General Chemistry: Bonding Theories, Molecular Geometry, Periodic Trends, and Quantum Chemistry

Vocabulary practice flashcards covering covalent bonding, molecular orbital diagrams, hybridization, VSEPR geometries, ionic lattices, periodic properties, and foundational quantum chemistry based on CHEM 110 lectures.

Bonding Molecular Orbital

A molecular orbital formed from the in-phase linear combination of atomic orbitals (constructive interference) that increases electron probability density ($\Psi^2$) in the internuclear region and has lower energy than the parent atomic orbitals.

Antibonding Molecular Orbital

A molecular orbital formed from the out-of-phase linear combination of atomic orbitals (destructive interference) that results in decreased electron probability density between the nuclei, produces a nodal plane, and has higher energy than the parent atomic orbitals.

$s\text{-}p$ Orbital Mixing

An interaction occurring in homonuclear diatomic molecules lighter than oxygen ($\text{Li}_2$ through $\text{N}_2$) where mixing of $2s$ and $2p$ orbitals inverts the normal energy ordering, causing the $\pi_{2p}$ orbitals to be lower in energy than the $\sigma_{2p}$ orbital.

Bond Order

A theoretical index of bond stability defined by the formula: $\text{Bond Order} = \frac{1}{2}(\text{number of bonding electrons} - \text{number of antibonding electrons})$.

Paramagnetism

A magnetic property observed in a chemical species (atom, ion, or molecule) that contains one or more unpaired electrons, causing it to be attracted into an external magnetic field.

Diamagnetism

A magnetic property observed in a chemical species in which all electrons are paired, causing it to be weakly repelled by an external magnetic field.

Valence Bond Theory

A chemical bonding theory stating that a covalent bond forms when valence atomic orbitals of two atoms overlap and share a pair of electrons with opposite spins in the overlap region.

Hybridization

The mathematical mixing of non-equivalent atomic valence orbitals ($s$, $p$, $d$) on a single atom to produce a set of equivalent hybrid orbitals directed toward specific geometries.

Sigma ($\sigma$) Bond

A covalent bond formed by end-to-end orbital overlap that is cylindrically symmetrical along the internuclear bond axis, allowing free rotation.

Pi ($\pi$) Bond

A covalent bond formed by the side-to-side overlap of parallel unhybridized $p$ orbitals, resulting in electron density concentrated above and below the internuclear axis with a nodal plane along the axis.

$sp^3$ Hybridization

The mixing of one $s$ orbital and three $p$ orbitals to produce four equivalent hybrid orbitals arranged in a tetrahedral geometry with bond angles of $109.5^\circ$.

$sp^2$ Hybridization

The mixing of one $s$ orbital and two $p$ orbitals to yield three equivalent hybrid orbitals oriented in a trigonal planar geometry with ideal bond angles of $120^\circ$, leaving one unhybridized $p$ orbital.

$sp$ Hybridization

The mixing of one $s$ orbital and one $p$ orbital to produce two equivalent hybrid orbitals oriented linearly at $180^\circ$, leaving two unhybridized perpendicular $p$ orbitals available for $\pi$ bonding.

$sp^3d$ Hybridization

The combination of one $s$, three $p$, and one $d$ orbital to yield five equivalent hybrid orbitals arranged in a trigonal bipyramidal geometry with equatorial angles of $120^\circ$ and axial angles of $90^\circ$.

$sp^3d^2$ Hybridization

The combination of one $s$, three $p$, and two $d$ orbitals producing six equivalent hybrid orbitals directed toward the vertices of an octahedron with $90^\circ$ bond angles.

VSEPR Theory

Valence Shell Electron Pair Repulsion theory; a model proposing that electron groups surrounding a central atom arrange themselves as far apart as possible to minimize electrostatic repulsions.

Electron Group

Any collection of valence electrons around an atom that repels other collections; specifically defined as a lone pair, a single bond, a multiple bond (double or triple), or a single unpaired electron.

Trigonal Bipyramidal Geometry

The molecular shape corresponding to five electron groups with no lone pairs ($\text{AX}_5$), possessing axial bonds at $90^\circ$ and equatorial bonds at $120^\circ$.

Octahedral Geometry

The molecular shape characterized by six electron groups and six bonding groups ($\text{AX}_6$), with mutual bond angles of $90^\circ$.

Polar Molecule

A molecule that possesses a nonzero net dipole moment ($\mu \neq 0$) resulting from asymmetric bond polarities that do not cancel vectorially.

Lattice Energy

The standard enthalpy change associated with the complete separation of one mole of a solid ionic compound into its constituent gaseous ions: $\text{MX}(s) \rightarrow \text{M}^+(g) + \text{X}^-(g)$.

Born-Haber Cycle

A thermodynamic cycle based on Hess's Law used to calculate lattice energy indirectly from experimentally measurable values such as enthalpy of formation, sublimation, ionization energy, bond dissociation, and electron affinity.

Electronegativity ($\chi$)

The relative ability of an atom bonded within a molecule to attract the shared bonding electron density toward itself.

Polar Covalent Bond

A covalent bond formed between two atoms with an electronegativity difference ($\Delta\chi$) typically between $0.5$ and $1.9$, causing unequal electron sharing and partial charges ($\delta^+$ and $\delta^-$).

Formal Charge

The hypothetical charge an atom in a molecule would have if bonding electrons were shared equally: $\text{FC} = \text{valence } e^- - \text{lone pair } e^- - \frac{1}{2}(\text{bonding } e^-)$.

Expanded Octet

An exception to the octet rule occurring in central atoms from Period 3 and below that utilize available $d$ orbitals to accommodate more than 8 valence electrons.

Free Radical

An odd-electron chemical species that possesses an unpaired valence electron, rendering it highly reactive and paramagnetic.

Aufbau Principle

The guideline stating that electrons sequentially occupy the lowest-energy available subshells before filling higher-energy subshells when constructing the ground-state electron configuration.

Hund's Rule

The rule stating that when degenerate orbitals of equal energy are available, the lowest-energy configuration maximizes the number of unpaired electrons with parallel spins.

Pauli Exclusion Principle

A quantum mechanical principle stating that no two electrons in the same atom can share the identical set of four quantum numbers ($n$, $l$, $m_l$, $m_s$), limiting any single orbital to at most two electrons of opposite spin.

Effective Nuclear Charge ($Z_{\text{eff}}$)

The net positive nuclear charge experienced by an outer electron, calculated as the actual nuclear charge ($Z$) minus the shielding constant ($S$) produced by intervening electrons: $Z_{\text{eff}} = Z - S$.

Orbital Penetration

The spatial effect wherein an electron in an orbital with lower angular momentum has a higher probability density close to the nucleus, shielding outer orbitals and establishing the subshell energy order $s < p < d < f$ for a given principal quantum number.

Ionization Energy

The energy required for the complete removal of one mole of electrons from one mole of gaseous atoms or positive ions, which is always an endothermic quantity with a positive sign.

Electron Affinity

The energy change in $\text{kJ/mol}$ that accompanies the addition of one mole of electrons to one mole of gaseous atoms or ions to form negative ions.

Stern-Gerlach Experiment

An experiment directing a beam of silver atoms through an inhomogeneous magnetic field, demonstrating that electron spin is quantized into two discrete orientations ($m_s = +\frac{1}{2}$ and $m_s = -\frac{1}{2}$).

Radial Node

A spherical surface at a certain distance ($r$) from the nucleus where the probability density ($\Psi^2$) of finding an electron is zero, calculated by the formula: $\text{Radial nodes} = n - 1 - l$.

Angular Node

A planar or conical region passing through the nucleus where the angular wave function equals zero, whose total count is directly equal to the angular momentum quantum number ($l$).

Photoelectric Effect

The phenomenon in which electrons are ejected from a metal surface when irradiated with light whose frequency is equal to or greater than a threshold frequency ($\nu \ge \nu_0$), governed by $E_{\text{photon}} = \text{KE}_{\text{electron}} + \Phi$.

Threshold Frequency ($\nu_0$)

The minimum frequency of incident light required to eject an electron from a specific metal surface during the photoelectric effect, below which no electrons are emitted regardless of light intensity.

Work Function ($\Phi$)

The minimum energy required to overcome the electrostatic attraction binding an electron to a metal surface, defined as: $\Phi = h\nu_0$.

Blackbody Radiation

The characteristic thermal electromagnetic radiation emitted by an idealized, perfectly absorbing and emitting object, whose peak emission wavelength ($\lambda_{\text{max}}$) shifts to shorter wavelengths as temperature increases.

de Broglie Wavelength

The wavelength associated with any moving particle of matter having momentum ($p$), expressed by the equation: $\lambda = \frac{h}{p} = \frac{h}{m u}$.

Heisenberg Uncertainty Principle

A quantum fundamental principle stating that the simultaneous position ($x$) and momentum ($p$) of a particle cannot be measured with arbitrary precision: $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$.

Wavefunction ($\Psi$)

A mathematical solution to the Schrödinger equation characterized by quantum numbers ($n$, $l$, $m_l$) whose square ($\Psi^2$) describes the probability density of finding an electron in a given region of space.

Bohr Stationary State

A quantized, circular orbit in Bohr's atomic model where an orbiting electron moves without radiating energy, changing states only by absorbing or emitting a photon of energy $\Delta E = h\nu$.