Chapter1

Chapter One: Atomic Structure and Bonding

The Nucleus and Electron Cloud

• Nucleus: Contains positively charged protons and uncharged neutrons.

• Electron Cloud: Composed of negatively charged electrons, which are described as both particles and waves.

Layout of the Periodic Table

• Atomic Number: Indicates the number of protons in the nucleus.

• Rows (Periods): Elements in the same row are similar in size.

• Columns (Groups): Elements in the same column (Main Group Elements identified as $1A$ through $8A$) have similar electronic and chemical properties.

• Transition Metals: Located in the center (groups $3B$ through $2B$).

• Lanthanides and Actinides: Detailed at the bottom of the table.

Isotopes and Atomic Weight

• Isotopes: Atoms of the same element that differ in the number of neutrons. For example, Carbon has two major isotopes:

  • $^{12}C$: $98.9\%$ relative abundance.

  • $^{13}C$: $1.1\%$ relative abundance.

• Atomic Weight: A weighted average of the mass of all naturally occurring isotopes. For carbon, this is $12.011\,g/mol$.

The Uniqueness of Carbon

Carbon is special because of its location on the periodic table (Group $IVA$ of the second period):

• Bond Stability: Carbon-Carbon ($C-C$) forms relatively strong covalent bonds, leading to stable compounds with long lifetimes.

• Tetravalency: Carbon forms $4$ bonds. These can be single, double, or triple bonds, which dictates geometry and reactivity.

• Structural Diversity: Carbon can form long chains, rings, and branched compounds, allowing for infinite $3-D$ geometries.

• Bonding Versatility: Carbon bonds to most main group elements with differing electronegativities, giving rise to various functional groups and chemical reactivities.

Orbital Theory and Electron Configuration

Characteristics of Orbitals

• Wave Functions: Electrons are described by wave functions (orbitals) that define the probability of an electron's location based on quantum mechanics.

• Properties: An orbital specifies energy, size, shape, and orientation ($s, p, d, f$).

• Organization: Orbitals are arranged in shells, which gives rise to the periodic table's layout.

Specific Orbitals in Organic Chemistry

Organic chemistry primarily focuses on $s$ and $p$ orbitals:

• s Orbitals: These have a sphere of electron density. They are lower in energy than other orbitals within the same shell.

• p Orbitals: These have a dumbbell shape. They contain a node (a region of zero probability of finding electron density) at the nucleus. They are higher in energy than $s$ orbitals.

Second Row Elements

• Shell Capacity: The first shell has one orbital ($1s$), holding a maximum of $2$ electrons ($H$ and $He$). The second shell has four orbitals: one $2s$ and three $2p$ orbitals.

• Electron Maximum: With four orbitals, each holding $2$ electrons, the second row has a maximum capacity of $8$ electrons. This row consists of eight elements (from $Li$ to $Ne$).

Bonding

General Principles

Bonding is the joining of two atoms in a stable arrangement. This allows atoms to attain a complete outer shell of valence electrons and a stable noble gas configuration.

• Ionic Bonds: Result from the transfer of electrons from one element to another. Usually occurs between elements on the far-left (forming positive cations) and elements on the far-right (forming negative anions) of the periodic table. Example: Sodium Chloride ($NaCl$).

• Covalent Bonds: Result from the sharing of electrons between two nuclei. Carbon and Hydrogen typically participate in covalent bonding.

Second Row Element Bonding Constraints

Second-row elements can have no more than $8$ electrons around them.

• Neutral Molecules: Atoms with $1, 2, \text{ or } 3$ valence electrons form $1, 2, \text{ or } 3$ bonds, respectively. Atoms with $4$ or more valence electrons form enough bonds to reach an octet.

• Lone Pairs: When elements form fewer than $4$ bonds, their octets include both bonding (shared) and nonbonding (unshared) electrons. Unshared electrons are called lone pairs.

Usual Bonding Patterns for Neutral Atoms

• H: $1$ bond, $0$ lone pairs.

• C: $4$ bonds, $0$ lone pairs.

• N: $3$ bonds, $1$ lone pair.

• O: $2$ bonds, $2$ lone pairs.

• Halogens (X: F, Cl, Br, I): $1$ bond, $3$ lone pairs.

Lewis Structures

General Rules

1. Draw only valence electrons.

2. A solid line represents a two-electron covalent bond.

3. Give every second-row element an octet of electrons, if possible.

4. Give each hydrogen two electrons.

Formal Charge

Formal charge identifies how the number of electrons around an atom compares to its valence electrons. An atom "owns" all its unshared electrons and half of its shared electrons.

$\text{Formal Charge} = (\text{Number of valence electrons}) - (\text{Number of electrons owned})$

Patterns for Formal Charge

• Carbon ($4$ valence $e^-$):

  • $+1$: $3$ bonds, $0$ lone pairs (Carbocation).

  • $0$: $4$ bonds, $0$ lone pairs.

  • $-1$: $3$ bonds, $1$ lone pair (Carbanion).

• Nitrogen ($5$ valence $e^-$):

  • $+1$: $4$ bonds, $0$ lone pairs (Ammonium ion).

  • $0$: $3$ bonds, $1$ lone pair.

  • $-1$: $2$ bonds, $2$ lone pairs (Amide ion).

• Oxygen ($6$ valence $e^-$):

  • $+1$: $3$ bonds, $1$ lone pair (Onium ion).

  • $0$: $2$ bonds, $2$ lone pairs.

  • $-1$: $1$ bond, $3$ lone pairs (Oxide ion).

Isomers

Constitutional isomers are different molecules that share the same molecular formula but have a different arrangement of atoms. Example: Ethanol and dimethyl ether ($C_2H_6O$).

Exceptions to the Octet Rule

• Groups $2A$ and $3A$: Elements like Beryllium ($Be$) in $H-Be-H$ (4 electrons) and Boron ($B$) in $BF_3$ (6 electrons) often have fewer than $8$ electrons.

• Third Row Elements: Can have expanded octets. Examples include:

  • Dimethyl Sulfoxide (DMSO): Sulfur has $10$ electrons.

  • Sulfuric Acid ($H_2SO_4$): Sulfur has $12$ electrons.

  • Alendronic Acid: Phosphorus has $10$ electrons.

Resonance

Resonance occurs when a single Lewis structure cannot adequately represent a molecule. Resonance structures (resonance forms) are separated by a double-headed arrow.

Resonance Theory Principles

1. Resonance Hybrid: The true structure is a composite weighted average of all resonance forms. The hybrid is more stable than any individual structure because charge is delocalized.

2. Not Real: Resonance structures do not represent real structures; they are not in equilibrium. Electrons do not move back and forth between forms.

3. Not Isomers: Resonance structures differ only in the arrangement of electrons, not atoms.

Rules for Drawing Resonance Structures

• Rule [1]: Only multiple bonds and nonbonded (lone pair) electrons change position. Atoms and single bonds remain stationary.

• Rule [2]: All structures must have the same number of unpaired electrons.

• Rule [3]: Structures must be valid Lewis structures (check the Octet rule for second-row elements and ensure Hydrogen has only $2$ electrons).

• Charge Conservation: The overall charge of each resonance structure must be the same.

Curved Arrow Notation

• Tail: Starts at the electron pair (bond or lone pair) being "moved."

• Head: Points to the new location of the electron pair.

Evaluating Resonance Stability (Major vs. Minor Contributors)

Major contributors (the "better" structures) have

1. More bonds and fewer charges (No charge separation is best).

2. Every atom following the octet rule (This is priority).

3. Negative charges on more electronegative atoms for anions.

4. Positive charges on less electronegative atoms for cations (provided octets are satisfied).

Priority Order: No (or minimal) charge separation > Octets > Electronegativity.

Determining Molecular Shape

Bond Length and Angle

• Bond Length: Decreases across a row (as atom size decreases) and increases down a column (as atom size increases).

  • $H-H$: $0.74\,\text{Å}$

  • $C-H$: $1.09\,\text{Å}$

  • $C-Cl$: $1.77\,\text{Å}$

  • $C-I$: $2.13\,\text{Å}$

  • Note: $1\,angstrom = 1 \times 10^{-9}\,meters = 100\,picometers$.

• VSEPR Theory: Groups (atoms or lone pairs) stay as far apart as possible to minimize repulsion.

Common Geometries

• Two Groups: Linear ($180^\text{o}$ angle). Elements like $Be$ in $BeH_2$ or Carbon in $HC \equiv CH$.

• Three Groups: Trigonal Planar ($120^\text{o}$ angle). Elements like $B$ in $BF_3$ or Carbon in $CH_2=CH_2$.

• Four Groups: Tetrahedral ($109.5^\text{o}$ angle). Carbon in $CH_4$.

Lone Pairs and Geometry

Lone pairs count as a "group" for electronic geometry but modify the molecular geometry:

• Ammonia ($NH_3$): Tetrahedral electronic geometry, trigonal pyramid molecular geometry. Bond angle is smaller than $109.5^\text{o}$ due to lone pair repulsion.

• Water ($H_2O$): Tetrahedral electronic geometry, bent molecular geometry. Bond angle is even smaller due to two lone pairs.

Drawing Organic Molecules

Condensed Structures

• Bond lines are omitted; atoms are drawn next to each other.

• Parentheses denote identical groups ($CH_3$ units bonded to the same atom).

• Lone pairs are typically omitted.

• Double and triple bonds are usually kept for clarity.

Skeletal Structures

• Carbon atoms are assumed at every junction or end of a line.

• Hydrogens on carbons are omitted; they are assumed present to satisfy Carbon's tetravalency.

• All heteroatoms (non-Carbon/Hydrogen) and the Hydrogens attached to them must be drawn explicitly.

• Charges on Carbon replace a Hydrogen atom; negative carbons have one lone pair, positive carbons (carbocations) have none.

Hybridization

Hybridization is the mathematical combination of atomic orbitals ($s$ and $p$) to form hybrid orbitals of equivalent shape and energy.

Types of Hybridization

1. sp3: Mixing one $2s$ and three $2p$ orbitals. Results in four tetrahedral orbitals ($109.5^\text{o}$). Used for single bonds (e.g., Methane, Ethane).

2. sp2: Mixing one $2s$ and two $2p$ orbitals. Results in three trigonal planar orbitals ($120^\text{o}$) and one unhybridized $p$ orbital. Used for double bonds (e.g., Ethylene).

3. sp: Mixing one $2s$ and one $2p$ orbital. Results in two linear orbitals ($180^\text{o}$) and two unhybridized $p$ orbitals. Used for triple bonds (e.g., Acetylene).

Sigma ($\sigma$) and Pi ($\pi$) Bonds

• Sigma ($\sigma$) Bond: Concentrates electron density along the axis between nuclei. Usually formed by hybridized orbital overlap. Permits free rotation (unless in a ring).

• Pi ($\pi$) Bond: Formed by side-by-side overlap of unhybridized $p$ orbitals. Found in double (one $\sigma$, one $\pi$) and triple (one $\sigma$, two $\pi$) bonds. Restricts rotation.

Hybridization and Bond Properties

• s-Character: As s-character increases (sp^3 [25\%] < sp^2 [33\%] < sp [50\%]), the hybrid orbital holds electrons closer to the nucleus.

• Bond Strength: Higher s-character leads to shorter and stronger bonds.

  • $C-C$ in Ethane: $1.53\,\text{Å}$, $88\,kcal/mol$.

  • $C=C$ in Ethylene: $1.34\,\text{Å}$, $152\,kcal/mol$.

  • $C \equiv C$ in Acetylene: $1.21\,\text{Å}$, $200\,kcal/mol$.

Bond Polarity

• Electronegativity: Measure of an atom's attraction for electrons in a bond. Trends: Increases across a row and up a column.

• Nonpolar Bonds: Equal sharing of electrons (e.g., $C-C$, $C-H$).

• Polar Bonds: Unequal sharing due to electronegativity differences (e.g., $C-O$, $C-Cl$). Creates a dipole moment, denoted by $\delta+$ (electron deficient) and $\delta-$ (electron rich).

Molecular Polarity

A molecule is polar if it has individual bond dipoles that do not cancel out.

• Polar Molecule: Water ($H_2O$) - bond dipoles reinforce each other.

• Nonpolar Molecule: Carbon Dioxide ($CO_2$) - bond dipoles cancel due to linear geometry; Boron Trichloride ($AlCl_3$) - dipoles cancel in trigonal planar geometry.

• Significance: Polarity heavily influences physical properties (explored in Chapter 3).