Chemical Bonding, Molecular Geometry, and Molecular Orbital Theory

Comprehensive practice flashcards covering models of chemical bonding, ionic lattice energies, covalent potential energy curves, Lewis structures, formal charges, VSEPR geometries, dipole moments, Valence Bond theory, hybridization, and Molecular Orbital theory.

How do ionic, covalent, and metallic bonding differ in terms of electron behavior and typical constituent elements?

Ionic bonding involves the transfer of electrons and usually occurs between a metal and a nonmetal; covalent bonding involves the sharing of electrons and usually occurs between nonmetals; metallic bonding involves electron pooling and occurs when metals bond to each other.

What is lattice energy ($\Delta H^\circ_{\text{lattice}}$), and how is it related to ionic bond strength?

$\Delta H^\circ_{\text{lattice}}$ is the enthalpy change required to separate $1\,\text{mole}$ of an ionic solid into gaseous ions; it serves as a direct quantitative measure of the strength of an ionic bond.

According to Coulomb's Law, what mathematical relationship describes the electrostatic energy between two charged particles?

$$\text{Electrostatic energy} \propto \frac{\text{charge A} \times \text{charge B}}{\text{distance}}$$

Why does $\text{MgO}$ have a significantly larger lattice energy ($3923\,\text{kJ}$) than $\text{LiF}$ ($1050\,\text{kJ}$)?

The product of the charges in $\text{MgO}$ ($+2 \times -2 = -4$) is $4\times$ larger than that in $\text{LiF}$ ($+1 \times -1 = -1$); with approximately similar ionic sizes, lattice energy increases roughly proportionally with the charge product.

Between $\text{RbI}$ and $\text{NaBr}$, which compound has the larger lattice energy and why?

$\text{NaBr}$ has the larger lattice energy because both compounds contain single-charged ions, but $\text{Na}^+$ and $\text{Br}^-$ are smaller in ionic radius than $\text{Rb}^+$ and $\text{I}^-$, resulting in a shorter internuclear distance.

Between $\text{KCl}$ and $\text{CaS}$, which compound has the larger lattice energy and why?

$\text{CaS}$ has the larger lattice energy because $\text{Ca}^{2+}$ and $\text{S}^{2-}$ carry twice the ionic charges of $\text{K}^+$ and $\text{Cl}^-$, and ionic charge differences outweigh small differences in ionic radius.

What are the bond energy and bond length of the $H_2$ molecule at the potential energy minimum?

The bond energy of $H_2$ is $432\,\text{kJ/mol}$ (the energy required to break the bond) and its bond length is $0.74\,\text{Å}$ ($74\,\text{pm}$).

What general relationships exist among bond order, bond length, and bond energy?

For a given pair of bonded atoms, a higher bond order results in a shorter bond length and a higher bond energy (stronger bond).

How is the enthalpy of reaction ($\Delta H^\circ_{\text{rxn}}$) calculated using bond energies?

$\Delta H^\circ_{\text{rxn}} = \sum BE_{\text{reactants}} - \sum BE_{\text{products}}$, where the sum of product bond energies is subtracted from the sum of reactant bond energies.

What is the calculated $\Delta H^\circ_{\text{rxn}}$ for $H_2 + F_2 \rightarrow 2HF$, given bond energies of $432\,\text{kJ/mol}$ ($H_2$), $159\,\text{kJ/mol}$ ($F_2$), and $565\,\text{kJ/mol}$ ($HF$)?

$\Delta H^\circ_{\text{rxn}} = (432 + 159) - 2(565) = 591 - 1130 = -539\,\text{kJ}$ for $2\,\text{moles}$ of $HF$ formed (an exothermic reaction).

What is electronegativity (EN), and what are the most and least electronegative elements on the Pauling scale?

Electronegativity is an atom's tendency to attract shared electrons toward itself in a covalent bond; fluorine is the most electronegative ($EN = 4.0$), while cesium and francium are the least ($EN = 0.70$).

What are the electronegativity difference ($\Delta EN$) ranges used to classify covalent and ionic character?

Nonpolar covalent: $\Delta EN = 0$; mostly covalent: $\Delta EN \le 0.4$; polar covalent: $0.4 \le \Delta EN \le 1.7$; mostly ionic: $\Delta EN \ge 1.7$.

What is the mathematical formula for the formal charge of an atom in a Lewis structure?

$$\text{Formal charge} = \text{\# valence } e^- - \text{\# bonds} - \text{\# unshared electrons}$$

What is the measured bond length of the two identical bonds in the ozone ($O_3$) resonance hybrid?

$1.28\,\text{Å}$, which is intermediate between a single and double bond due to electron-pair delocalization across all three oxygen atoms.

What are the three common categories of exceptions to the octet rule?

1. Expanded valence shells in nonmetals of period 3 and higher (e.g., $H_2SO_4$, $PCl_5$); 2. Incomplete octets in period 2 elements like boron and beryllium (e.g., $BF_3$, $BeCl_2$); 3. Odd-electron free radicals (e.g., $NO_2$).

In VSEPR theory, why do lone pairs preferentially occupy equatorial positions rather than axial positions in a trigonal bipyramidal arrangement?

Equatorial-equatorial repulsions are weaker than axial-equatorial repulsions, so placing nonbonding electron pairs in equatorial positions minimizes electron-pair repulsions.

What molecular geometry and electron-group arrangement are illustrated in this VSEPR diagram of an $AX_4E$ molecule with one equatorial lone pair?

A seesaw molecular geometry arising from a trigonal bipyramidal electron-group arrangement (e.g., $SF_4$).

According to VSEPR theory, what molecular geometry and ideal bond angles are shown in this diagram for an $AX_4E_2$ molecule such as $XeF_4$?

Square planar geometry with ideal bond angles of $90^\circ$, derived from an octahedral electron-group arrangement where two lone pairs occupy opposite positions.

How do nonbonding lone pairs and double bonds alter ideal VSEPR bond angles?

A lone pair repels bonding pairs more than bonding pairs repel each other (e.g., $SnCl_2$ has a bond angle of $95^\circ$ instead of $120^\circ$); double bonds have greater electron density and repel adjacent single bonds more strongly (e.g., $CH_2O$ $H-C-H$ angle is $116^\circ$ instead of $120^\circ$).

How are the fractional charges ($\delta$) calculated for $HF$, given a dipole moment of $1.91\,D$ and a bond length of $0.92\,\text{Å}$?

$$\delta = \frac{\mu}{e \times d \times 3.00 \times 10^{29}\,\text{D}/(\text{C}\cdot\text{m})} = \frac{1.91\,D}{1.60 \times 10^{-19}\,\text{C} \times 0.92 \times 10^{-10}\,\text{m} \times 3.00 \times 10^{29}\,\text{D}/(\text{C}\cdot\text{m})} = \frac{1.91}{4.42} \approx 0.4$$

Why is carbon tetrachloride ($CCl_4$) nonpolar while chloroform ($CHCl_3$) has a net dipole moment of $1.0\,D$?

$CCl_4$ has four identical polar $C-Cl$ bonds arranged symmetrically in a tetrahedral shape so their dipoles cancel completely; in $CHCl_3$, the $C-H$ bond dipole does not cancel the three $C-Cl$ bond dipoles, leaving a net molecular dipole.

In Valence Bond (VB) theory, what are the two main conditions required for a covalent bond to form between two atoms?

Atomic orbitals on the bonded atoms must overlap in space, and the overlapping region must be occupied by a pair of electrons with opposite (antiparallel) spins.

What atomic orbital overlaps form the single covalent bonds in $H_2$, $F_2$, and $HF$ under Valence Bond theory?

$H_2$ forms by overlap of two $1s$ orbitals; $F_2$ forms by overlap of two singly occupied $2p$ orbitals; $HF$ forms by overlap of the $1s$ orbital of $H$ and a singly occupied $2p$ orbital of $F$.

In valence bond theory, what type of bond and orbital overlap is depicted between the two carbon atoms in ethane ($C_2H_6$)?

A sigma ($\sigma$) bond formed by the end-to-end overlap of two $sp^3$ hybrid orbitals.

What are the orbital mixing recipes, resulting hybrid orbital numbers, and geometric orientations for $sp$, $sp^2$, and $sp^3$ hybridization?

$sp$: one $s$ + one $p$ gives two $sp$ orbitals (linear, $180^\circ$, two unhybridized $p$ remain); $sp^2$: one $s$ + two $p$ gives three $sp^2$ orbitals (trigonal planar, $120^\circ$, one unhybridized $p$ remains); $sp^3$: one $s$ + three $p$ gives four $sp^3$ orbitals (tetrahedral, $109.5^\circ$, no unhybridized $p$ remain).

What is the hybridization and bond angle in ammonia ($NH_3$) and water ($H_2O$) according to VB theory?

Both central atoms are $sp^3$ hybridized; $NH_3$ has one lone pair with a measured bond angle of $107^\circ$, and $H_2O$ has two lone pairs with a measured bond angle of $104.5^\circ$.

What are the orbital hybridizations of the carbon and oxygen atoms in methanol ($CH_3OH$)?

Both the carbon atom and the oxygen atom are $sp^3$ hybridized.

How do sigma ($\sigma$) and pi ($\pi$) bonds differ in terms of orbital overlap, symmetry, and nodal planes?

A $\sigma$ bond is formed by end-to-end orbital overlap, has cylindrical symmetry with maximum electron density on the internuclear axis, and has no angular nodes; a $\pi$ bond is formed by side-to-side overlap of parallel $p$ orbitals and has a nodal plane containing the internuclear axis.

Why is rotation restricted around a carbon-carbon double bond, and what chemical consequence does this restriction cause?

Rotating around the double bond axis disrupts the parallel side-to-side overlap of the unhybridized $p$ orbitals that form the $\pi$ bond; this restricted rotation permits the existence of distinct, stable cis and trans stereoisomers (such as cis- and trans-1,2-dichloroethylene).

What is the orbital composition of the bonds in acetone, $(CH_3)_2CO$?

The methyl carbon atoms are $sp^3$ hybridized forming $\sigma$ bonds to $H(1s)$ and the central carbon; the central carbon and the carbonyl oxygen are both $sp^2$ hybridized, joined by a double bond consisting of one $\sigma$ bond ($sp^2-sp^2$ overlap) and one $\pi$ bond (overlap of unhybridized $2p$ orbitals).

Why does Molecular Orbital (MO) theory succeed where Lewis structures fail regarding the electronic ground state of $O_2$?

The Lewis structure depicts $O_2$ with all electrons paired, but MO theory correctly places two unpaired electrons into separate, degenerate $\pi^*_{2p}$ antibonding orbitals according to Hund's rule, accounting for liquid oxygen's paramagnetism.

What is the Molecular Orbital theory formula for bond order?

$$\text{Bond order} = \frac{1}{2}(\text{\# of electrons in bonding MOs} - \text{\# of electrons in antibonding MOs})$$

What are the molecular orbital bond orders for $O_2$, $O_2^+$, and $O_2^-$?

$O_2 = \frac{1}{2}(8 - 4) = 2$; $O_2^+ = \frac{1}{2}(8 - 3) = 2.5$; $O_2^- = \frac{1}{2}(8 - 5) = 1.5$.

How does removing an electron affect the bond energy and bond length of $N_2$ versus $O_2$?

In $N_2$, removing an electron from the $\sigma_{2p}$ bonding orbital yields $N_2^+$ with a lower bond order ($2.5$ vs $3$), leading to a weaker and longer bond; in $O_2$, removing an electron from a $\pi^*_{2p}$ antibonding orbital yields $O_2^+$ with a higher bond order ($2.5$ vs $2$), leading to a stronger and shorter bond.

What is the difference in molecular orbital energy ordering between $N_2$ and $O_2$, and what causes it?

In $N_2$, strong $2s-2p_z$ mixing raises $\sigma_{2p}$ above $\pi_{2p}$, giving the valence order $\sigma_{2s} < \sigma^*_{2s} < \pi_{2p} < \sigma_{2p}$; in $O_2$, the energy gap between $2s$ and $2p$ is larger, resulting in negligible mixing so $\sigma_{2p}$ lies below $\pi_{2p}$.

What technique and chemical species are highlighted in this 2004 report describing the first three-dimensional tomographic reconstruction of a single molecular orbital?

Tomographic imaging of the highest occupied molecular orbital (HOMO) of dinitrogen ($N_2$) using intense femtosecond ($10^{-15}\,\text{s}$) laser pulses at the Canadian National Research Council (CNRC).

What photochemical process initiates vision in the retina, and on what timescale does it occur?

Absorption of a photon causes a $\pi^* \leftarrow \pi$ excitation that induces cis-to-trans photoisomerization of 11-cis retinal to all-trans retinal in the protein rhodopsin, occurring in approximately $200\,\text{femtoseconds}$.

What role do the Schumann-Runge absorption bands ($175\text{--}200\,\text{nm}$) of $O_2$ play in stratospheric chemistry?

They absorb harmful UV radiation, exciting $O_2$ from the $X^3\Sigma^-_g$ ground state to the $B^3\Sigma^-_u$ state, which photodissociates into oxygen atoms that react via $O + O_2 \rightarrow O_3$ to produce ozone.