Exercises

Explain how σ and π bonds are similar and how they are different.

Use valence bond theory to explain the bonding in O₂. Sketch the overlap of the atomic orbitals involved in the bonds in O₂.

A friend tells you N₂ has three π bonds due to overlap of the three p-orbitals on each N atom. Do you agree?

Why is the concept of hybridization required in valence bond theory?

Explain why a carbon atom cannot form five bonds using sp³d hybrid orbitals.

A molecule with the formula AB₃ could have one of four different shapes. Give the shape and the hybridization of the central A atom for each.

Sulfuric acid is manufactured by a series of reactions represented by the following equations:
${\text{S}}_8(s)+8{\text{O}}_2(g)⟶8{\text{SO}}_2(g)$
$2\text{S}{\text{O}}_2(g)+{\text{O}}_2(g)⟶2{\text{SO}}_3(g)$
${\text{SO}}_3(g)+{\text{H}}_2\text{O}(l)⟶{\text{H}}_2{\text{SO}}_4(l)$

Draw a Lewis structure, predict the molecular geometry by VSEPR, and determine the hybridization of sulfur for the following:

(a) circular S₈ molecule

(b) SO₂ molecule

(c) SO₃ molecule

(d) H₂SO₄ molecule (the hydrogen atoms are bonded to oxygen atoms)

Analysis of a compound indicates that it contains 77.55% Xe and 22.45% F by mass.

(a) What is the empirical formula for this compound? (Assume this is also the molecular formula in responding to the remaining parts of this exercise).

(b) Write a Lewis structure for the compound.

(c) Predict the shape of the molecules of the compound.

(d) What hybridization is consistent with the shape you predicted?

Strike-anywhere matches contain a layer of KClO₃ and a layer of P₄S₃. The heat produced by the friction of striking the match causes these two compounds to react vigorously, which sets fire to the wooden stem of the match. KClO₃ contains the ${\text{ClO}}_3{}^{\text{−}}$ ion. P₄S₃ is an unusual molecule with the skeletal structure.

(a) Write Lewis structures for P₄S₃ and the ${\text{ClO}}_3{}^{–}$ ion.

(b) Describe the geometry about the P atoms, the S atom, and the Cl atom in these species.

(c) Assign a hybridization to the P atoms, the S atom, and the Cl atom in these species.

(d) Determine the oxidation states and formal charge of the atoms in P₄S₃ and the ${\text{ClO}}_3{}^{–}$ ion.

Write Lewis structures for NF₃ and PF₅. On the basis of hybrid orbitals, explain the fact that NF₃, PF₃, and PF₅ are stable molecules, but NF₅ does not exist.

The bond energy of a C–C single bond averages 347 kJ mol⁻¹; that of a $\text{C}\equiv \text{C}$ triple bond averages 839 kJ mol⁻¹. Explain why the triple bond is not three times as strong as a single bond.

A useful solvent that will dissolve salts as well as organic compounds is the compound acetonitrile, H₃CCN. It is present in paint strippers.

(a) Write the Lewis structure for acetonitrile, and indicate the direction of the dipole moment in the molecule.

(b) Identify the hybrid orbitals used by the carbon atoms in the molecule to form σ bonds.

(c) Describe the atomic orbitals that form the π bonds in the molecule. Note that it is not necessary to hybridize the nitrogen atom.

Identify the hybridization of the central atom in each of the following molecules and ions that contain multiple bonds:

(a) ClNO (N is the central atom)

(b) CS₂

(c) Cl₂CO (C is the central atom)

(d) Cl₂SO (S is the central atom)

(e) SO₂F₂ (S is the central atom)

(f) XeO₂F₂ (Xe is the central atom)

(g) ${\text{ClOF}}_2{}^{\text{+}}$ (Cl is the central atom)

For each of the following molecules, indicate the hybridization requested and whether or not the electrons will be delocalized:

(a) ozone (O₃) central O hybridization

(b) carbon dioxide (CO₂) central C hybridization

(c) nitrogen dioxide (NO₂) central N hybridization

(d) phosphate ion $({\text{PO}}_4{}^{\mathrm{3-}})$ central P hybridization

Draw the orbital diagram for carbon in CO₂ showing how many carbon atom electrons are in each orbital.

How are the following similar, and how do they differ?

(a) σ molecular orbitals and π molecular orbitals

(b) ψ for an atomic orbital and ψ for a molecular orbital

(c) bonding orbitals and antibonding orbitals

Can a molecule with an odd number of electrons ever be diamagnetic? Explain why or why not.

Why are bonding molecular orbitals lower in energy than the parent atomic orbitals?

Explain why an electron in the bonding molecular orbital in the H₂ molecule has a lower energy than an electron in the 1s atomic orbital of either of the separated hydrogen atoms.

Determine the bond order of each member of the following groups, and determine which member of each group is predicted by the molecular orbital model to have the strongest bond.

(a) H₂, ${\text{H}}_2{}^{\text{+}},$ ${\text{H}}_2{}^{\text{−}}$

(b) O₂, ${\text{O}}_2{}^{\text{2+}},$ ${\text{O}}_2{}^{\text{2−}}$

(c) Li₂, ${\text{Be}}_2{}^{\text{+}},$ Be₂

(d) F₂, ${\text{F}}_2{}^{\text{+}},$ ${\text{F}}_2{}^{\text{−}}$

(e) N₂, ${\text{N}}_2{}^{\text{+}},$ ${\text{N}}_2{}^{\text{−}}$

Compare the atomic and molecular orbital diagrams to identify the member of each of the following pairs that has the highest first ionization energy (the most tightly bound electron) in the gas phase:

(a) H and H₂

(b) N and N₂

(c) O and O₂

(d) C and C₂

(e) B and B₂

A friend tells you that the 2s orbital for fluorine starts off at a much lower energy than the 2s orbital for lithium, so the resulting σ_2s molecular orbital in F₂ is more stable than in Li₂. Do you agree?

What charge would be needed on F₂ to generate an ion with a bond order of 2?

Explain why ${\text{N}}_2{}^{\text{2+}}$ is diamagnetic, while ${\text{O}}_2{}^{\text{4+}},$ which has the same number of valence electrons, is paramagnetic.