Bonding, Resonance, Octet Rule Exceptions, and VSEPR Theory

Bond Properties and Resonance Structures

Carbon-Carbon Bond Properties Analysis:
- Carbon-Carbon Single Bond:
  - Average Bond Length: $154$ picometers ( $pm$ ).
  - Bond Strength: $356$ kilojoules per mole ( $kJ/mol$ ). This represents the energy required to break the bond, with higher numbers indicating stronger bonds. (Further discussion on bond strength and energies will be in Chapter 9).
  - Involves sharing of two electrons.
- Carbon-Carbon Double Bond:
  - Average Bond Length: $134$ $pm$ .
  - Bond Strength: $598$ $kJ/mol$ .
  - Explanation: The bond is stronger and shorter because it involves sharing four electrons instead of two, pulling the carbons tighter and closer together.
Benzene as an Example for Resonance:
- Expected Structure (if drawn with simple Lewis rules): We would expect alternating single ( $154$ $pm$ ) and double ( $134$ $pm$ ) bonds, leading to short and long bond lengths.
- Experimental Data (actual structure): X-ray crystallography shows all carbon-carbon bonds in benzene are the same length.
  - Actual Bond Length: $139$ $pm$ .
  - This value is intermediate: shorter than a single bond ( $154$ $pm$ ) but longer than a double bond ( $134$ $pm$ ). It's approximately midway between the two.
- Resonance Representation: Due to the experimental observation that cannot be accurately represented by a single Lewis structure, benzene is often drawn with a circle inside the hexagon.
  - This circle signifies that chemical bond electrons (specifically, pi electrons) are delocalized and shared evenly among all carbon atoms in the ring.
- Limitations of Lewis Structures: Standard Lewis structures (with alternating single and double bonds) are inadequate to depict the actual structure of benzene.
  - Attempting to represent even sharing with dotted lines for double bonds leads to an incorrect electron count (e.g., five bonds to carbon), highlighting the inadequacy.
- Take-Home Message for Resonance:
  - Molecules represented by resonance structures do not oscillate between individual forms; they exist as a single, hybrid structure that is an average of all contributing resonance forms.
  - It looks "somewhere in between" the drawn resonance structures.
  - Lewis structures are limited; resonance structures are a way to represent a single molecule as every possible orientation of electrons that could happen.
  - Resonance structures only occur where p-orbitals overlap (to be discussed further in Chapter 5).
Resonance and Reactivity (Nucleophiles Example):
- Consider a compound with a carbon double-bonded to an oxygen (carbonyl group).
- Electronegativity: Oxygen (3.5) is more electronegative than carbon (2.5), leading to a polar bond.
- Dipole Moment: Represented by a dipole arrow or partial charges ( $ext{C}^{ ext{+ extgreek{d}}}$ and $ext{O}^{ ext{- extgreek{d}}}$ ).
- Nucleophile Interaction: Nucleophiles (electron-rich species) are attracted to partial positive charges.
- Unexpected Reactivity: Sometimes, a nucleophile can add to a different carbon atom than expected based on simple polarity (e.g., to the end carbon in a conjugated system).
- Explanation via Resonance: Drawing resonance structures for the compound can show other carbons bearing a positive charge, explaining the observed dual reactivity and product formation. For instance, removing an electron pair onto the oxygen can result in a positive charge on another carbon, making it susceptible to nucleophilic attack.

Formal Charge Rules and Lewis Structure Selection

Formal Charge Calculation:
- Formal Charge = (Valence Electrons) - (Non-bonding Electrons) - (0.5 * Bonding Electrons).
Principles for "Best" Lewis Structures (based on Electroneutrality Principle):
1. Minimize Charges: The most stable Lewis structures have formal charges as close to zero as possible ( $0$ is ideal, $+1/-1$ is better than $+2/-2$ ).
2. Electronegativity Placement: If charges are unavoidable:
  - Negative formal charges should be on the most electronegative atom.
  - Positive formal charges should be on the least electronegative atom.
3. "Closed Shell Structures": For main group elements, all atoms (except hydrogen) should preferably have a full octet. This is usually the primary consideration.
Example: Carbon Dioxide ( $CO_2$ ):
- Structure 1 (Expected): Carbon double-bonded to two oxygens. All formal charges are zero. All atoms (C and O) have full octets. This is the best Lewis structure.
- Structure 2 (Resonance Form): Carbon triple-bonded to one oxygen and single-bonded to another. This leads to formal charges of $+1$ on one oxygen and $-1$ on the other. While plausible resonance structures, the neutral form is generally preferred because it minimizes charge.
  - Note: These two resonance structures are equivalent; one can be derived from the other by pushing electrons.
- Structure 3 (Incorrect Connectivity): Carbon single-bonded to one oxygen, which is then bonded to another oxygen. This would result in a $+2$ charge on the central oxygen and a $-2$ charge on the carbon. This structure is incorrect because the highly electronegative oxygen bears a positive charge, violating formal charge rules and suggesting incorrect connectivity.
Example: Cyanate Ion ( $CNO^-$ ):
- Overall charge of $-1$ . Electronegativities: O ( $3.5$ ), N ( $3.0$ ), C ( $2.5$ ).
- Best Structure: The one where the negative charge is located on the most electronegative atom, oxygen, with carbon and nitrogen being neutral. Other resonance structures might exist, but the one placing the negative charge on oxygen contributes most significantly.

Drawing Lewis Structures with Charge

General Rule for Total Valence Electrons:
- For positive ions (cations): Subtract one electron from the total valence electrons for each positive charge.
- For negative ions (anions): Add one electron to the total valence electrons for each negative charge.
Example: Ammonium Ion ( $NH_4^+$ ):
- Valence electrons: Nitrogen ( $5$ ) + $4$ Hydrogens ( $4 imes 1$ ) - $1$ (for $+1$ charge) = $8$ valence electrons.
- Structure: Nitrogen in the center, single-bonded to four hydrogens.
- Formal Charge (Nitrogen): $5$ (valence) - $0$ (lone pairs) - $4$ (bonds) = $+1$ .
Example: Chlorate Ion ( $ClO_3^-$ ):
- Valence electrons: Chlorine ( $7$ ) + $3$ Oxygens ( $3 imes 6$ ) + $1$ (for $-1$ charge) = $7 + 18 + 1 = 26$ valence electrons.
- Steps:
  1. Central Atom: Chlorine (least electronegative).
  2. Single Bonds: Connect Cl to all three O atoms ( $3 imes 2 = 6$ electrons used). Remaining electrons: $26 - 6 = 20$ .
  3. Terminal Atom Octets: Place $6$ electrons (3 lone pairs) on each oxygen ( $3 imes 6 = 18$ electrons used). Remaining electrons: $20 - 18 = 2$ .
  4. Central Atom Octet: Place remaining $2$ electrons on chlorine (1 lone pair).
- Initial Lewis Structure Check: All O and Cl atoms have full octets.
- Initial Formal Charges:
  - Chlorine: $7$ (valence) - $2$ (lone pair) - $3$ (bonds) = $+2$ .
  - Oxygen (all identical): $6$ (valence) - $6$ (lone pairs) - $1$ (bond) = $-1$ . Total charge: $+2 + (3 imes -1) = -1$ . This matches the ion's charge.

Exceptions to the Octet Rule

1. Expanded Octets (Elements in the Third Row or Higher):
- Reason: These elements (e.g., S, P, Cl in the third row, or heavier elements) have vacant d-orbitals (e.g., 3s, 3p, 3d) which can accept additional electrons beyond a stable octet.
- Identification: The primary driver for forming expanded octets is to minimize or eliminate formal charges on the central atom.
- Example: Chlorate Ion ( $ClO_3^-$ ) Revisited:
  - Initial formal charges: Cl ( $+2$ ), O ( $-1$ ).
  - Charge Reduction: To reduce the $+2$ charge on chlorine, lone pairs from oxygen atoms can be converted into double bonds with chlorine.
    - Converting one O lone pair to a double bond: Cl becomes $+1$ , that O becomes $0$ . This is a better structure.
    - Converting a second O lone pair to a double bond: Cl becomes $0$ , that O becomes $0$ . Two oxygens are now $0$ , one is $-1$ . This is the best structure.
  - Electron Count for Cl: In the best structure for $ClO_3^-$ (with two Cl=O double bonds and one Cl-O single bond), chlorine has $2$ (lone pair) + $2 imes 4$ (double bonds) + $2$ (single bond) = $12$ electrons around it. This is an expanded octet.
- Common Expanded Octet Behaviors:
  - Sulfur (S): Often forms stable compounds with $8$ or $12$ electrons.
  - Phosphorus (P): Often forms stable compounds with $8$ or $10$ electrons.
- Examples:
  - Sulfuric Acid ( $H<em>2SO</em>4$ ): Lewis structure with sulfur double-bonded to two oxygens, and single-bonded to two other oxygens (which are also bonded to hydrogens). This results in zero formal charges on all atoms and sulfur having $12$ electrons.
  - Phosphoric Acid ( $H<em>3PO</em>4$ ): Involves phosphorus mostly with $10$ electrons (one P=O double bond, three P-O single bonds, each O single-bonded to H) and zero formal charges on all atoms.
2. Electron-Deficient Atoms:
- Atoms: Boron (B) and Aluminum (Al).
- Preference: These atoms are often stable with only $6$ valence electrons around them (not a full octet). While they can be found with $8$ electrons, the $6$ electron configuration is often preferred if it minimizes formal charges.
- Example: Boron Trifluoride ( $BF_3$ ):
  - Valence electrons: Boron ( $3$ ) + $3$ Fluorines ( $3 imes 7$ ) = $24$ valence electrons.
  - Structure: Boron single-bonded to three fluorines. Each fluorine has $3$ lone pairs. Boron has $6$ electrons.
  - Formal Charges (6-electron B): Boron ( $3 - 0 - 3 = 0$ ), Fluorine ( $7 - 6 - 1 = 0$ ). All atoms are neutral.
  - Alternative (8-electron B): If a fluorine forms a double bond with boron (to give B an octet), B's formal charge becomes $-1$ ( $3 - 0 - 4 = -1$ ), and that fluorine's formal charge becomes $+1$ ( $7 - 4 - 2 = +1$ ). This is a less favorable structure because a highly electronegative atom (F) has a positive formal charge, and a less electronegative atom (B) has a negative formal charge.
  - Conclusion: The structure with boron having $6$ electrons and all atoms being neutral is the better Lewis structure for $BF_3$ .
3. Odd Electron Molecules (Radicals):
- Definition: Molecules that have an unpaired electron.
- Octet Rule Violation: The octet rule cannot be satisfied because $8$ is an even number, and an odd number of total electrons will always result in at least one unpaired electron.
- Example: Nitric Oxide (NO):
  - Valence electrons: Nitrogen ( $5$ ) + Oxygen ( $6$ ) = $11$ valence electrons.
  - Drawing the Lewis structure: After forming bonds and completing octets as much as possible, one electron will be left unpaired on either nitrogen or oxygen.
  - Formal charges can still be zero, even with an unpaired electron. For example, if N has a double bond to O, N has 1 lone electron and O has two lone pairs. Formal charge on N: $5 - 1 ext{ (unpaired electron)} - 4 ext{ (double bond)} = 0$ . Formal charge on O: $6 - 4 ext{ (lone pairs)} - 4 ext{ (double bond)} = 0$ .
  - Molecules with unpaired electrons are called radicals and are typically highly reactive.

VSEPR Theory (Valence Shell Electron Pair Repulsion)

Core Principle: Regions of electron density around a central atom repel each other and will arrange themselves to be as far apart as possible to minimize repulsion.
What constitutes a "Region of Electron Density" (or Electron Pair Domain):
- 1. Lone Pairs: Non-bonding electron pairs.
- 2. Single Bonds: A single bond between two atoms.
- 3. Double Bonds: A double bond between two atoms (counted as one region).
- 4. Triple Bonds: A triple bond between two atoms (counted as one region).
- 5. Radicals: An unpaired electron.
- All these are negatively charged regions that repel each other.
Five Basic Electron Geometries:
1. Two Electron Regions:
  - Electron Geometry: Linear.
  - Bond Angle: $180^ ext{o}$ .
  - Example: $CO_2$ (carbon has two double bonds, so two regions of electron density, arranged linearly).
2. Three Electron Regions:
  - Electron Geometry: Trigonal Planar.
  - Bond Angle: $120^ ext{o}$ .
  - Shape: Flat (planar).
  - Example: Formaldehyde ( $CH_2O$ ). The oxygen has two lone pairs, which exert a slightly greater repulsion than bonding pairs, causing minor deviations from $120^ ext{o}$ (e.g., $116^ ext{o}$ and $121^ ext{o}$ ). However, the base is still considered trigonal planar.
  - Drawing Convention (for 3D representation):
    - Wedges: Indicate a bond coming out of the plane of the paper/board towards the viewer.
    - Dashes: Indicate a bond going behind the plane of the paper/board away from the viewer.
    - Straight Lines: Indicate a bond lying in the plane of the paper/board.
3. Four Electron Regions:
  - Electron Geometry: Tetrahedral.
  - Bond Angle: Approx. $109.5^ ext{o}$ (e.g., methane, $CH_4$ ).
  - Shape: A symmetrical 3D arrangement, where all bonds are spread as far apart as possible (not $90^ ext{o}$ as might be drawn on a 2D plane).
  - Drawing Convention: Often uses wedges and dashes to represent its 3D nature effectively.
4. Five Electron Regions:
  - Electron Geometry: Trigonal Bipyramidal.
  - Bond Angles:
    - Equatorial-Equatorial: $120^ ext{o}$ .
    - Axial-Equatorial: $90^ ext{o}$ .
  - Shape: Consists of three groups in a flat, trigonal planar arrangement (called equatorial positions) and two groups perpendicular to this plane, one above and one below (called axial positions).
  - Nomenclature: "Trigonal" refers to the triangular plane, and "bipyramidal" refers to the two pyramids (one on top, one on bottom) formed by connecting the axial groups to the equatorial groups.
5. Six Electron Regions:
  - Electron Geometry: Octahedral.
  - Bond Angle: All angles are $90^ ext{o}$ .
  - Shape: All six groups are equidistant from each other, forming a symmetrical 3D shape.
  - Nomenclature: "Octahedral" refers to an octahedron (an 8-sided polyhedron), where all faces are triangles. All positions are equivalent in terms of bond angle from the center.
Application: Given a Lewis structure, one must be able to identify the number of electron regions around the central atom and predict its electron geometry. These are fundamental for predicting molecular geometry (which will be discussed further in the upcoming activity).