurs, leading to an electron being completely freed from the atom.

• Degenerate Orbitals:

  • For n > 1, significant degeneracy exists; e.g., there are 6 orbitals at n=2 and 9 orbitals at n=3. These structural nuances are pivotal in understanding chemical behavior.

Hydrogen Absorption Spectrum

• Quantum Mechanics and Emission Lines:

  • Quantum mechanics plays a crucial role in predicting the wavelengths of emission lines during electron transitions between energy states:

  • E_{photon} = E_{initial} - E_{final}

  • This precision aids in determining elemental compositions in astrophysics and materials science.

Multi-Electron Atoms & Light Absorption

• Multi-electron atoms exhibit specific electronic transitions, due to their complex interactions.

  • Examples illustrate diverse spectral lines across elements based on electron configurations—e.g., Lithium has 30 lines while Cesium has 645 lines.

Quantum Numbers Overview

• Definition and Types:

  • Quantum Numbers define different properties of atomic orbitals:

    • Principal quantum number (n): Indicates the shell and size of the orbital(s).

    • Angular Momentum Quantum Number (ℓ): Determines the shape of the orbital, ranging from ℓ = 0 to n-1.

    • Magnetic Quantum Number (mℓ): Defines the orientation of the orbital, with values from -ℓ to +ℓ.

    • Spin Magnetic Quantum Number (ms): Represents the orientation of electron spin which can either be +½ or -½.

• Pauli Exclusion Principle:

  • No two electrons in an atom can have the same set of four quantum numbers, ensuring the uniqueness of each electron’s state.

Atomic Orbital Shapes

• Types of Orbitals:

  • s: Contains 1 subshell, has a spherical shape, can hold a maximum of 2 electrons.

  • p: Comprises 3 subshells, characterized by a daisy-like shape, accommodating 6 electrons.

  • d: Involves 5 subshells, presents complex shapes, can hold 10 electrons.

  • f: Contains 7 subshells, exhibits highly intricate shapes, can hold 14 electrons.

Rules for Electron Placement in Orbitals

• Aufbau Principle: Electrons fill lower-energy orbitals before occupying higher energy states, which is vital for understanding chemical bonding.

• Pauli Exclusion Principle: Reinforces that each orbital can only hold a maximum of two electrons with opposite spins.

• Hund's Rule: Electrons will maximize the number of unpaired electrons within degenerate orbitals before pairing occurs, impacting magnetic properties and bonding behavior.

Orbital Diagrams for Multielectron Atoms

• Examples of Electron Configurations:

  • Lithium: [He] 2s¹

  • Carbon: [He] 2s² 2p²

  • Neon: [Ne] 2s² 2p⁶ (denotes complete octet, signifying stability).

Isoelectronic Ions/Atoms

• Isoelectronic species share identical electron counts and similar configurations, crucial for comparison in chemical reactivity and properties, e.g.:

  • Na⁺, Mg²⁺, O²⁻, F⁻, Ne.

Energy of Orbitals and Order of Filling

• Orbital filling order is illustrated via diagrams showcasing the relative energy levels of the s, p, d, and f blocks.

Ionization Energy (IE)

• Definition: The energy requisite for detaching an electron from an atom, critical for understanding reactivity and ion formation.

• Example: The first ionization energy (IE₁) for Magnesium is 738 kJ/mol, indicating its reactivity.

Electron Affinities (EA)

• Definition: Represents the energy change upon adding an electron to an atom, influencing an atom’s ability to gain electrons.

• Process:

  • Cl(g) + e⁻ → Cl⁻ (g)

  • Periodic trends reveal that EA becomes more negative moving across a period and up a group in the periodic table, indicating increased electron affinity.

Periodic Trends in Atomic and Ionic Radii

• Atomic Radii: Increase down a group due to additional electron shells while decreasing across a period as nuclear charge amplifies.

• Ionic Sizes: Cations are consistently smaller than their corresponding parent atoms, whereas anions expand due to electron repulsion effects.

Bond Lengths

• Influencing Factors: The identity of the atoms involved and the type of bond established dictate the bond lengths observed; bond orders affect lengths typically with single bonds being the longest, followed by double, then triple bonds which are the shortest.

Selected Average Covalent Bond Lengths and Energies

• Key bond lengths and energies include:

  • C-C: 154 pm, Energy: 348 kJ/mol.

Summary of Molecules and Greenhouse Effect

• Greenhouse gases, such as CO₂ and CH₄, are crucial for trapping heat in the atmosphere, leading to global warming concerns.

• Understanding the dynamics of chemical bonds—ionic, covalent, and metallic—underpins discussions around the greenhouse effect and climate change.

Chapter 8 Outline

Content Overview

• 8.1 Types of Chemical Bonds

• 8.2 Lewis Structures

• 8.3 Polar Covalent Bonds

• 8.4 Resonance

• 8.5 Formal Charge

• 8.6 Understanding Bond Lengths and Strengths

This detailed overview incorporates fundamental concepts and vital information related to the global impact of chemistry for engineering, emphasizing the intricate relationships between quantum mechanics, atomic structure, and ecological considerations.