AP Chemistry 2.7: VSEPR and Bond Hybridization

What are axial and equatorial positions in a trigonal bipyramidal arrangement?

Axial positions lie above and below the central atom and have three $90^\circ$ interactions. Equatorial positions lie around the central atom and have more space because they involve $120^\circ$ angles.

Where do lone pairs preferentially reside in a trigonal bipyramidal electron-pair geometry?

Lone pairs occupy equatorial positions because these positions minimize the number of strong $90^\circ$ repulsions. This placement is important for structures such as SF₄ and ClF₃.

What are the electron-pair geometry and molecular structure of SF₄?

The electron-pair geometry is trigonal bipyramidal. One equatorial lone pair produces a seesaw molecular structure.

What are the electron-pair geometry and molecular structure of ClF₃?

The electron-pair geometry is trigonal bipyramidal. Two equatorial lone pairs leave three bonded atoms in a T-shaped molecular structure.

What are the electron-pair geometry and molecular structure of XeF₂?

The electron-pair geometry is trigonal bipyramidal, with three lone pairs occupying equatorial positions. The two fluorine atoms occupy axial positions, giving a linear molecular structure.

How are two lone pairs arranged in an octahedral electron-pair geometry?

They are placed opposite each other, $180^\circ$ apart, to minimize lone pair–lone pair repulsion. The remaining four bonds form a square planar molecular structure.

What are the electron-pair geometry and molecular structure of XeF₄?

The electron-pair geometry is octahedral. Two lone pairs occupy opposite positions, leaving four fluorine atoms in a square planar molecular structure.

How is VSEPR applied to a molecule with multiple central atoms, such as glycine?

Each interior atom is analyzed independently as a local center by counting its own electron regions. The overall molecular shape depends on how these local geometries are connected and oriented.

What is hybridization?

Hybridization is the mixing of atomic orbitals on the same atom to form equivalent hybrid orbitals oriented for bonding or for accommodating lone pairs.

How can the hybridization of a central atom be predicted?

Count the electron regions around the atom, including bonding regions and lone pairs. The steric number corresponds to the number of hybrid orbitals: 2 for $sp$, 3 for $sp^2$, 4 for $sp^3$, 5 for $sp^3d$, and 6 for $sp^3d^2$.

What hybridization corresponds to two electron regions?

Two electron regions correspond to $sp$ hybridization and a linear electron geometry with an ideal angle of $180^\circ$.

What hybridization corresponds to three electron regions?

Three electron regions correspond to $sp^2$ hybridization and a trigonal planar electron geometry with ideal angles of approximately $120^\circ$.

What hybridization corresponds to four electron regions?

Four electron regions correspond to $sp^3$ hybridization and a tetrahedral electron geometry with ideal angles of $109.5^\circ$.

What hybridization corresponds to five electron regions?

Five electron regions correspond to $sp^3d$ hybridization and a trigonal bipyramidal electron geometry.

What hybridization corresponds to six electron regions?

Six electron regions correspond to $sp^3d^2$ hybridization and an octahedral electron geometry.

What is a sigma ($\sigma$) bond?

A sigma bond forms through direct, head-on overlap of orbitals along the internuclear axis. Every single bond contains one sigma bond.

What is a pi ($\pi$) bond?

A pi bond forms through sideways overlap of parallel unhybridized orbitals, usually p orbitals, above and below the internuclear axis.

How many sigma and pi bonds are in single, double, and triple bonds?

A single bond contains one $\sigma$ bond; a double bond contains one $\sigma$ and one $\pi$ bond; a triple bond contains one $\sigma$ and two $\pi$ bonds.

How does hybridization relate to sigma and pi bonding?

Hybrid orbitals commonly form sigma bonds or hold lone pairs. Unhybridized p orbitals can overlap sideways to form pi bonds, so double and triple bonds require available unhybridized orbitals.

Why is rotation restricted around a double bond?

Rotation would disrupt the sideways overlap that forms the pi bond. A double bond therefore contains a rigid sigma-plus-pi bonding arrangement.

Polar covalent bond

A covalent bond in which electrons are shared unequally because the bonded atoms have different electronegativities. The more electronegative atom has partial negative charge, $\delta^-$, and the other has partial positive charge, $\delta^+$.

How does electronegativity difference affect a bond dipole?

A larger electronegativity difference generally produces greater charge separation and a larger bond dipole moment. The dipole direction points toward the more electronegative atom.

Bond dipole moment

A vector that represents the magnitude and direction of charge separation in a polar bond. It points from the less electronegative, partially positive atom toward the more electronegative, partially negative atom.

What quantitative relationship defines a bond dipole moment?

The magnitude is given by $\mu=Qr$, where $Q$ is the magnitude of the separated partial charge and $r$ is the distance between the charges.

Molecular dipole moment

The net vector sum of all bond dipole moments in a molecule, taking the three-dimensional molecular structure into account. It measures the molecule's overall separation of charge.

What two conditions must be met for a molecule to be polar?

The molecule must contain at least one polar covalent bond, and its molecular geometry must prevent all bond dipoles from canceling. A molecule with a net dipole moment is polar.

How can molecular polarity be determined from a Lewis structure?

Use electronegativities to identify polar bonds, use VSEPR to determine the three-dimensional molecular structure, and then add the bond dipole vectors. If the vector sum is zero, the molecule is nonpolar; otherwise it is polar.

Why is CO₂ nonpolar even though each C=O bond is polar?

CO₂ is linear, so the two equal C=O bond dipoles point in opposite directions and cancel. Its net dipole moment is zero.

Why is H₂O polar even though it has two identical O–H bonds?

Water has a bent molecular structure caused by two lone pairs on oxygen. The two O–H bond dipoles therefore do not point in opposite directions and their vector sum is nonzero.

Why is BF₃ nonpolar?

BF₃ has three identical polar B–F bonds arranged symmetrically in a trigonal planar geometry. Their dipole vectors cancel, giving a net dipole moment of zero.

Why is NH₃ polar?

NH₃ has polar N–H bonds and a trigonal pyramidal structure caused by a lone pair on nitrogen. The bond dipoles do not cancel, so ammonia has a net molecular dipole.

Can a molecule with identical polar bonds still be polar?

Yes. If the molecular geometry is not sufficiently symmetric, identical bond dipoles may have a nonzero vector sum. H₂S and NH₃ are examples.

Why is CH₃Cl polar?

The tetrahedral molecule has three slightly polar C–H bonds and a more strongly polar C–Cl bond. Because the bond dipoles are not symmetrically canceled, CH₃Cl has a net dipole moment directed generally toward chlorine.

What is the net dipole moment of a homonuclear diatomic molecule such as N₂?

It is zero because the two atoms have identical electronegativities and the bond has no charge separation. Such molecules are nonpolar.

How do the molecular structures of CH₄, PF₅, and SF₆ relate to their polarity?

Each has identical bonds arranged in a highly symmetric geometry—tetrahedral, trigonal bipyramidal, and octahedral, respectively. Their bond dipoles cancel, so all three molecules are nonpolar.

What happens to polar molecules in an external electric field?

They tend to align with the field, placing their partially positive end toward the negative plate and their partially negative end toward the positive plate. Nonpolar molecules do not have a permanent dipole for this type of alignment.

How does polarity affect solubility?

Polar solvents generally dissolve polar substances, while nonpolar solvents generally dissolve nonpolar substances. This reflects favorable interactions between substances with similar charge distributions.

Bond angle

The angle between two bonds that share a common atom, usually measured in degrees.

What does VSEPR theory predict?

Valence shell electron-pair repulsion theory predicts the three-dimensional arrangement of electron regions around a central atom and the approximate molecular shape and bond angles.

Electron region

A region of electron density around a central atom, such as a lone pair or a single, double, or triple bond. Each bond, regardless of its order, counts as one electron region in VSEPR analysis.

What fundamental assumption does VSEPR theory make about electron regions?

Electron regions in the valence shell of a central atom arrange themselves as far apart as possible to minimize electrostatic repulsions.

What are the five basic electron-pair geometries and their numbers of electron regions?

Two regions give linear geometry, three give trigonal planar, four give tetrahedral, five give trigonal bipyramidal, and six give octahedral geometry.

Electron-pair geometry versus molecular structure

Electron-pair geometry includes both bonding pairs and lone pairs around the central atom. Molecular structure describes only the positions of bonded atoms, so it can differ from the electron-pair geometry when lone pairs are present.

How do you use VSEPR theory to determine a molecule's shape?

Draw the Lewis structure, count electron regions around the central atom, identify the corresponding electron-pair geometry, and then use the number and placement of lone pairs to determine the molecular structure.

What is the molecular structure of a central atom with two electron regions and no lone pairs?

It is linear, with an ideal bond angle of $180^\circ$. BeF₂ and CO₂ are examples.

What are the electron-pair geometry and molecular structure of BCl₃?

Both are trigonal planar because boron has three bonding regions and no lone pairs. The ideal bond angles are approximately $120^\circ$.

What are the electron-pair geometry and molecular structure of CH₄?

Both are tetrahedral because carbon has four bonding regions and no lone pairs. The ideal H–C–H bond angle is $109.5^\circ$.

What are the electron-pair geometry and molecular structure of NH₃?

The electron-pair geometry is tetrahedral, but the molecular structure is trigonal pyramidal because nitrogen has three bonds and one lone pair. Its bond angles are slightly less than $109.5^\circ$.

What are the electron-pair geometry and molecular structure of H₂O?

The electron-pair geometry is tetrahedral, while the molecular structure is bent because oxygen has two bonds and two lone pairs. The H–O–H angle is approximately $104.5^\circ$.

What is the relative order of VSEPR repulsions?

Lone pair–lone pair repulsion is strongest, followed by lone pair–bonding pair repulsion, then bonding pair–bonding pair repulsion: $\text{LP–LP}>\text{LP–BP}>\text{BP–BP}$.

Why are bond angles in NH₃ and H₂O smaller than the ideal tetrahedral angle?

Lone pairs occupy more space and repel more strongly than bonding pairs, compressing the angles between bonds. Thus NH₃ has angles slightly below $109.5^\circ$, and H₂O is compressed to about $104.5^\circ$.

What is the relative size of electron regions in VSEPR theory?

From largest to smallest, electron regions generally occupy space in the order: lone pair $>$ triple bond $>$ double bond $>$ single bond.

How does a multiple bond affect nearby bond angles?

A multiple bond contains more electron density than a single bond, so it repels neighboring regions more strongly. For example, in formaldehyde, the angle adjacent to the C=O bond is slightly larger than $120^\circ$, while the angle between the C–H bonds is slightly smaller.

What are the electron-pair geometry and molecular structure of H₃O⁺?

The electron-pair geometry is tetrahedral because there are four electron regions around oxygen. Three O–H bonds and one lone pair give a trigonal pyramidal molecular structure.

How does resonance affect VSEPR counting in CO₃²⁻?

Carbonate has three electron regions around carbon and no lone pairs, so both its electron-pair geometry and molecular structure are trigonal planar. Resonance makes all three C–O bonds equivalent, but each still counts as one region.