Comprehensive Notes on Chemical Bonding, Molecular Structure, and Valence Bond Theory

Foundations of Chemical Bonding and Energy

• Effective Nuclear Charge and Valence Electrons:

  • A valence (outermost) electron experiences simultaneous electrostatic attraction to the protons within the nucleus and repulsion from intervening core electrons.

  • Effective nuclear charge ($Z_{\text{eff}}$) governs periodic properties including atomic and ionic radii, ionization energy, electron affinity, and metallic character (reactivity).

  • Valence electrons dictate chemical reactivity and participate directly in bond formation.

• Energy Manifestations in Chemical Entities:

  • Potential Energy (PE): Represents energy stored due to position. Within chemical systems, potential energy is stored in:

  • Intramolecular chemical bonds (electrostatic forces binding atoms or ions together).

  • Intermolecular forces (attractions between discrete molecular entities).

  • Kinetic Energy (KE): Represents energy associated with motion. Within chemical substances, kinetic energy manifests as:

  • Vibrational motion (oscillation of bonded atoms about equilibrium internuclear axes).

  • Rotational motion (rotation of molecules about their centers of mass).

  • Translational motion (linear displacement of particles through space).

• Thermodynamics of Bond Formation and Dissociation:

  • Chemical bonds form because bonded atoms attain a lower, more stable potential energy state compared to separated, isolated atoms.

  • Molecular and ionic systems adhere to the Principle of Conservation of Energy, operating toward thermodynamic minimization of potential energy.

  • Bond Formation: Always an exothermic process; energy is released into the surroundings ($\Delta H < 0$).

  • Bond Cleavage: Always an endothermic process; energy must be absorbed from the surroundings to overcome stabilizing attractions ($\Delta H > 0$).

• Elemental Classification and Standard Molecular Representation:

  • Elements are categorized into metals, nonmetals, and metalloids across the periodic table, which determines the nature of the chemical bonds formed.

  • Visual molecular modeling uses standardized colors to represent element types in ball-and-stick and space-filling representations:

  • Hydrogen: White

  • Boron: Pink

  • Carbon: Black

  • Nitrogen: Blue

  • Oxygen: Red

  • Fluorine: Yellow-green

  • Sodium: Light gray / Silver

  • Phosphorus: Orange

  • Sulfur: Yellow

  • Chlorine: Green

  • Bromine: Orange-brown / Red-brown

  • Iodine: Purple / Violet

Classification and Characteristics of Chemical Bonds

• Primary Classes of Chemical Bonds:

  • Ionic Bonds:

  • Constituents: Metal combined with nonmetal (or polyatomic ions).

  • Mechanism: Complete transfer of one or more valence electrons from the metal (forming a cation) to the nonmetal (forming an anion).

  • Binding Force: Non-directional electrostatic attraction between oppositely charged ions.

  • Covalent Bonds:

  • Constituents: Two or more nonmetals.

  • Mechanism: Mutual sharing of localized valence electron pairs between atoms.

  • Binding Force: Simultaneous electrostatic attraction of two positive nuclei for a shared pool of localized bonding electrons.

  • Metallic Bonds:

  • Constituents: Metal atoms bonded to metal atoms.

  • Mechanism: Valence electrons become delocalized or "pooled" across an array of metal atoms, creating a sea of mobile electrons surrounding stationary metal cations.

• Empirical Bond Type Identification:

  • $\text{Na}$ and $\text{Br}$: Metal + Nonmetal $\rightarrow$ Ionic bond

  • $\text{P}$ and $\text{Cl}$: Nonmetal + Nonmetal $\rightarrow$ Covalent bond

  • $\text{N}$ and $\text{H}$: Nonmetal + Nonmetal $\rightarrow$ Covalent bond

  • $\text{Cu}$ and $\text{F}$: Metal + Nonmetal $\rightarrow$ Ionic bond

  • $\text{B}$ and $\text{Cl}$: Metalloid/Nonmetal + Nonmetal $\rightarrow$ Covalent bond

  • $\text{C}$ and $\text{H}$: Nonmetal + Nonmetal $\rightarrow$ Covalent bond

  • $\text{Ca}$ and $\text{O}$: Metal + Nonmetal $\rightarrow$ Ionic bond

• Lewis Theory and the Octet Rule:

  • Formulated by Gilbert N. Lewis: "When atoms bond, they lose, gain, or share electrons to attain a filled outer layer of eight electrons."

  • Octet Rule: Tendency of main-group atoms to interact until they are enveloped by eight valence electrons, matching the exceptionally stable electron configuration of a noble gas ($ns^2np^6$).

  • Duet Rule: For light elements such as $\text{H}$, $\text{He}$, $\text{Li}^+$, and $\text{Be}^{2+}$, stability corresponds to a filled $1s$ orbital accommodating a maximum of two electrons ($1s^2$).

• Lewis Dot Symbols:

  • Display the elemental chemical symbol surrounded by dots representing individual valence electrons.

  • Execution: Place dots singly on each of the four cardinal quadrants (top, bottom, left, right) around the symbol before pairing them up.

  • Exception: Helium ($\text{He}$) possesses two valence electrons shown paired together in a single orbital ($1s^2$).

Ionic Bonding, Crystal Lattices, and Lattice Energy

• Nature of Ionic Compounds:

  • Ionic bonds do not yield discrete, isolated molecules. Instead, electrostatic interactions extend in all directions, causing ions to assemble into an extended three-dimensional crystal lattice.

  • The chemical formula of an ionic compound constitutes a formula unit, representing the lowest whole-number ratio of cations to anions that establishes electrical neutrality.

• Ionic Crystal Formation:

  • Cations ($\text{M}^{n+}$) result from the loss of valence electrons, contracting the electron cloud due to increased effective nuclear charge and loss of the outermost principal energy level.

  • Anions ($\text{X}^{m-}$) result from the gain of valence electrons, expanding the electron cloud due to increased inter-electronic repulsions among valence electrons.

  • Example with Potassium and Chlorine:

  • Neutral Potassium ($\text{K}$): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^1$

  • Potassium Cation ($\text{K}^+$): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^0$ (yields an octet in the preceding principal energy level, $n=3$

  • Lewis electron dot reaction: $\text{K}\cdot + \cdot\ddot{\text{Cl}}: \rightarrow \text{K}^+ [:\ddot{\text{Cl}}:]^-$

• Lattice Energy ($U$):

  • Defined formally as the energy required to completely separate one mole of a solid ionic compound into its isolated gaseous constituent ions (endothermic representation):     $\text{MX}(s) \rightarrow \text{M}^+(g) + \text{X}^-(g) \quad \Delta H > 0$

  • The reverse reaction, assembling the solid crystal lattice from its gaseous ions, releases an equivalent quantity of energy and is highly exothermic ($\Delta H < 0$).

  • Governed quantitatively by Coulomb's Law:     $E_{\text{el}} \propto \frac{Q_1 Q_2}{d}$

  • $Q_1$ and $Q_2$ represent the magnitudes of the ionic charges.

  • $d$ represents the internuclear distance between the cation and anion ($r_{\text{cation}} + r_{\text{anion}}$).

• Trends in Lattice Energy:

  • Effect of Ion Size: As ionic radius increases, internuclear distance $d$ increases, attenuating coulombic attraction and reducing lattice energy.

  • Series of alkali metal chlorides:

    • $\text{LiCl}$: Interionic distance = $241\,\text{pm}$; Lattice Energy = $-834\,\text{kJ}\,\text{mol}^{-1}$ (or $860\,\text{kJ}\,\text{mol}^{-1}$ endothermic separation)

    • $\text{NaCl}$: Interionic distance = $276\,\text{pm}$; Lattice Energy = $-788\,\text{kJ}\,\text{mol}^{-1}$ (or $787\,\text{kJ}\,\text{mol}^{-1}$ endothermic separation)

    • $\text{KCl}$: Interionic distance = $314\,\text{pm}$; Lattice Energy = $-701\,\text{kJ}\,\text{mol}^{-1}$ (or $699\,\text{kJ}\,\text{mol}^{-1}$ endothermic separation)

    • $\text{CsCl}$: Interionic distance = $348\,\text{pm}$; Lattice Energy = $-657\,\text{kJ}\,\text{mol}^{-1}$

  • Effect of Ionic Charge: Higher ionic charge magnitudes dominate over size differences, producing significantly larger lattice energies.

  • Comparing $\text{NaF}$ vs. $\text{MgO}$:

    • $\text{NaF}$ ($\text{Na}^+$, $\text{F}^-$): Internuclear distance $d = 235\,\text{pm}$; Lattice Energy = $910\,\text{kJ}\,\text{mol}^{-1}$

    • $\text{MgO}$ ($\text{Mg}^{2+}$, $\text{O}^{2-}$): Internuclear distance $d = 212\,\text{pm}$; Lattice Energy = $3890\,\text{kJ}\,\text{mol}^{-1}$

    • Product of charges in $\text{MgO}$ is $|(+2)(-2)| = 4$, compared to $|(+1)(-1)| = 1$ in $\text{NaF}$, yielding an approximate four-fold increase in stabilization energy.

• Quantitative Reference Data for Selected Ionic Compounds:

  | Compound | Lattice Energy ($\text{kJ}\,\text{mol}^{-1}$) | Melting Point ($^{\circ}\text{C}$) |   | :--- | :--- | :--- |   | $\text{LiF}$ | $1017$ | $845$ |   | $\text{LiCl}$ | $860$ | $610$ |   | $\text{LiBr}$ | $787$ | $550$ |   | $\text{LiI}$ | $732$ | $450$ |   | $\text{NaCl}$ | $787$ | $801$ |   | $\text{NaBr}$ | $736$ | $750$ |   | $\text{NaI}$ | $686$ | $662$ |   | $\text{KCl}$ | $699$ | $772$ |   | $\text{KBr}$ | $689$ | $735$ |   | $\text{KI}$ | $632$ | $680$ |   | $\text{MgCl}_2$ | $2527$ | $714$ |   | $\text{Na}_2\text{O}$ | $2570$ | Sublimes at $1275$ |   | $\text{MgO}$ | $3890$ | $2800$ |

• Physical Properties of Ionic Substances:

  • Melting and Boiling Points: Exceptionally high because thermal energy must overcome massive coulombic lattice energies throughout the extended solid network.

  • Mechanical Properties: Hard, rigid, and brittle; mechanical stress shifts planes of ions, aligning like charges that generate catastrophic electrostatic repulsions, cleaving the crystal.

  • Electrical Conductivity:

  • Solid state: Non-conductive; charged ions occupy fixed positions within the rigid crystal lattice and cannot migrate.

  • Molten state: Highly conductive; thermal energy breaks down the rigid lattice, allowing freely moving ions to carry electric current.

  • Aqueous solution: Readily conductive; water hydrates and dissociates the ions into mobile solvated species that migrate toward applied electrical potentials.

Covalent Bonding and Molecular Properties

• Valence Bond Perspective of Covalent Bond Formation:

  • Covalent bonds form when half-filled atomic orbitals overlap in space, pairing their opposing electron spins to create a shared bonding region.

  • Overlap examples:

  • Overlap of two $1s$ orbitals in dihydrogen ($\text{H}_2$).

  • Overlap of a $1s$ orbital of hydrogen with a $2p$ orbital of fluorine in hydrogen fluoride ($\text{HF}$).

• Potential Energy Dynamics vs. Internuclear Distance:

  • Large Separation: Potential energy is defined as zero; no attractive or repulsive interactions occur.

  • Intermediate Separation (Approaching atoms): Electrostatic attraction between the nucleus of one atom and the electron cloud of the other pulls atoms together, lowering the potential energy.

  • Optimal Internuclear Distance (Bond Length): Point of minimum potential energy representing the most stable equilibrium state. Attractive forces balance inter-electronic and internuclear repulsions.

  • Excessive Proximity: Nuclear-nuclear and core-core electron repulsions spike precipitously, driving potential energy upward sharply.

• Bond Order Metrics:

  • Single Bond (Bond Order = 1): One electron pair ($2\,e^-$) shared between two bonded atoms (e.g., $\text{H}-\text{H}$, $\text{Cl}-\text{Cl}$, $\text{CH}_4$).

  • Double Bond (Bond Order = 2): Two electron pairs ($4\,e^-$) shared between two bonded atoms (e.g., $\text{O}=\text{C}=\text{O}$, $\text{H}_2\text{C}=\text{CH}_2$).

  • Triple Bond (Bond Order = 3): Three electron pairs ($6\,e^-$) shared between two bonded atoms (e.g., $\text{N}\equiv\text{N}$, $\text{H}-\text{C}\equiv\text{C}-\text{H}$, $\text{C}\equiv\text{O}$).

• Correlations Between Bond Order, Bond Length, and Bond Strength:

  • For bonds connecting identical or chemically comparable pairs of atoms:

  • As bond order increases, bond length decreases.

  • As bond order increases, bond dissociation energy ($\Delta H$) increases.

  • General trend: Triple bond < Double bond < Single bond in length; Single bond < Double bond < Triple bond in strength.

• Bond Dissociation Energies ($\Delta H$, in $\text{kJ}\,\text{mol}^{-1}$):

  • Hydrogen Bonds:

  • $\text{H}-\text{H}$: $436\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{H}-\text{O}$: $460\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{H}-\text{F}$: $569\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{H}-\text{Cl}$: $432\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{H}-\text{Br}$: $366\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{H}-\text{I}$: $298\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{H}-\text{C}$: $410\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{H}-\text{N}$: $390\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{H}-\text{S}$: $340\,\text{kJ}\,\text{mol}^{-1}$

  • Carbon Bonds:

  • $\text{C}-\text{H}$: $410\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{C}-\text{O}$: $350\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{C}-\text{F}$: $450\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{C}-\text{Cl}$: $330\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{C}-\text{Br}$: $270\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{C}-\text{I}$: $240\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{C}-\text{C}$: $350\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{C}-\text{N}$: $300\,\text{kJ}\,\text{mol}^{-1}$

  • $\text{C}-\text{S}$: $260\,\text{kJ}\,\text{mol}^{-1}$

• Halogen Diatomic Bond Length Progression:

  • $\text{F}_2$: $143\,\text{pm}$

  • $\text{Cl}_2$: $199\,\text{pm}$

  • $\text{Br}_2$: $228\,\text{pm}$

  • $\text{I}_2$: $266\,\text{pm}$

  • As atomic radius expands down Group 17, valence orbitals become more diffuse, shifting equilibrium bond lengths to larger distances.

• Physical Properties of Covalent Molecular Compounds:

  • Melting and Boiling Points: Substantially lower than those of ionic compounds. Phase transitions disrupt weak intermolecular forces (dispersion, dipole-dipole, hydrogen bonding), leaving the strong intramolecular covalent bonds intact.

  • Electrical Conductivity: Molecular liquids and solids do not conduct electricity in pure form due to the absence of mobile ions or delocalized electrons. Certain molecular compounds (such as hydrogen halides and oxoacids) conduct in aqueous solution due to chemical ionization upon reaction with water (e.g., $\text{HCl}(g) + \text{H}_2\text{O}(l) \rightarrow \text{H}_3\text{O}^+(aq) + \text{Cl}^-(aq)$).

Electronegativity, Bond Polarity, and Dipole Moments

• Electronegativity ($\text{EN}$):

  • The relative ability of an atom bonded within a chemical molecule to attract shared electron pairs toward itself.

  • Periodic Trends:

  • Increases across a period from left to right (due to rising $Z_{\text{eff}}$ and decreasing atomic radius).

  • Increases up a group from bottom to top (due to smaller atomic radius bringing the nucleus closer to valence shells).

  • Fluorine ($\text{F}$) is the most electronegative element ($\text{EN} = 4.0$); Cesium ($\text{Cs}$) and Francium ($\text{Fr}$) are the least electronegative ($\text{EN} = 0.7$).

• Pauling Electronegativity Reference Values:

  • Group 1 (1A): $\text{H}$ ($2.1$), $\text{Li}$ ($1.0$), $\text{Na}$ ($0.9$), $\text{K}$ ($0.8$), $\text{Rb}$ ($0.8$), $\text{Cs}$ ($0.7$), $\text{Fr}$ ($0.7$)

  • Group 2 (2A): $\text{Be}$ ($1.5$), $\text{Mg}$ ($1.2$), $\text{Ca}$ ($1.0$), $\text{Sr}$ ($1.0$), $\text{Ba}$ ($0.9$), $\text{Ra}$ ($0.9$)

  • Transition Elements: $\text{Sc}$ ($1.3$), $\text{Ti}$ ($1.5$), $\text{V}$ ($1.6$), $\text{Cr}$ ($1.6$), $\text{Mn}$ ($1.5$), $\text{Fe}$ ($1.8$), $\text{Co}$ ($1.9$), $\text{Ni}$ ($1.9$), $\text{Cu}$ ($1.9$), $\text{Zn}$ ($1.6$), $\text{Y}$ ($1.2$), $\text{Zr}$ ($1.4$), $\text{Nb}$ ($1.6$), $\text{Mo}$ ($1.8$), $\text{Tc}$ ($1.9$), $\text{Ru}$ ($2.2$), $\text{Rh}$ ($2.2$), $\text{Pd}$ ($2.2$), $\text{Ag}$ ($1.9$), $\text{Cd}$ ($1.7$), $\text{La}$ ($1.1$), $\text{Hf}$ ($1.3$), $\text{Ta}$ ($1.5$), $\text{W}$ ($1.7$), $\text{Re}$ ($1.9$), $\text{Os}$ ($2.2$), $\text{Ir}$ ($2.2$), $\text{Pt}$ ($2.2$), $\text{Au}$ ($2.4$), $\text{Hg}$ ($1.9$)

  • Group 13 (3A): $\text{B}$ ($2.0$), $\text{Al}$ ($1.5$), $\text{Ga}$ ($1.6$), $\text{In}$ ($1.7$), $\text{Tl}$ ($1.8$)

  • Group 14 (4A): $\text{C}$ ($2.5$), $\text{Si}$ ($1.8$), $\text{Ge}$ ($1.8$), $\text{Sn}$ ($1.8$), $\text{Pb}$ ($1.9$)

  • Group 15 (5A): $\text{N}$ ($3.0$), $\text{P}$ ($2.1$), $\text{As}$ ($2.0$), $\text{Sb}$ ($1.9$), $\text{Bi}$ ($1.9$)

  • Group 16 (6A): $\text{O}$ ($3.5$), $\text{S}$ ($2.5$), $\text{Se}$ ($2.4$), $\text{Te}$ ($2.1$), $\text{Po}$ ($2.0$)

  • Group 17 (7A): $\text{F}$ ($4.0$), $\text{Cl}$ ($3.0$), $\text{Br}$ ($2.8$), $\text{I}$ ($2.5$), $\text{At}$ ($2.2$)

  • Group 18 (8A): $\text{Kr}$ ($3.0$), $\text{Xe}$ ($2.6$)

• Electronegativity Difference ($\Delta\text{EN}$) and the Bonding Continuum:

  • Chemical bonds occupy a continuous spectrum defined by the absolute difference in electronegativity ($\Delta\text{EN} = |\text{EN}_1 - \text{EN}_2|$):

  • $\Delta\text{EN} < 0.4$ (or $0.5$): Nonpolar Covalent Bond (uniform electron sharing; equal distribution of electron density).

  • $0.4 \le \Delta\text{EN} < 2.0$: Polar Covalent Bond (asymmetrical electron sharing; distinct partial charges $\delta^+$ and $\delta^-$).

  • $\Delta\text{EN} \ge 2.0$: Ionic Bond (electron transfer creates separate, fully charged cations and anions).

  • Exemplary Calculations:

  • $\text{F}_2$: $\Delta\text{EN} = |4.0 - 4.0| = 0.0 \rightarrow$ Pure Nonpolar Covalent

  • $\text{HCl}$: $\Delta\text{EN} = |3.0 - 2.1| = 0.9 \rightarrow$ Polar Covalent

  • $\text{HF}$: $\Delta\text{EN} = |4.0 - 2.1| = 1.9 \rightarrow$ Highly Polar Covalent

  • $\text{LiF}$: $\Delta\text{EN} = |4.0 - 1.0| = 3.0 \rightarrow$ Ionic

• Representing Polar Bonds and Bond Dipoles:

  • Partial Charge Notation: Use lower-case Greek delta with signs ($\delta^+$ and $\delta^-$). The atom with greater electronegativity carries $\delta^-$, and the more electropositive atom carries $\delta^+$.

  • Dipole Vector Notation: A crossed arrow points along the bond axis. The plus-sign tail ($\mapsto$) sits at the electropositive atom ($\delta^+$), while the arrow head points directly toward the more electronegative atom ($\delta^-$).

  • Practice Example ($\text{P}-\text{F}$ bond):

  • Electronegativities: $\text{P} = 2.1$, $\text{F} = 4.0$ ($\Delta\text{EN} = 1.9$

  • Partial charges: $\overset{\delta^+}{\text{P}}-\overset{\delta^-}{\text{F}}$

  • Dipole moment vector: $\text{P} \longrightarrow \text{F}$ (with cross at $\text{P}$, indicating $+\rightarrow$)

Systematic Chemical Nomenclature

• Nomenclature of Binary Ionic Compounds:

  • Composed of a monatomic metal cation and a monatomic nonmetal anion.

  • Rule: State the full elemental name of the metal cation first, followed by the base name of the nonmetal anion modified with the suffix -ide.

  • Numerical prefixes (mono-, di-, tri-, etc.) are never used for ionic compounds.

  • Examples:

  • $\text{KCl}$: Potassium chloride

  • $\text{Li}_2\text{O}$: Lithium oxide

  • $\text{CaS}$: Calcium sulfide

  • $\text{Mg}_3\text{N}_2$: Magnesium nitride

• Ionic Compounds with Multivalent Cations (Stock System):

  • Metals capable of forming more than one stable ionic charge (predominantly transition metals and post-transition metals) must specify the cation oxidation state with a Roman numeral enclosed in parentheses directly following the metal name.

  • Examples:

  • $\text{CuNO}_3$: Copper(I) nitrate

  • $\text{CrO}$: Chromium(II) oxide

  • $\text{Cr}_2\text{O}_3$: Chromium(III) oxide

  • $\text{Fe}_3(\text{PO}_4)_2$: Iron(II) phosphate

  • $\text{FeBr}_3$: Iron(III) bromide

  • $\text{VO}$: Vanadium(II) oxide

  • $\text{V}_2\text{O}_3$: Vanadium(III) oxide

  • $\text{PbO}_2$: Anions provide $2 \times (-2) = -4$; thus Lead is $+4 \rightarrow$ Lead(IV) oxide

  • $\text{Cu}_2\text{S}$: Sulfide is $-2$; two coppers balance with $+2 \rightarrow$ Copper(I) sulfide

  • $\text{PdCl}_4$: Chlorides provide $4 \times (-1) = -4 \rightarrow$ Palladium(IV) chloride

  • $\text{Sn}_3\text{P}_4$: Phosphides provide $4 \times (-3) = -12$; three tins provide $+12 \rightarrow$ Tin(IV) phosphide

• Writing Neutral Formulas for Ionic Compounds:

  • Sum of positive charges must balance sum of negative charges:     $n(\text{cation charge}) + m(\text{anion charge}) = 0$

  • Subscripts must reflect the smallest whole-number ratio.

  • Use parentheses around polyatomic ions whenever a subscript of two or greater is appended:

  • $\text{Zn}^{2+} + \text{N}^{3-} \rightarrow \text{Zn}_3\text{N}_2$

  • $\text{Al}^{3+} + \text{O}^{2-} \rightarrow \text{Al}_2\text{O}_3$

  • $\text{NH}_4^+ + \text{SO}_4^{2-} \rightarrow (\text{NH}_4)_2\text{SO}_4$

  • $\text{Mg}^{2+} + \text{NO}_3^- \rightarrow \text{Mg}(\text{NO}_3)_2$

  • $\text{Ca}^{2+} + \text{PO}_4^{3-} \rightarrow \text{Ca}_3(\text{PO}_4)_2$

• Polyatomic Ions and Oxyanion Suffix Conventions:

  • -ide: Suffix used for monatomic anions and a few polyatomic ions ($\text{OH}^-$, $\text{CN}^-$, $\text{O}_2^{2-}$).

  • -ate: Designated for the base, most common oxyanion member of a periodic family.

  • -ite: Designates an oxyanion containing exactly one fewer oxygen atom than the corresponding -ate ion, retaining an identical overall charge.

  • Extended Halogen Oxyanion Series:

  • Per-…-ate ($+1\,\text{O}$ relative to -ate): $\text{ClO}_4^-$ (Perchlorate), $\text{BrO}_4^-$ (Perbromate), $\text{IO}_4^-$ (Periodate)

  • -ate (Base oxyanion): $\text{ClO}_3^-$ (Chlorate), $\text{BrO}_3^-$ (Bromate), $\text{IO}_3^-$ (Iodate)

  • -ite ($-1\,\text{O}$ relative to -ate): $\text{ClO}_2^-$ (Chlorite), $\text{BrO}_2^-$ (Bromite), $\text{IO}_2^-$ (Iodite)

  • Hypo-…-ite ($-2\,\text{O}$ relative to -ate): $\text{ClO}^-$ (Hypochlorite), $\text{BrO}^-$ (Hypobromite), $\text{IO}^-$ (Hypoiodite)

  • Mnemonic device ("Nick the Camel ate a Clam Supper in Phoenix"):

  • First letter(s) indicate the central element.

  • Number of consonants specifies the count of oxygen atoms.

  • Number of vowels specifies the magnitude of the negative charge.

  • Nick: Nitrate $\rightarrow \text{N}$, 3 consonants, 1 vowel $\rightarrow \text{NO}_3^-$

  • Camel: Carbonate $\rightarrow \text{C}$, 3 consonants, 2 vowels $\rightarrow \text{CO}_3^{2-}$

  • Clam: Chlorate $\rightarrow \text{Cl}$, 3 consonants, 1 vowel $\rightarrow \text{ClO}_3^-$

  • Supper: Sulfate $\rightarrow \text{S}$, 4 consonants, 2 vowels $\rightarrow \text{SO}_4^{2-}$

  • Phoenix: Phosphate $\rightarrow \text{P}$, 4 consonants, 3 vowels $\rightarrow \text{PO}_4^{3-}$

• Comprehensive Table of Required Polyatomic Ions:

  | Name | Formula | Name | Formula |   | :--- | :--- | :--- | :--- |   | Acetate | $\text{C}_2\text{H}_3\text{O}_2^-$ or $\text{CH}_3\text{COO}^-$ | Sulfate | $\text{SO}_4^{2-}$ |   | Carbonate | $\text{CO}_3^{2-}$ | Sulfite | $\text{SO}_3^{2-}$ |   | Hydrogen carbonate (Bicarbonate) | $\text{HCO}_3^-$ | Hydrogen sulfate (Bisulfate) | $\text{HSO}_4^-$ |   | Nitrite | $\text{NO}_2^-$ | Hydrogen sulfite (Bisulfite) | $\text{HSO}_3^-$ |   | Nitrate | $\text{NO}_3^-$ | Hydroxide | $\text{OH}^-$ |   | Phosphate | $\text{PO}_4^{3-}$ | Cyanide | $\text{CN}^-$ |   | Phosphite | $\text{PO}_3^{3-}$ | Permanganate | $\text{MnO}_4^-$ |   | Chromate | $\text{CrO}_4^{2-}$ | Ammonium | $\text{NH}_4^+$ |   | Dichromate | $\text{Cr}_2\text{O}_7^{2-}$ | Peroxide | $\text{O}_2^{2-}$ |   | Thiosulfate | $\text{S}_2\text{O}_3^{2-}$ | Hypochlorite | $\text{ClO}^-$ |   | Chlorite | $\text{ClO}_2^-$ | Chlorate | $\text{ClO}_3^-$ |   | Perchlorate | $\text{ClO}_4^-$ | | |

• Hydrate Nomenclature:

  • Ionic compounds with a specific stoichiometric ratio of water molecules incorporated into their crystalline lattice.

  • Named as the anhydrous ionic compound followed by the Greek numerical prefix and the word hydrate.

  • Example: $\text{CuSO}_4 \cdot 5\text{H}_2\text{O}$ is copper(II) sulfate pentahydrate; the water-free salt $\text{CuSO}_4$ is termed copper(II) sulfate (anhydrous form).

• Nomenclature of Binary Molecular Compounds:

  • Applied to compounds formed between nonmetals.

  • Element with the lower group number is listed first. If both elements belong to the same periodic group, the element with the greater row (period) number is written first.

  • Greek numerical prefixes specify the count of atoms:

  • $1 = \text{mono-}$ (omitted if on the first element)

  • $2 = \text{di-}$

  • $3 = \text{tri-}$

  • $4 = \text{tetra-}$

  • $5 = \text{penta-}$

  • $6 = \text{hexa-}$

  • $7 = \text{hepta-}$

  • $8 = \text{octa-}$

  • $9 = \text{nona-}$

  • $10 = \text{deca-}$

  • Examples:

  • $\text{ClF}_3$: Chlorine trifluoride

  • $\text{SO}_2$: Sulfur dioxide

  • $\text{P}_4\text{O}_{10}$: Tetraphosphorus decoxide (prefix "a" dropped before "o")

  • $\text{N}_2\text{O}_4$: Dinitrogen tetroxide

  • $\text{CBr}_4$: Carbon tetrabromide

• Acid Nomenclature:

  • Binary Acids (Hydrogen + Halogen/Nonmetal):

  • Prefix hydro- + base name of nonmetal + suffix -ic acid.

  • $\text{HF}(aq)$: Hydrofluoric acid

  • $\text{HCl}(aq)$: Hydrochloric acid

  • $\text{HBr}(aq)$: Hydrobromic acid

  • $\text{HI}(aq)$: Hydroiodic acid

  • $\text{H}_2\text{S}(aq)$: Hydrosulfuric acid

  • Oxyacids (Hydrogen + Oxyanion):

  • If the oxyanion ends in -ate, replace with -ic acid:

    • $\text{HNO}_3$ ($\text{NO}_3^-$ = nitrate): Nitric acid

    • $\text{H}_2\text{SO}_4$ ($\text{SO}_4^{2-}$ = sulfate): Sulfuric acid

    • $\text{H}_3\text{PO}_4$ ($\text{PO}_4^{3-}$ = phosphate): Phosphoric acid

    • $\text{HClO}_3$ ($\text{ClO}_3^-$ = chlorate): Chloric acid

    • $\text{HClO}_4$ ($\text{ClO}_4^-$ = perchlorate): Perchloric acid

  • If the oxyanion ends in -ite, replace with -ous acid:

    • $\text{HNO}_2$ ($\text{NO}_2^-$ = nitrite): Nitrous acid

    • $\text{H}_2\text{SO}_3$ ($\text{SO}_3^{2-}$ = sulfite): Sulfurous acid

    • $\text{HClO}_2$ ($\text{ClO}_2^-$ = chlorite): Chlorous acid

    • $\text{HClO}$ ($\text{ClO}^-$ = hypochlorite): Hypochlorous acid

Stoichiometry, Molar Mass, and Quantitative Conversions

• Formula Weight and Molar Mass Foundations:

  • Formula Weight (molecular weight) represents the sum of atomic masses of all atoms present in a compound's chemical formula.

  • Worked Examples of Molar Mass Determinations:

  • Sulfuric Acid ($\text{H}_2\text{SO}_4$):       $2 \times 1.00794\,\text{amu} (\text{H}) = 2.01588\,\text{amu}$       $1 \times 32.065\,\text{amu} (\text{S}) = 32.065\,\text{amu}$       $4 \times 15.9994\,\text{amu} (\text{O}) = 63.9976\,\text{amu}$       $\text{Formula Weight} = 98.0784\,\text{amu} \longrightarrow 1\,\text{mol of } \text{H}_2\text{SO}_4 = 98.08\,\text{g}$

  • Calcium Chloride ($\text{CaCl}_2$):       $1 \times 40.078\,\text{amu} (\text{Ca}) = 40.078\,\text{amu}$       $2 \times 35.453\,\text{amu} (\text{Cl}) = 70.906\,\text{amu}$       $\text{Formula Weight} = 110.984\,\text{amu} \longrightarrow 1\,\text{mol of } \text{CaCl}_2 = 110.98\,\text{g}$

  • Calcium Phosphate ($\text{Ca}_3(\text{PO}_4)_2$):       $3 \times 40.078\,\text{g}\,\text{mol}^{-1} (\text{Ca}) = 120.234\,\text{g}\,\text{mol}^{-1}$       $2 \times 30.974\,\text{g}\,\text{mol}^{-1} (\text{P}) = 61.948\,\text{g}\,\text{mol}^{-1}$       $8 \times 15.999\,\text{g}\,\text{mol}^{-1} (\text{O}) = 127.992\,\text{g}\,\text{mol}^{-1}$       $\text{Molar Mass} = 310.17\,\text{g}\,\text{mol}^{-1}$

• Quantitative Mole Conversion Pathways:

  • Mass to Moles: Divide mass in grams by molar mass ($\text{g}\,\text{mol}^{-1}$

  • Moles to Mass: Multiply moles by molar mass ($\text{g}\,\text{mol}^{-1}$

  • Moles to Number of Particles/Atoms/Molecules: Multiply by Avogadro's number ($6.022 \times 10^{23}\,\text{particles}\,\text{mol}^{-1}$

  • Number of Particles to Moles: Divide by Avogadro's number.

  • Volume of Ideal Gas at STP ($0\,^{\circ}\text{C}$, $1\,\text{atm}$) to Moles: Divide volume in liters by $22.4\,\text{L}\,\text{mol}^{-1}$.

• Stoichiometric Worked Calculation Examples:

  • Conversion of $62.5\,\text{g}$ of Magnesium ($\text{Mg}$) to moles:     $62.5\,\text{g}\,\text{Mg} \times \frac{1\,\text{mol}\,\text{Mg}}{24.305\,\text{g}\,\text{Mg}} = 2.57\,\text{mol}\,\text{Mg}$

  • Determination of atom count in $47.1\,\text{g}$ of Vanadium ($\text{V}$):     $47.1\,\text{g}\,\text{V} \times \frac{1\,\text{mol}\,\text{V}}{50.942\,\text{g}\,\text{V}} \times \frac{6.022 \times 10^{23}\,\text{atoms}}{1\,\text{mol}\,\text{V}} = 5.57 \times 10^{23}\,\text{atoms of V}$

  • Moles in $128\,\text{g}$ of Calcium Phosphate ($\text{Ca}_3(\text{PO}_4)_2$):     $128\,\text{g}\,\text{Ca}_3(\text{PO}_4)_2 \times \frac{1\,\text{mol}\,\text{Ca}_3(\text{PO}_4)_2}{310.17\,\text{g}\,\text{Ca}_3(\text{PO}_4)_2} = 0.413\,\text{mol}\,\text{Ca}_3(\text{PO}_4)_2$

  • Grams of Calcium in $20.0\,\text{g}$ of Calcium Nitrate, $\text{Ca}(\text{NO}_3)_2$ ($\text{Molar mass} = 164.10\,\text{g}\,\text{mol}^{-1}$     $20.0\,\text{g}\,\text{Ca}(\text{NO}_3)_2 \times \frac{1\,\text{mol}\,\text{Ca}(\text{NO}_3)_2}{164.10\,\text{g}\,\text{Ca}(\text{NO}_3)_2} \times \frac{1\,\text{mol}\,\text{Ca}}{1\,\text{mol}\,\text{Ca}(\text{NO}_3)_2} \times \frac{40.078\,\text{g}\,\text{Ca}}{1\,\text{mol}\,\text{Ca}} = 4.89\,\text{g}\,\text{Ca}$

  • Mass of Oxygen in $79.2\,\text{g}$ of Potassium Carbonate, $\text{K}_2\text{CO}_3$:

  • Molar mass of $\text{K}_2\text{CO}_3 = 2(39.098) + 12.011 + 3(15.999) = 138.21\,\text{g}\,\text{mol}^{-1}$     $\text{Mass O} = 79.2\,\text{g}\,\text{K}_2\text{CO}_3 \times \frac{1\,\text{mol}\,\text{K}_2\text{CO}_3}{138.21\,\text{g}\,\text{K}_2\text{CO}_3} \times \frac{3\,\text{mol}\,\text{O}}{1\,\text{mol}\,\text{K}_2\text{CO}_3} \times \frac{15.999\,\text{g}\,\text{O}}{1\,\text{mol}\,\text{O}} = 27.5\,\text{g}\,\text{O}$

  • Number of Oxygen Atoms in $79.2\,\text{g}$ of Potassium Carbonate, $\text{K}_2\text{CO}_3$:     $\text{Atoms O} = 79.2\,\text{g}\,\text{K}_2\text{CO}_3 \times \frac{1\,\text{mol}\,\text{K}_2\text{CO}_3}{138.21\,\text{g}\,\text{K}_2\text{CO}_3} \times \frac{3\,\text{mol}\,\text{O}}{1\,\text{mol}\,\text{K}_2\text{CO}_3} \times \frac{6.022 \times 10^{23}\,\text{atoms}}{1\,\text{mol}\,\text{O}} = 1.03 \times 10^{24}\,\text{atoms of O}$

Lewis Structures and Octet Rule Exceptions

• Step-by-Step Methodology for Constructing Lewis Structures:

  • Step 1: Calculate total valence electrons by summing valence electrons from all participating neutral atoms. For polyatomic anions, add one electron per negative charge. For polyatomic cations, subtract one electron per positive charge.

  • Step 2: Arrange skeletal connectivity. The central atom is the element with the lowest electronegativity, excluding Hydrogen which must always remain terminal. Join central and terminal atoms with single ($2\,e^-$) covalent bonds.

  • Step 3: Distribute lone pairs to terminal atoms until each terminal atom achieves a complete valence octet (hydrogen is satisfied with two electrons).

  • Step 4: Place any remaining valence electrons on the central atom as lone pairs, even if doing so results in an expanded valence shell exceeding eight electrons.

  • Step 5: If the central atom lacks an octet after distributing all valence electrons, convert nonbonding lone pairs from surrounding terminal atoms into shared multiple bonds (double or triple bonds).

• Three Major Exceptions to the Octet Rule:

  • 1. Odd-Electron Molecules (Free Radicals):

  • Species bearing an odd number of total valence electrons, making complete octet pairing mathematically impossible.

  • Example: Nitric oxide ($\text{NO}$) with 11 valence electrons ($5 + 6 = 11$). Lewis structure contains an unpaired electron residing on Nitrogen ($\cdot\ddot{\text{N}}=\ddot{\text{O}}$).

  • 2. Electron-Deficient / Incomplete Octets:

  • Certain stable elements bond with fewer than eight valence electrons.

  • Beryllium ($\text{Be}$) stably coordinates two electron pairs ($4\,e^-$ total), as in $\text{BeCl}_2$ ($:\ddot{\text{Cl}}-\text{Be}-\ddot{\text{Cl}}:$) or $\text{BeBr}_2$.

  • Boron ($\text{B}$) stably coordinates three electron pairs ($6\,e^-$ total), as in $\text{BF}_3$ or $\text{BCl}_3$.

  • 3. Expanded Octets (Hypervalent Molecules):

  • Central atoms positioned in Period 3 or below in the periodic table can accommodate 10, 12, or more valence electrons.

  • Enabled energetically by the proximity and accessibility of unfilled $d$ subshell orbitals ($3d$, $4d$, etc.) which participate in hybrid bonding.

  • Elements in Period 2 ($\text{C}$, $\text{N}$, $\text{O}$, $\text{F}$) possess only $2s$ and $2p$ valence orbitals and can never exceed an octet.

  • Prominent expanded octet examples:

    • $\text{PCl}_5$: Phosphorus bonded to 5 chlorine atoms ($10\,e^-$ around $\text{P}$

    • $\text{SF}_4$: Sulfur with 4 single bonds and 1 lone pair ($10\,e^-$ around $\text{S}$

    • $\text{SF}_6$: Sulfur with 6 single bonds ($12\,e^-$ around $\text{S}$

    • $\text{BrF}_5$: Bromine with 5 single bonds and 1 lone pair ($12\,e^-$ around $\text{Br}$

    • $\text{XeF}_2$: Xenon with 2 single bonds and 3 lone pairs ($10\,e^-$ around $\text{Xe}$

    • $\text{ICl}_4^-$: Iodine with 4 single bonds and 2 lone pairs ($12\,e^-$ around $\text{I}$

Formal Charge Analysis and Resonance Theory

• Formal Charge Determination:

  • Defined as the theoretical electrical charge assigned to an individual atom within a molecule or polyatomic ion, assuming equal sharing of all bonding electrons regardless of electronegativity:     $\text{Formal Charge} = V - \left(N + \frac{1}{2}B\right)$

  • $V$ = Number of valence electrons in the free, neutral atom (from periodic group number).

  • $N$ = Number of nonbonding valence electrons (individual lone-pair dots).

  • $B$ = Number of bonding electrons shared in bonds ($\frac{1}{2}B$ equals total number of covalent bond lines attached to the atom).

• Evaluative Guidelines for Preferential Lewis Structures:

  • The sum of all formal charges in a neutral molecule must equal zero.

  • The sum of all formal charges in a polyatomic ion must equal the overall net charge of the ion.

  • Lewis structures with minimal or zero formal charges across individual atoms are thermodynamically preferred.

  • When formal charges cannot be eliminated, negative formal charges should reside on the most electronegative atoms.

  • Structures placing identical sign formal charges on adjacent bonded atoms are unfavorable.

  • Period 3 and heavier elements will preferentially form double bonds to expand their octet if doing so eliminates unfavorable formal charges on central and terminal atoms.

• Worked Formal Charge Calculations:

  • Carbon Monoxide ($\text{C}\equiv\text{O}$):

  • Total valence electrons = $4 + 6 = 10$

  • Structure: $:\text{C}\equiv\text{O}:$

  • Formal charge on $\text{C}$: $4 - (2 + 3) = -1$

  • Formal charge on $\text{O}$: $6 - (2 + 3) = +1$

  • Net sum = $(-1) + (+1) = 0$

  • Nitrite Ion ($\text{NO}_2^-$):

  • Lewis structure: $[:\ddot{\text{O}}=\ddot{\text{N}}-\ddot{\text{O}}:]^-$

  • Double-bonded Oxygen: $6 - (4 + 2) = 0$

  • Central Nitrogen: $5 - (2 + 3) = 0$

  • Single-bonded Oxygen: $6 - (6 + 1) = -1$

  • Net sum = $0 + 0 + (-1) = -1$

  • Phosphate Ion ($\text{PO}_4^{3-}$):

  • Structure A (strict octet): Four single $\text{P}-\text{O}$ bonds. Central $\text{P}$ formal charge = $5 - (0 + 4) = +1$; each of 4 Oxygens = $6 - (6 + 1) = -1$.

  • Structure B (expanded octet): One $\text{P}=\text{O}$ double bond, three single $\text{P}-\text{O}^-$ bonds. Central $\text{P}$ formal charge = $5 - (0 + 5) = 0$; double-bonded Oxygen = $6 - (4 + 2) = 0$; three single-bonded Oxygens = $-1$ each. Structure B is preferred because it eliminates formal charge on the central phosphorus atom.

• Resonance Theory and Delocalization:

  • Resonance Structures: When two or more valid, equivalent Lewis structures can be drawn for a single molecule or ion that differ solely in the spatial placement of electrons, while maintaining identical atomic skeletal connectivity.

  • Resonance Hybrid: The true physical molecule is not an oscillating blend of individual resonance contributors, but a stable composite hybrid wherein electron density is delocalized over the molecular framework.

  • Resonance Rules:

  • Atomic connectivity and nuclear positions must remain identical across all structures.

  • The total count of valence electrons must remain identical.

  • The sum of all formal charges must remain identical.

• Classic Resonance Case Studies:

  • Nitrate Ion ($\text{NO}_3^-$):

  • Three equivalent resonance forms exist, each possessing one $\text{N}=\text{O}$ double bond and two $\text{N}-\text{O}$ single bonds.

  • Experimental bond length measurement shows all three nitrogen-oxygen bonds are indistinguishable, possessing an identical intermediate length and a bond order of $1.33$ ($\frac{4\,\text{bonds}}{3\,\text{positions}}$).

  • Carbonate Ion ($\text{CO}_3^{2-}$):

  • Three equivalent resonance forms with one $\text{C}=\text{O}$ double bond and two $\text{C}-\text{O}$ single bonds, yielding equivalent bond orders of $1.33$.

  • Formate Ion ($\text{HCO}_2^-$):

  • Two equivalent resonance structures sharing the double bond character equally between both oxygen atoms ($\text{H}-\text{C}(=\text{O})-\text{O}^- \longleftrightarrow \text{H}-\text{C}(-\text{O}^-)=\text{O}$).

Valence Shell Electron Pair Repulsion Theory and Molecular Geometry

• Fundamentals of VSEPR Theory:

  • Electron groups (bonding domains and nonbonding lone pairs) surrounding a central atom repel each other electrostatically and orient themselves as far apart as possible in three-dimensional space to minimize repulsive potential energy.

  • Domain Counting Rules:

  • Each nonbonding lone pair = 1 electron domain.

  • Each covalent bond = 1 electron domain, regardless of whether it is a single, double, or triple bond.

• Five Fundamental Electron Domain Geometries (EDG):

  • 2 Electron Domains: Linear ($180^{\circ}$ bond angle)

  • 3 Electron Domains: Trigonal Planar ($120^{\circ}$ bond angle)

  • 4 Electron Domains: Tetrahedral ($109.5^{\circ}$ bond angle)

  • 5 Electron Domains: Trigonal Bipyramidal (Equatorial-equatorial = $120^{\circ}$, Axial-equatorial = $90^{\circ}$, Axial-axial = $180^{\circ}$)

  • 6 Electron Domains: Octahedral ($90^{\circ}$ and $180^{\circ}$ bond angles)

• Molecular Geometry (MG) Designations ($\text{AB}_n\text{E}_m$):

  • $\text{A}$ = central atom; $\text{B}$ = bonding atoms; $n$ = number of bonding atoms; $\text{E}$ = nonbonding lone pairs; $m$ = number of lone pairs.