Ch. 9: Electrons in Atoms and the Periodic Table

Electromagnetic Spectrum & Light

The electromagnetic spectrum encompasses all types of electromagnetic radiation, including visible light, ultraviolet, infrared, and more. Light exhibits both wave-like and particle-like properties.

• Wavelength (\( \lambda \)): The distance between two consecutive peaks of a wave, typically measured in meters (m) or nanometers (nm).

• Frequency (\( \nu \)): The number of wave cycles that pass a given point per second, measured in hertz (Hz).

• Energy (E): The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength.

Key Equations:

• (Energy is proportional to frequency)

• (Energy is inversely proportional to wavelength)

• (Speed of light equation, where \( c = 3.00 \times 10^8 \) m/s)

• (Planck's equation, where \( h = 6.626 \times 10^{-34} \) J·s)

Example: Ultraviolet light has a shorter wavelength and higher energy than visible light.

Bohr Model of the Atom

The Bohr model describes electrons in fixed orbits (energy levels) around the nucleus, each characterized by a principal quantum number (n).

• Orbits (n): Electrons occupy discrete energy levels (n = 1, 2, 3, ...).

• Atomic Spectrum: When electrons move between orbits, they absorb or emit photons of specific wavelengths, producing line spectra.

• Energy Differences: Larger changes in n (\( \Delta n \)) correspond to larger energy changes (\( \Delta E \)), resulting in shorter wavelengths (\( \lambda \)).

• Limitation: The Bohr model accurately describes only the hydrogen atom.

Example: The Balmer series in hydrogen's emission spectrum corresponds to electron transitions ending at n = 2.

Quantum Mechanical Theory

The quantum mechanical model extends to all elements, describing electrons as occupying orbitals within principal shells and subshells.

• Principal Shell (n): Main energy level (n = 1, 2, 3, ...).

• Subshells: Each shell contains one or more subshells (s, p, d, f):

  • n = 1: s

  • n = 2: s, p

  • n = 3: s, p, d

  • n = 4: s, p, d, f

Example: The third shell (n = 3) contains s, p, and d subshells.

Electron Configurations & Orbital Diagrams

Electron configurations show the arrangement of electrons in an atom's orbitals. Orbital diagrams use arrows to represent electron spins.

• Writing Configurations: List subshells in order of increasing energy, filling according to the Aufbau principle.

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of quantum numbers; each orbital holds a maximum of two electrons with opposite spins.

• Hund’s Rule: Electrons fill degenerate orbitals singly before pairing up.

• Periodic Table: The periodic table can be used to determine electron configurations by blocks (s, p, d, f).

• Valence Electrons: Electrons in the outermost shell, important for chemical reactivity.

Example: The electron configuration of oxygen (Z = 8) is 1s2 2s2 2p4.

Trends in the Periodic Table

Periodic trends describe how certain properties of elements change across periods and down groups.

• Atomic Size: Increases down a group, decreases across a period.

• Ionization Energy: The energy required to remove an electron; decreases down a group, increases across a period.

• Metallic Character: Increases down a group, decreases across a period.

Example: Sodium is larger and more metallic than chlorine.

Ch. 10: Chemical Bonding

Lewis Structures

Lewis structures represent the arrangement of valence electrons in atoms, ions, and molecules using dots and lines.

• Elements: Show valence electrons as dots around the element symbol.

• Covalent Compounds: Atoms share electron pairs to achieve octets.

• Ionic Compounds: Electrons are transferred from metals to nonmetals, forming cations and anions.

Example: The Lewis structure of H2O shows two lone pairs on oxygen and two O–H bonds.

Resonance Structures

Some molecules can be represented by two or more valid Lewis structures, called resonance structures.

• Octet Rule: Atoms tend to form bonds to achieve eight valence electrons (exceptions exist).

Example: The carbonate ion (CO32–) has three resonance structures.

VSEPR Theory

Valence Shell Electron Pair Repulsion (VSEPR) theory predicts the 3D shape of molecules based on electron pair repulsion.

• Electronic Geometry: Arrangement of all electron groups (bonding and lone pairs) around the central atom.

• Molecular Geometry: Arrangement of only the atoms (ignoring lone pairs).

• 3D Structure: Determined by minimizing repulsions between electron groups.

Example: Methane (CH4) has a tetrahedral geometry.

Electronegativity and Polarity

Electronegativity is the ability of an atom to attract shared electrons. Differences in electronegativity lead to bond polarity.

• Polar Bonds: Electrons are shared unequally, creating dipole moments.

• Non-Polar Bonds: Electrons are shared equally.

• Polar vs. Non-Polar Molecules: Molecular shape and bond polarity determine overall molecular polarity.

Example: Water (H2O) is a polar molecule; carbon dioxide (CO2) is non-polar despite having polar bonds.

Ch. 11: Gases

Kinetic Molecular Theory of Gases

This theory explains the behavior of gases in terms of particles in constant, random motion.

• Gas particles are in continuous, rapid motion.

• Collisions between particles and with container walls are elastic.

• Gas particles have negligible volume compared to the container.

• No attractive or repulsive forces between particles.

Example: Explains why gases fill their containers uniformly.

Pressure: Definition and Units

Pressure is the force exerted per unit area by gas particles colliding with container walls.

• Common Units: Atmosphere (atm), Pascal (Pa), torr, mmHg.

• 1 atm = 101,325 Pa = 760 mmHg = 760 torr

Gas Laws

Gas laws describe the relationships between pressure, volume, temperature, and amount of gas.

• Boyle’s Law: (at constant T and n)

• Charles’ Law: (at constant P and n)

• Combined Gas Law:

• Avogadro’s Law: (at constant P and T)

• Ideal Gas Law: (R = 0.0821 L·atm/mol·K)

Example: Doubling the temperature (in Kelvin) of a gas at constant pressure doubles its volume (Charles’ Law).

Mixture of Gases and Partial Pressures

In a mixture, each gas exerts a partial pressure proportional to its mole fraction.

• Dalton’s Law:

• Partial Pressure: where is the mole fraction of gas i.

Example: In air, nitrogen and oxygen contribute most to the total pressure.

Gases in Chemical Reactions

Gas laws are used to relate the quantities of gases involved in chemical reactions.

• Stoichiometry: Use molar ratios from balanced equations to relate volumes or moles of gases.

• Using Ideal Gas Law: Calculate moles or volume of a gas under non-standard conditions.

• STP (Standard Temperature and Pressure): 0°C (273.15 K) and 1 atm; at STP, 1 mole of gas occupies 22.4 L.

Example: Calculate the volume of CO2 produced from the combustion of methane at STP.