Chemical Bonding and Lewis Structures

Core Concepts of Chemical Bonding

• Chemical bonding describes the forces that hold atoms together to form compounds with increased stability.

• Primary learning objectives in chemical bonding include:

  • Defining bond types based on electron behavior and electronegativity differences.

  • Visualizing and modeling how atoms share or transfer valence electrons to achieve stable electronic configurations.

Classification of Bonds by Electronegativity Difference

• Electronegativity (EN) difference ($\Delta\text{EN}$) is calculated as the absolute value of the difference in electronegativity between two bonded atoms:   $\Delta\text{EN} = |\text{EN}_A - \text{EN}_B|$

• Bond classifications are established by the value of $\Delta\text{EN}$:

  • Non-polar Covalent Bond: $\Delta\text{EN} \le 0.4$. Characterized by equal or near-equal sharing of electrons between atoms.

  • Polar Covalent Bond: $0.4 < \Delta\text{EN} < 2.0$. Characterized by unsymmetrical or partial transfer of electron density toward the more electronegative atom.

  • Ionic Bond: $\Delta\text{EN} \ge 2.0$, or bonds formed between a metal and a nonmetal. Characterized by complete electron transfer from one atom to another, creating discrete ions.

• Percent Ionic Character relative to $\Delta\text{EN}$:

  • Homonuclear diatomic molecules (e.g., $Cl_2$) have $\Delta\text{EN} = 0$ and $0\%$ ionic character.

  • Heteronuclear covalent molecules (e.g., $IBr$, $HI$, $ICl$, $HBr$, $HCl$) display small $\Delta\text{EN}$ values and ionic character below $25\%$.

  • Molecules such as $HF$ have $\Delta\text{EN} \approx 1.9$ with approximately $40\%$ ionic character, straddling the polar covalent boundary.

  • Alkali metal halides (e.g., $LiI$, $LiBr$, $LiCl$, $LiF$, $KI$, $KBr$, $KCl$, $KF$, $CsI$, $CsCl$, $CsF$, $NaCl$) exhibit high $\Delta\text{EN}$ values with percent ionic character ranging from $50\%$ to over $90\%$.

The Ionic Bond

• An ionic bond is defined as the electrostatic force of attraction that holds oppositely charged ions together in an ionic compound.

• Formation mechanism illustrated by Lithium Fluoride ($LiF$):

  • Neutral atoms:

  • Lithium ($Li$): Electronic configuration $1s^2 2s^1$

  • Fluorine ($F$): Electronic configuration $1s^2 2s^2 2p^5$

  • Ionization reactions:     $Li \rightarrow Li^+ + e^-$     $\text{Configuration of } Li^+: 1s^2\ \text{or } [He]$     $e^- + F \rightarrow F^-$     $\text{Configuration of } F^-: 1s^2 2s^2 2p^6\ \text{or } [Ne]$

  • Combined net reaction:     $Li^+ + F^- \rightarrow LiF$

• In this process, lithium transfers its valence electron from the $2s$ orbital to fluorine's incomplete $2p$ orbital, allowing both resulting ions ($Li^+$ and $F^-$) to attain noble gas electron configurations.

Covalent Bonds and Valence Electron Sharing

• A covalent bond is a chemical bond in which two or more electrons are shared by two atoms.

• Atoms share valence electrons to achieve a complete octet ($8$ valence electrons) or duet ($2$ valence electrons for hydrogen), imitating the chemical stability of noble gases.

• Example of single covalent bond formation in Fluorine gas ($F_2$):

  • Each neutral fluorine atom possesses $7$ valence electrons.

  • When two fluorine atoms combine, each contributes $1$ electron to form a single shared electron pair:     $7\,e^- + 7\,e^- \rightarrow 8\,e^-\ \text{per atom}$

• Terminology in Lewis structures:

  • Lone pairs (nonbonding electrons): Pairs of valence electrons belonging exclusively to one atom that are not involved in bonding.

  • Single covalent bond: A single pair of shared electrons connecting two atoms, often represented as a single dash ($\text{---}$).

Polar Covalent Bonds and Electron Distribution

• A polar covalent bond (or polar bond) is a covalent bond with greater electron density concentrated around one of the two bonded atoms.

• Characterized by partial charges caused by unequal electronegativity:

  • $\delta^+$ (partial positive charge): Assigned to the electron-poor region (lower electronegativity atom).

  • $\delta^-$ (partial negative charge): Assigned to the electron-rich region (higher electronegativity atom).

• Example of Hydrogen Fluoride ($HF$):

  • Fluorine attracts the shared pair far more strongly than Hydrogen.

  • Hydrogen atom acts as the $\delta^+$ (electron poor) center.

  • Fluorine atom acts as the $\delta^-$ (electron rich) center.

Multiple Covalent Bonds

• Single Bond: Two atoms share $1$ pair of electrons ($2\,e^-$ total).

  • Example: Water ($H_2O$), where oxygen shares one electron pair with each of two hydrogen atoms.

• Double Bond: Two atoms share $2$ pairs of electrons ($4\,e^-$ total).

  • Example: Carbon dioxide ($CO_2$), written as $O=C=O$, where carbon forms a double bond with each oxygen atom, allowing all three atoms to attain $8$ valence electrons.

• Triple Bond: Two atoms share $3$ pairs of electrons ($6\,e^-$ total).

  • Example: Nitrogen gas ($N_2$), written as $N \equiv N$, where two nitrogen atoms share three pairs of electrons to complete their octets.

Practice Problems: Bond Type Determination

• Classification of specific bonded pairs based on electronegativity values and metal/nonmetal rules:

  • $H - C$: Non-polar covalent ($\Delta\text{EN} \le 0.4$)

  • $N - O$: Polar covalent ($0.4 < \Delta\text{EN} < 2.0$)

  • $Na - Cl$: Ionic (metal + nonmetal, $\Delta\text{EN} \ge 2.0$)

  • $H - F$: Polar covalent ($0.4 < \Delta\text{EN} < 2.0$)

  • $Mg - O$: Ionic (metal + nonmetal, $\Delta\text{EN} \ge 2.0$)

  • $P - Cl$: Polar covalent ($0.4 < \Delta\text{EN} < 2.0$)

Step-by-Step Guidelines for Writing Lewis Structures

1. Determine Skeletal Structure: Connect atoms with single bonds. Place the least electronegative element in the central position.

2. Hydrogen Placement Rule: Hydrogen ($H$) requires only $1$ bond ($2$ shared electrons) and must always be placed as a terminal (end) atom.

3. Halogen Placement Rule: Halogens usually form only $1$ single bond unless bound directly to another halogen or central electronegative nonmetal.

4. Calculate Total Available Valence Electrons ($A$):

   • Sum the valence electrons of all isolated constituent atoms.

   • For polyatomic anions: Add $1\,e^-$ for each negative charge.

   • For polyatomic cations: Subtract $1\,e^-$ for each positive charge.

   • All available electrons ($A$) must be present in the final Lewis structure.

5. Calculate Total Needed Electrons ($N$):

   • Hydrogen needs $2$ electrons.

   • Every non-hydrogen atom needs $8$ electrons.

   • Formula:      $N = 2 \times (\text{number of } H \text{ atoms}) + 8 \times (\text{number of non-}H \text{ atoms})$

6. Calculate Shared Electrons ($S$):

   • Formula:      $S = N - A$

   • The number of covalent bonds equals $\frac{S}{2}$. Multiple bonds (double or triple) are required if $\frac{S}{2}$ exceeds the number of single bonds needed to connect the skeleton.

7. Distribute Remaining Nonbonding Electrons:

   • Calculate nonbonding electrons: $A - S$.

   • Place remaining electrons as lone pairs to complete octets for terminal atoms first, placing any excess on the central atom.

Worked Examples: Drawing Lewis Structures

• Nitrogen Trifluoride ($NF_3$):

  • Central atom: Nitrogen ($N$) [less electronegative than Fluorine].

  • Available electrons $A$:     $A = 5\,(N) + 3 \times 7\,(F) = 26\,e^-$

  • Needed electrons $N$:     $N = 8\,(N) + 3 \times 8\,(F) = 32\,e^-$

  • Shared electrons $S$:     $S = 32 - 26 = 6\,e^-\ \quad (3 \text{ single bonds})$

  • Nonbonding electrons:     $A - S = 26 - 6 = 20\,e^-\ \quad (10 \text{ lone pairs})$

  • Structure: Central $N$ atom single-bonded to three terminal $F$ atoms; $N$ carries $1$ lone pair, and each $F$ carries $3$ lone pairs.

• Carbonate Ion ($CO_3^{2-}$):

  • Central atom: Carbon ($C$).

  • Available electrons $A$:     $A = 4\,(C) + 3 \times 6\,(O) + 2\,(\text{charge}) = 24\,e^-$

  • Needed electrons $N$:     $N = 8\,(C) + 3 \times 8\,(O) = 32\,e^-$

  • Shared electrons $S$:     $S = 32 - 24 = 8\,e^-\ \quad (4 \text{ total bonds})$

  • Nonbonding electrons:     $A - S = 24 - 8 = 16\,e^-\ \quad (8 \text{ lone pairs})$

  • Structure: Carbon is double-bonded to one Oxygen atom and single-bonded to two Oxygen atoms. The complete assembly is enclosed in brackets with a $2-$ superscript.

• Ammonium Ion ($NH_4^+$):

  • Central atom: Nitrogen ($N$).

  • Available electrons $A$:     $A = 5\,(N) + 4 \times 1\,(H) - 1\,(\text{charge}) = 8\,e^-$

  • Needed electrons $N$:     $N = 8\,(N) + 4 \times 2\,(H) = 16\,e^-$

  • Shared electrons $S$:     $S = 16 - 8 = 8\,e^-\ \quad (4 \text{ single bonds})$

  • Nonbonding electrons:     $A - S = 8 - 8 = 0\,e^-$

  • Structure: Central $N$ single-bonded to four $H$ atoms with zero nonbonding electrons, enclosed in brackets with a $+$ charge.

Formal Charge Analysis and Plausibility Criteria

• An atom's formal charge is defined as the difference between the number of valence electrons in an isolated free atom and the number of electrons assigned to that atom in a Lewis structure.

• Formula for Formal Charge:   $\text{Formal Charge} = (\text{Valence } e^- \text{ free atom}) - (\text{Nonbonding } e^-) - (\text{Total number of bonds})$   (where total number of bonds equals $\frac{1}{2}$ of bonding electrons).

• Sum Rule: The sum of formal charges of all atoms in a molecule or ion must equal the overall net charge of the species:   $\sum \text{Formal Charges} = \text{Overall Charge}$

• Rules for evaluating formal charges to select the most plausible Lewis structure:

  1. Zero Formal Charge Rule: For neutral molecules, a Lewis structure in which all formal charges are zero is preferable to one with non-zero formal charges.

  2. Magnitude Rule: Structures with small formal charges ($0, +1, -1$) are significantly more plausible than structures with larger formal charges ($+2, -2$, etc.).

  3. Charge Separation Rule: Structures without adjacent charges of the same sign (e.g., $++$ or $--$) are more plausible.

  4. Electronegativity Rule: Among candidate structures with similar formal charge distributions, the most plausible structure places negative formal charges on the more electronegative atoms.

Formal Charge Worked Example: Formaldehyde ($CH_2O$)

• Total available valence electrons:   $A = 4\,(C) + 6\,(O) + 2 \times 1\,(H) = 12\,e^-$

• Evaluation of Structure Candidate 1 ($H - C - O - H$ arrangement):

  • Carbon atom ($3$bonds,$2 nonbonding electrons):\n    \text{Formal Charge}_C = 4 - 2 - 3 = -1\n - Oxygen atom ($3 bonds, $2$ nonbonding electrons):     $\text{Formal Charge}_O = 6 - 2 - 3 = +1$

  • Hydrogen atoms ($1$bond,$0 nonbonding electrons):\n    \text{Formal Charge}_H = 1 - 0 - 1 = 0\n - Assessment: Unfavorable due to non-zero formal charges (-1$on$C$,$+1$on electronegative$O).\n- **Evaluation of Structure Candidate 2 (H_2C=O arrangement)**:\n - Carbon atom ($4 bonds, $0$ nonbonding electrons):     $\text{Formal Charge}_C = 4 - 0 - 4 = 0$

  • Oxygen atom ($2$bonds,$4 nonbonding electrons):\n    \text{Formal Charge}_O = 6 - 4 - 2 = 0\n - Hydrogen atoms ($1 bond, $0$ nonbonding electrons):     $\text{Formal Charge}_H = 1 - 0 - 1 = 0$

  • Assessment: Optimal and correct structure because formal charges are zero across all atoms.

Resonance Structures

• A resonance structure is one of two or more valid Lewis structures for a single molecule or polyatomic ion that cannot be represented accurately by only one Lewis structure.

• Example of Ozone ($O_3$):

  • Double bond and single bond locations alternate between equivalent outer oxygen atoms:     $[:\ddot{O} - \overset{+}{\ddot{O}} = \ddot{O}:] \longleftrightarrow [:\ddot{O} = \overset{+}{\ddot{O}} - \ddot{O}:^-]$

  • Neither structure alone describes the true electron distribution; the actual molecule is a hybrid of all valid resonance structures.

Resonance Worked Example: Nitrous Oxide ($N_2O$)

• Atomic connectivity: $N - N - O$

• Total available valence electrons:   $A = 5\,(N) + 5\,(N) + 6\,(O) = 16\,e^-$

• Resonance Structure 1:   $[:N \equiv N^+ - \ddot{O}:^-]$

  • Formal Charge calculations:

  • Terminal Nitrogen: $5 - 2 - 3 = 0$

  • Central Nitrogen: $5 - 0 - 4 = +1$

  • Oxygen: $6 - 6 - 1 = -1$

• Resonance Structure 2:   $[\ddot{N}^- = N^+ = \ddot{O}]$

  • Formal Charge calculations:

  • Terminal Nitrogen: $5 - 4 - 2 = -1$

  • Central Nitrogen: $5 - 0 - 4 = +1$

  • Oxygen: $6 - 4 - 2 = 0$

• Resonance Structure 3:   $[:N^{2-} - N^+ \equiv O^+]$

  • Formal Charge calculations:

  • Terminal Nitrogen: $5 - 6 - 1 = -2$

  • Central Nitrogen: $5 - 0 - 4 = +1$

  • Oxygen: $6 - 2 - 3 = +1$

• Relative Plausibility / Relative Importance Ranking:

  1. Structure 1 ($:N \equiv N^+ - \ddot{O}:^-$) - Major Contributor: Most stable because the negative formal charge resides on Oxygen, which is more electronegative than Nitrogen ($\text{EN}_O > \text{EN}_N$), and overall formal charges are low ($0, +1, -1$).

  2. Structure 2 ($\ddot{N}^- = N^+ = \ddot{O}$) - Secondary Contributor: Less stable than Structure 1 because the negative formal charge is placed on the less electronegative Nitrogen atom.

  3. Structure 3 ($:N^{2-} - N^+ \equiv O^+$) - Minor Contributor: Least plausible and least important due to a large formal charge magnitude ($-2$ on terminal $N$) and a positive formal charge ($+1$) placed on the highly electronegative Oxygen atom.