Orgo chem Aug 27th

Atomic Structure and Isotopes

Atoms consist of a dense nucleus (protons and neutrons) surrounded by rapidly moving electrons in an electron cloud. The electrons occupy a relatively large volume compared to the nucleus.
Atomic number (Z) is the number of protons in the nucleus. All atoms with the same Z belong to the same element.
- If Z = 6, the element is carbon, regardless of the neutron count or isotope.
Mass number (A) is the total number of protons and neutrons: A = Z + N, where N is the number of neutrons.
Isotopes are atoms with the same Z (same element) but different N (different A).

Atomic Mass Units and Isotopic Abundance

Atomic mass units (AMU) are defined as 1/12 of the mass of a carbon-12 atom:
$1\,\text{amu} = \frac{m(^{12}\mathrm{C})}{12}$
The atomic mass listed on the periodic table is a weighted average of the isotopes of that element, reflecting their natural abundances.
- Common isotopes for carbon: $^{12}\mathrm{C}$, $^{13}\mathrm{C}$, $^{14}\mathrm{C}$ (in nature, $^{12}\mathrm{C}$ is the most abundant).
- The table value for carbon is about $12.011\,\text{u}$ because it averages $^{12}\mathrm{C}$, $^{13}\mathrm{C}$, and trace amounts of $^{14}\mathrm{C}$.
Weighted average concept (as used for natural elements):
$\bar{M} = \sumi fi Mi, \quad \sumi fi = 1,$ where $fi$ are fractional abundances and $M_i$ are the isotope masses.

Isotopes and Element Identity

The element is defined by Z (the atomic number).
The isotope identity is defined by A (or equivalently N): $A = Z + N.$
For example, all carbon atoms have Z = 6; isotopes differ in N (e.g., $^{12}\mathrm{C}$ vs $^{13}\mathrm{C}$ vs $^{14}\mathrm{C}$).

Electron Structure and Valence Electrons

Electrons fill shells around the nucleus; inner core electrons are tightly bound, outer shell electrons (valence electrons) participate in bonding.
The outermost electrons (valence electrons) are the key players in bonding and chemical reactivity.
Lewis structures are built from valence electrons and show how atoms share or transfer electrons.
Atoms strive for a stable (low-energy) configuration, typically achieved by attaining a noble gas electron configuration in the valence shell.
Helium (Z = 2) is an exception: it achieves stability with 2 electrons (a duet) in its only shell.
Most atoms seek a noble-gas configuration with 8 electrons in their valence shell (octet rule). Hydrogen, however, seeks a duet (2 electrons).

The Octet Rule and Stability

The octet rule states that atoms tend to bond so that their valence shell has 8 electrons (except H which aims for 2).
Stability is associated with lower energy; bond formation generally lowers overall energy, making the bonded state more stable than isolated atoms.

Ionic vs Covalent Bonding; Electronegativity

Ionic bonds: electrons are transferred from one atom to another, creating ions that attract via electrostatic forces.
- Example: Lithium and fluorine form LiF. Li tends to give up an electron; F tends to gain one.
- Resulting ions: Li⁺ (achieves a noble gas config) and F⁻ (achieves Ne-like config).
Covalent bonds: electrons are shared between atoms rather than transferred, with bonding characterized by electron sharing in molecular orbitals.
Electronegativity (EN): the tendency of an atom to attract electron density in a bond.
- EN generally increases from left to right across a period and from bottom to top within a group.
- More electronegative atoms pull electron density more strongly; large EN differences promote ionic character; smaller EN differences lead to covalent character.
Bond types on a continuum:
- Large EN differences -> ionic bonds (fully transfer electrons, e.g., LiF).
- Small EN differences -> covalent bonds (shared electrons; may be nonpolar or polar depending on EN difference).
Dipole moments arise in polar covalent bonds when EN difference is significant (e.g., H–Cl is polar).
Nonpolar covalent bonds occur when EN difference is small (e.g., C–H differences are small; sometimes considered nonpolar).

Electronegativity Trends and Examples

Fluorine is the most electronegative element; other highly EN elements include oxygen, nitrogen, chlorine.
Example trends referenced in lecture:
- Hydrogen–chlorine: significant EN difference -> polar covalent bond.
- Carbon–hydrogen: small EN difference -> typically nonpolar covalent bond.

Lewis Structures: Building Blocks and Examples

Step-by-step approach to drawing Lewis structures:
1) Count total valence electrons for all atoms in the molecule (use group numbers from the periodic table): e.g., C has 4, N has 5, O has 6, H has 1, etc.
2) If a species is an ion, adjust the total by subtracting electrons for a positive charge and adding electrons for a negative charge (e.g., +1 means remove one electron; −1 means add one electron).
3) Choose a central atom (usually the least electronegative, not H) and connect peripheral atoms with single bonds (
each bond uses 2 electrons).
4) Distribute remaining electrons as lone pairs to satisfy the octet/duet rule (H gets a duet, others aim for an octet).
5) If any atom lacks a full octet, form multiple bonds (double or triple bonds) by shifting electrons.
6) Check formal charges to ensure the structure is reasonable (minimize formal charges; as in some cases, nonzero formal charges are required in resonance forms).
Formal charge (FC) definition and calculation:
- General rule used in the talk: FC can be computed as
  $\text{FC} = V - (L + \tfrac{B}{2})$
  where:
- V = number of valence electrons for the atom (from the periodic table),
- L = number of lone-pair electrons on the atom, and
- B = number of electrons shared in bonds (i.e., two electrons per bond counted toward the atom's sharing).
- Some students use the equivalent expression FC = (valence electrons) − (nonbonding electrons) − (shared electrons)/2.
Ammonia and ammonium example from the lecture:
- Ammonia, NH₃:
- N has valence electrons V = 5; three N–H bonds (6 bonding electrons) and one lone pair (2 nonbonding electrons).
- FC(N) = 5 − (2 + 6/2) = 0.
- Ammonium, NH₄⁺:
- If the molecule bears a +1 charge, electron count reduces by 1 (overall + charge).
- In NH₄⁺, N forms four N–H bonds (8 bonding electrons) and has no lone pairs.
- FC(N) = 5 − (0 + 8/2) = 5 − 4 = +1; the overall +1 charge is consistent with the species.
Example with water and carbonate-style species (illustrative from transcript):
- H₂O:
- O has valence 6; two bonds (4 bonding electrons) and two lone pairs (4 nonbonding electrons).
- FC(O) = 6 − (4 + 4/2) = 6 − (4 + 2) = 0.
- A carbonate-like species (CO₃²⁻) often involves resonance structures where some oxygens are double-bonded (0 FC) and others are single-bonded with −1 FC; the sum of charges equals the overall 2− charge.
- Note: The transcript included a step-by-step calculation that used a mistaken valence count for oxygen in that specific example; in standard chemistry, O has 6 valence electrons. The carbonate example demonstrates the concept of formal charges and resonance rather than a single static Lewis structure.
Expanded octets and exceptions (as described):
- Boron (group 13) typically forms three bonds and can have only six electrons around it (an incomplete octet).
- Period 3 elements and beyond (e.g., phosphorus, sulfur) can exhibit expanded octets, accommodating more than eight electrons around the central atom (e.g., P in PF₅ with 10 electrons around; S in SF₆ with 12 electrons around).
- This is due to availability of d-orbitals in heavier elements to accommodate extra electron density.
Representing bonds and geometry:
- Elementary Lewis structures can be drawn as dots (lone pairs) and lines (bonds). A single bond is two electrons, a double bond is four electrons, etc.
- The regions around a central atom correspond to bonds and lone pairs, and their arrangement gives molecular geometry (e.g., trigonal planar for ethene fragment, planar arrangement when necessary).
- Wedge/dash notation indicates stereochemical orientation in 3D space (front/back).
Example molecules discussed in