Inorganic Chemistry I Notes — Chapters 1 & 2: Basic Concepts, Atomic Structure, Bonding, and Molecular Shape
Basic Concepts of Inorganic Chemistry (Chapters 1 & 2)
Inorganic vs Organic chemistry
Inorganic chemistry studies properties and reactions of inorganic compounds (all compounds except most carbon-based chains/rings called organic compounds).
Overlap with organometallic chemistry; distinction is not absolute.
Fundamental particles of the atom
Protons, neutrons, electrons
Atomic number Z = number of protons = number of electrons in a neutral atom
Mass number A = Z + number of neutrons
Isotopes: atoms with same Z but different A (different neutron numbers)
Quantum Theory and Wave Mechanics (basic ideas)
Quantum mechanics describes atomic/subatomic systems using wave-like properties of matter.
Wave-particle duality: particles can be described by waves (de Broglie concept).
The wave nature of electrons helps interpret atomic spectra and electronic configurations.
Wave function Ψ describes the state of an electron; probability density is Ψ^2.
In atoms, the wavefunction can be separated into radial and angular parts:
\Psi(\mathbf{r}) = \Psi{\text{radial}}(r) \Psi{\text{angular}}(\theta, \phi) = R(r) A(\theta, \phi)The Schrödinger equation governs these wavefunctions; solutions are atomic orbitals.
Foundational relationships
de Broglie wavelength for a particle of momentum p = mv:
\lambda = \frac{h}{mv}Heisenberg's uncertainty principle:
\Delta x \; \Delta p \ge \frac{\hbar}{2}, \quad \text{where } \hbar = \frac{h}{2\pi}To describe an electron’s position probabilistically, use the probability density from the wavefunction.
Atomic orbitals and quantum numbers
Orbitals are labeled by a set of quantum numbers (n, l, ml) and the electron spin ms.
Principal quantum number: n = 1,2,3,\ldots
Orbital quantum number: l = 0,1,2,\ldots,(n-1)
Magnetic quantum number: m_l = -l, -l+1, \ldots, +l
Spin quantum number: m_s = +\frac{1}{2} \quad \text{or} \quad -\frac{1}{2}
The four most common orbital types: s (l=0), p (l=1), d (l=2), f (l=3).
An orbital is full when it contains two electrons with opposite spins (spin-paired).
Orbitals with the same energy are degenerate (in a single electron picture); multi-electron atoms break degeneracy due to electron–nucleus interactions.
Multi-electron atoms and the Periodic Table
In neutral multi-electron atoms, orbitals with the same n but different l are not degenerate.
The Aufbau principle describes how electrons fill orbitals in order of increasing energy.
Hund’s rule: for a set of degenerate orbitals, electrons occupy empty orbitals singly with parallel spins before pairing.
Pauli exclusion principle: no two electrons in an atom can have the same set of four quantum numbers; each orbital accommodates at most two electrons with opposite spins.
Ground-state electronic configurations (conceptual)
After H, He is the next simplest; its two electrons involve attraction to the nucleus and repulsion between electrons.
Exact solutions for multi-electron atoms are not analytically available; approximate solutions are used.
In multi-electron atoms, same-n orbitals with different l are not degenerate.
Ionization energy and electron affinity
First ionization energy: energy required to remove the outermost electron from a neutral atom in the gas phase at 0 K:
X(g) \rightarrow X^+(g) + e^-Electron affinity: energy change when adding an electron to a gaseous atom (defined as the negative of the energy change at 0 K):
Y(g) + e^- \rightarrow Y^-(g)Attachment of an electron is usually exothermic; it can be endothermic for adding to an anion.
Electronegativity (Pauling scale)
Electronegativity: a measure of an atom’s ability to attract electrons in a molecule.
The Pauling scale is a practical empirical scale derived from thermochemical data.
Higher electronegativity means stronger pull on shared electrons.
Bonding Models: overview
Covalent bonding: electrons are shared between atoms.
Ionic bonding: electrons are transferred to form ions.
Lewis structures (Lewis dot structures) depict valence electrons and can rationalize molecular geometries.
Valence Bond (VB) theory: bonds arise from interaction of whole atoms; orbitals on atoms overlap to form bonds while retaining much of their character.
Molecular Orbital (MO) theory: electrons occupy molecular orbitals formed by overlapping atomic orbitals; electrons are delocalized over the molecule.
Lewis dot structures and the Octet Rule
Atoms tend to achieve eight valence electrons to imitate noble gas configurations (ns^2 np^6).
Example: O atom achieves eight valence electrons in O_2 and in oxide structures via sharing electrons.
Bond order concept:
A single bond corresponds to one shared electron pair (bond order = 1).
A double bond corresponds to two shared electron pairs (bond order = 2).
A triple bond corresponds to three shared electron pairs (bond order = 3).
Fractional bond orders (e.g., 1.5, 1.33) occur in resonance structures.
Common resonant structures can lead to average bond orders: e.g., NO2^- has bond order 1.5; NO3^- has average bond order 4/3 ≈ 1.33.
Resonance and Exceptions to the Octet Rule
Resonance structures: valid Lewis structures that contribute to the real structure; the actual structure is a resonance hybrid.
Examples:
Ozone (O_3) can be represented by two equivalent Lewis structures; the real structure has equivalent O–O bonds with bond order 1.5.
Nitrite (NO2^-) and Nitrate (NO3^-) show resonance; bond orders are 1.5 and 4/3 respectively.
Exceptions to the octet rule:
Some molecules have odd numbers of electrons (free radicals), making them highly reactive. Examples: NO, ClO2, NO2.
Heavier atoms (third period and beyond) may have expanded octets (e.g., PF5 with ten valence electrons on P; PF3 and [PO_4]^{3-} show expanded/delocalized valence structures).
BF_3 is often depicted with an incomplete octet on B (six electrons) in representative resonance structures.
Some species greatly exceed an octet (expanded valence): IF7 and XeF6 (I and Xe can accommodate 10 or more valence electrons).
Molecular Orbital (MO) Theory: basics
MO theory describes how MOs arise from interactions between atomic orbitals (AOs) of atoms in a molecule.
MO formation is allowed when orbital symmetries are compatible, overlap is significant, and the energy levels are reasonably close:
The number of MOs formed equals the number of AOs combined in the interaction.
A basis set of orbitals consists of the AOs available for interaction.
Isoelectronic species: species with the same number of electrons; often have similar structures (e.g., CH4, [BH4]^- and [NH_4]^+ are isoelectronic).
Dipole moments and molecular polarity
Symmetrical electron distribution in homonuclear diatomics leads to nonpolar bonds.
In heteronuclear diatomics, different electronegativities create polar bonds with a net dipole moment.
In polyatomic molecules, the net dipole moment depends on bond dipoles and molecular geometry. Shape strongly affects polarity.
Molecular Orbitals (specifics for light diatomics and isoelectronic concepts)
The Highest Occupied MO (HOMO) often has predominantly one type of atomic character; the Lowest Unoccupied MO (LUMO) is the first available antibonding/empty orbital.
In teaching MO diagrams for homonuclear diatomics (e.g., X2 with first-row p-block elements), the ordering of σ{2p} and π_{2p} MOs changes across the period:
As you move from Li to F, the 2s and 2p energy levels decrease due to increased effective nuclear charge, altering MO ordering and ground-state configurations.
An MO diagram example is provided for the X_2 series (with 2p-based ordering) to illustrate bonding/antibonding interactions and electronic configurations.
Molecular shape and the VSEPR model
Valence-shell electron-pair repulsion (VSEPR) theory predicts molecular shapes based on repulsions between electron pairs in the valence shell of the central atom E in EX_n.
Key repulsion hierarchy (greatest to least):
lone pair–lone pair > lone pair–bonding pair > bonding pair–bonding pair
For multiple bonds: repulsions decrease in the order: triple bond–single bond > double bond–single bond > single bond–single bond
Bonding electron density and electronegativity differences influence repulsions and geometry.
Common parent shapes (as used in teaching):
3-Coordinate: Trigonal planar; T-shaped; Trigonal pyramidal
4-Coordinate: Tetrahedral; Disphenoidal; Square planar
5-Coordinate: Trigonal bipyramidal; Square-based pyramidal; Pentagonal planar
6-Coordinate: Octahedral
7-Coordinate: Pentagonal bipyramidal
8-Coordinate: Square antiprismatic
Geometrical isomerism (spatial isomerism with the same formula):
For MX2Y2 or MX_2YZ (octahedral or related) — cis- and trans- isomers
For MX3Y3 (octahedral) — fac- and mer- isomers
In trigonal bipyramidal systems, axial and equatorial positions can lead to geometrical isomers
Examples of geometrical isomers:
Pt(PMe3)2Cl_2 with trans- and cis- forms
SnF2Me3 illustrated with cis/trans examples
fac- and mer- isomerism in octahedral MX3Y3 and related species
Summary of key equations and concepts (quick reference)
Atomic equation forms:
Ionization: X(g) \rightarrow X^+(g) + e^-
Electron affinity: Y(g) + e^- \rightarrow Y^-(g)
Bond order (from Lewis structures or MO considerations):
BO = \frac{Nb - Na}{2}where $Nb$ is the number of electrons in bonding MOs (or bonds) and $Na$ is the number of electrons in antibonding MOs
Octet rule and common exceptions (radicals, expanded octets, resonance, hypervalent species)
MO features:
Aufbau, Hund, and Pauli principles underlie electron configurations in atoms and molecules
Notional shapes and their corresponding electron-domain counts as provided in the course materials
Connections to broader themes and real-world relevance
Quantum mechanics explains electronic structure, spectroscopy, and chemical reactivity
Electronegativity and dipole moments underpin molecular polarity, reactivity trends, and intermolecular interactions
Lewis structures, resonance, and MO theory together explain bonding patterns in organic and inorganic molecules, including organometallic systems
VSEPR and geometrical isomerism help predict reactivity and properties of coordination compounds and transition metal complexes
Practical implications and examples mentioned in the material
Carbon-containing species and isoelectronic relationships (e.g., CH4, [BH4]^-, [NH_4]^+)
Typical molecules discussed: N2 (triple bond), CO2 (two C=O double bonds), SO2 (resonance with bond order ~1.5), ozone (O3) with resonance and equalized bonds
Free radicals (NO, ClO2, NO2) and their high reactivity due to odd electrons
Expanded octets in heavier elements (PF5; PF3; [PO_4]^{3-}) and exceptions to the octet rule
Exceptional cases of compounds with expanded valence such as IF7 and XeF6
Diatomic MO energy diagrams show how 2s/2p orbital energies evolve across the period, affecting MO ordering and bond strength
Suggested problems (from the transcript)
Chapter 1: 1.1, 1.3, 1.16, 1.19, 1.26, 1.37, 1.39
Chapter 2: 2.1, 2.2, 2.3, 2.4, 2.5, 2.9, 2.11, 2.13, 2.14, 2.17, 2.31
Quick cross-links to foundational principles
Quantum theory connects to spectroscopy and electronic configurations
Periodic trends (Z, effective nuclear charge) influence orbital energies and MO ordering
Bonding theories (VB vs MO) provide complementary lenses for understanding molecular structure and reactivity
Geometry, polar effects, and resonance influence physical properties and reactivity patterns in real-world compounds