General Chemistry Review: Atomic Structure, Bonding, Lewis Structures, and Molecular Geometry

Atomic Structure and Subatomic Particles

• Nucleus and Subatomic Particles:

  • The nucleus is located at the center of the atom and contains protons and neutrons.
  • Protons possess a positive ($+$) charge.
  • Neutrons carry no charge (neutral).
  • Electrons occupy the space surrounding the nucleus and carry a negative ($-$) charge.

• Atomic Number:

  • The atomic number is defined by the number of protons in an atom's nucleus.
  • The atomic number uniquely identifies the type of element (e.g., any atom with $6$ protons is carbon).

• Isotopes:

  • Isotopes are atoms of the same element that have the identical number of protons but different numbers of neutrons.
  • Because neutron count varies, isotopes of the same element have different atomic masses.

• Atomic Mass:

  • Atomic mass represents the weighted average mass of all naturally occurring isotopes of an element, weighted by their relative natural abundance.

Electronic Structure and Atomic Orbitals

• Spatial Localization of Electrons:

  • Electrons do not move freely in random space; they are confined to specific spatial regions surrounding the nucleus termed orbitals.

• Quantum Shells and Subshells Structure:

  • Shell $n = 1$:
  • Contains $1$ subshell: $s$
  • Designated Orbitals: $1s$
  • Shell $n = 2$:
  • Contains $2$ subshells: $s, p$
  • Designated Orbitals: $2s, 2p_x, 2p_y, 2p_z$
  • Shell $n = 3$:
  • Contains $3$ subshells: $s, p, d$
  • Designated Orbitals: $3s, 3p_x, 3p_y, 3p_z, 3d_{xy}, 3d_{yz}, 3d_{xz}, 3d_{x^2-y^2}, 3d_{z^2}$
  • Shell $n = 4$:
  • Contains $4$ subshells: $s, p, d, f$
  • Designated Orbitals: $4s, 4p_x, 4p_y, 4p_z, 4d_{xy}, \text{etc.}$

• Fundamental Rules Governing Atomic Structure:

  • Maximum electron capacity per shell $n$ is given by the formula:     $\text{Maximum electrons per shell} = 2n^2$
  • Each shell $n$ contains exactly $n$ subshells.
  • Subshell orbital breakdown:
  • An $s$ subshell consists of $1$ orbital.
  • A $p$ subshell consists of $3$ orbitals.
  • A $d$ subshell consists of $5$ orbitals.
  • An $f$ subshell consists of $7$ orbitals.
  • Each individual orbital can hold a maximum of $2$ electrons.
  • Electron Spin: The $2$ electrons occupying the same orbital must have opposite spins (spin-up and spin-down).
  • Relevance to Organic Chemistry: Organic chemistry predominantly focuses on $s$ and $p$ orbitals.

Orbital Energy Levels and Electron Configurations

• Energy Ordering and Aufbau Principle:

  • Orbital energy increases as principal quantum number $n$ and subshells increase.
  • The $(n+1)s$ orbitals are lower in energy than the $nd$ orbitals, and therefore $(n+1)s$ orbitals always fill before $nd$ orbitals.
  • General filling order of orbital energy levels:     $1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d \rightarrow 4p \rightarrow 5s \rightarrow 4d \rightarrow 5p \rightarrow 6s \rightarrow 4f \rightarrow 5d \rightarrow 6p \rightarrow 7s \rightarrow 5f \rightarrow 6d \rightarrow 7p$

• Periodic Table Block Divisions:

  • $s$     -block: Comprises Group $1$, Group $2$, and Helium.
  • $p$     -block: Comprises Groups $13$ through 18$.\n * d\n    -block: Comprises transition elements in Groups 3$through$12$.

• Valence Electrons:

  • Valence electrons are defined as the electrons located in the outermost, highest-energy shell ($n$).
  • Example (Carbon): Carbon has an atomic number of $6$ and electron configuration $1s^2 2s^2 2p^2$. Its highest energy shell is $n = 2$, giving Carbon a total of $4$ valence electrons.

Lewis Dot Structures of Atoms

• Definition and Convention:

  • Lewis dot structures visually display only the valence electrons of an atom surrounding its elemental symbol.

• Example (Sulfur, $S$):

  • Full Electron Configuration: $1s^2 2s^2 2p^6 3s^2 3p^4$
  • Filled Inner Shell Core: Equivalent to Neon, $[Ne] = 1s^2 2s^2 2p^6$
  • Valence Shell: $n = 3$, containing $3s^2 3p^4$ ($6$ valence electrons).
  • Lewis Dot Representation: Symbol $S$ surrounded by $6$ valence dots.
  • Standard representations apply systematically to elements $1$ through $18$.

Structural Theory of Matter and Energy of Bonding

• Core Principle of Structural Theory:

  • The chemical and physical behavior of a molecule depends not only on the identity of its constituent atoms, but also on the specific arrangement and sequence of bonding connections between those atoms.
  • Example: Two molecules can share the exact same molecular formula $C_2H_6O$ (e.g., Dimethyl Ether vs. Ethanol), yet display vastly different physical properties such as boiling points due to different bonding connectivities.

• Thermodynamics of Bond Formation and Cleavage:

  • Chemical bonds represent a stable, low-energy state compared to isolated free atoms.
  • Bond Formation: Releases energy (exothermic).
  • Bond Breaking: Requires/absorbs energy (endothermic).

• Evaluation of Chemical Bond Energetics:

  • Statement Analysis regarding 2 $H$ atoms forming 1 $H_2$ molecule:
  • Incorrect: Chemical bonds store energy, releasing energy when broken.
  • Incorrect: Chemical bonds store energy, absorbing energy when broken.
  • Incorrect: Chemical bonds are a low-energy state, releasing energy when broken.
  • Correct: Chemical bonds represent a low-energy state. Thus, when chemical bonds are broken, energy is absorbed.

Lewis Bonding Model and the Octet Rule

• The Octet Rule:

  • Atoms reach maximum thermodynamic stability when they possess a completely filled valence shell (an octet of $8$ valence electrons, or $2$ electrons for Helium and Hydrogen where $n = 1$).
  • Noble gases naturally exhibit filled valence shells ($8$ electrons, or $2$ for Helium).

• Pathways to Achieve a Filled Valence Shell:

  • Ion Formation: Gaining or losing electrons completely to form charged ions (anions or cations).
  • Covalent Bonding: Sharing pairs of valence electrons between atoms.

Step-by-Step Guide to Drawing Molecular Lewis Structures

1. Count Total Valence Electrons:

   • Calculate the sum of all valence electrons from all constituent atoms in the chemical formula.
   • For anions (negatively charged ions): Add $1$ electron for each unit of negative charge.
   • For cations (positively charged ions): Subtract $1$ electron for each unit of positive charge.

2. Establish Atom Connectivity:

   • Determine the spatial arrangement and connection order of central and outer atoms.

3. Draw Single Bonds:

   • Connect adjacent atoms using single covalent bonds.

4. Complete Valence Octets:

   • Distribute the remaining valence electrons as lone pairs to ensure every atom satisfies the octet rule ($2$ electrons for Hydrogen).

5. Form Multiple Bonds if Necessary:

   • If central atoms lack a full octet, convert nonbonding lone pairs into double or triple bonds.

6. Format Bond Types and Nonbonding Pairs:

   • Represent shared bonding electron pairs as continuous lines (single, double, or triple lines).
   • Represent nonbonding valence electron pairs (lone pairs) as pairs of dots.
   • Example application: Formaldehyde ($CH_2O$).

Typical Bonding Patterns and Coordinate Covalent Bonds

• Standard Neutral Bonding Configurations (Elements in Rows 1–2 and Halogens):

  • Carbon ($C$): Forms $4$ bonds and has $0$ lone pairs.
  • Nitrogen ($N$): Forms $3$ bonds and has $1$ lone pair.
  • Oxygen ($O$): Forms $2$ bonds and has $2$ lone pairs.
  • Hydrogen ($H$): Forms $1$ bond and has $0$ lone pairs.
  • Halogens ($X = F, Cl, Br, I$): Form $1$ bond and have $3$ lone pairs.
  • Note: Bonds can exist as single bonds or as multiple (double/triple) bonds connected to the same atom.

• Coordinate Covalent Bonds:

  • Definition: A specific type of covalent bond formed when one single atom donates both electrons ($2$ electrons) to the shared pair, while the receiving atom contributes zero electrons ($0$ electrons).
  • Example: Ammonium ion ($NH_4^+$), formed when the nonbonding lone pair on ammonia ($NH_3$) is donated to an electron-deficient hydrogen ion ($H^+$).

Electronegativity and Bond Polarity

• Bond Classification Criteria:

  • Bonds are categorized into three major types based on the difference in electronegativity (delta EN or absolute electronegativity difference) between the two bonded atoms:
  • Nonpolar Covalent Bond: Electronegativity difference is less than $0.5$ (\bdelta EN < 0.5).
  • Polar Covalent Bond: Electronegativity difference is between $0.5$ and $1.7$ (0.5 \bdelta EN \bdelta 1.7).
  • Ionic Bond: Electronegativity difference is greater than $1.7$ (\bdelta EN > 1.7; e.g., Potassium bromide, $K^+ Br^-$).

• Partial Charge Separation and Dipoles:

  • Polarization within a bond causes partial charge separation, denoted by partial positive (\bdelta^+) and partial negative (\bdelta^-) designations.
  • The bond dipole moment vector points from the partial positive charge (\bdelta^+) toward the partial negative charge (\bdelta^-).
  • Continuum Model: Numerical cutoffs serve as general guidelines; chemical bonds exist along a continuous spectrum of polarity rather than rigid categories.

• Example Bond Polarity Classifications:

  • $O-H$ bond: Polar covalent bond.
  • $C-H$ bond: Nonpolar covalent bond.
  • $C-O$ bond: Polar covalent bond.

Molecular Geometry and VSEPR Theory

• VSEPR Theory Principles:

  • Valence Shell Electron Pair Repulsion (VSEPR) theory determines 3D molecular geometry.
  • Principle: Electron pairs in the valence shell—whether participating in bonding or present as nonbonding lone pairs—repel each other electrostatically.
  • Consequently, electron pairs position themselves as far apart in 3D space as possible to minimize repulsions.

• Steric Number Formula:   $\text{Steric Number} = \text{Number of Bonded Atoms} + \text{Number of Lone Pairs}$

• Geometric Classifications Summary:

  • Steric Number $2$:
  • $2$ Bonds, $0$ Lone Pairs: Linear molecular geometry (Ideal bond angle = $180^\text{o}$). Example: Carbon dioxide ($CO_2$, $O=C=O$).
  • Steric Number $3$:
  • $3$ Bonds, $0$ Lone Pairs: Trigonal Planar molecular geometry (Ideal bond angle = $120^\text{o}$). Examples: Boron trifluoride ($BF_3$), Formaldehyde ($H_2C=O$).
  • $2$ Bonds, $1$ Lone Pair: Bent molecular geometry. Example: Sulfur dioxide ($SO_2$).
  • Steric Number $4$:
  • $4$ Bonds, $0$ Lone Pairs: Tetrahedral molecular geometry (Ideal bond angle = $109.5^\text{o}$). Example: Methane ($CH_4$).
  • $3$ Bonds, $1$ Lone Pair: Trigonal Pyramidal / Pyramidal molecular geometry. Example: Ammonia ($NH_3$).
  • $2$ Bonds, $2$ Lone Pairs: Bent molecular geometry. Example: Water ($H_2O$).

Molecular Polarity and Dipole Moments

• Requirements for Molecular Polarity:

  • Determining overall molecular polarity requires evaluating two fundamental parameters:
  1. The individual bond polarities (bond dipoles).
  2. The 3D spatial geometry of the molecule.

• Molecular Dipole Moment (\bmu):

  • The overall molecular dipole moment (\bmu) is defined as the vector sum of all individual bond dipole moments.
  • Units: Debye ($D$).
  • Electrostatic Potential Map Visualization: High electron density (\bdelta^-) is color-coded red, whereas low electron density (\bdelta^+) is color-coded blue.

• Dipole Cancellation Analysis (Carbon Dioxide Example):

  • Question: Are the individual $C=O$ bonds in $CO_2$ polar?
  • Answer: Yes, because oxygen is significantly more electronegative than carbon.
  • Question: Is $CO_2$ overall a polar molecule?
  • Answer: No. Because $CO_2$ possesses a linear molecular geometry ($180^\text{o}$ bond angle), the two equal bond dipoles point in exactly opposite directions and cancel each other out completely, yielding a net molecular dipole moment of zero (\bmu = 0\b,D).

• General Rule on Geometry and Polarity:

  • Highly symmetrical molecules containing polar individual bonds will be completely nonpolar overall if their 3D geometry causes the individual bond dipoles to cancel out vectorially.