Advanced Theories of Covalent Bonding

What is the hybridization of the selenium atom in SeF₄?

Acetic acid, H₃CC(O)OH, is the molecule that gives vinegar its odor and sour taste. What is the hybridization of the two carbon atoms in acetic acid?

Draw a curve that describes the energy of a system with H and CI atoms at varying distances. Then, find the minimum energy of this curve two ways.

(a) Use the bond energy found in Table 8.1 to calculate the energy for one single HCl bond (Hint: How many bonds are in a mole?)

(b) Use the enthalpy of reaction and the bond energies for \({{\rm{H}}_{\rm{2}}}\)and \({\rm{C}}{{\rm{l}}_{\rm{2}}}\) to solve for the energy of one mole of \({\rm{HCl}}\)bonds.

\({{\text{H}}_{\text{2}}}{\text{(g) + C}}{{\text{l}}_{\text{2}}}{\text{(g)}} \rightleftharpoons {\text{2HCl(g)}}\) ΔH°_rxn = −184.7 kJ/mol

Another acid in acid rain is nitric acid, HNO₃, which is produced by the reaction of nitrogen dioxide, NO₂, with atmospheric water vapor. What is the hybridization of the nitrogen atom in NO₂? (Note: the lone electron on nitrogen occupies a hybridized orbital just as a lone pair would.)

Label the molecular orbital shown as σ  or Π, bonding or antibonding, and indicate where the node occurs.

The main component of air is N₂. From the molecular orbital diagram of N₂, predict its bond order and whether it is diamagnetic or paramagnetic.

How many unpaired electrons would be present on a Be₂^2-  ion? Would it be paramagnetic or diamagnetic?

Explain how \({\rm{\sigma }}\) and \({\rm{\pi }}\) bonds are similar and how they are different.

Explain why bonds occur at specific average bond distances instead of the atoms approaching each other infinitely close.

Use valence bond theory to explain the bonding in\({{\rm{F}}_2},{\rm{HF}}\), and\({\rm{ClBr}}\). Sketch the overlap of the atomic orbitals involved in the bonds.

Use valence bond theory to explain the bonding in\({{\rm{O}}_{\rm{2}}}\). Sketch the overlap of the atomic orbitals involved in the bonds in \({{\rm{O}}_{\rm{2}}}\).

How many \({\rm{\sigma }}\)and \({\rm{\pi }}\)bonds are present in the molecule HCN?

A friend tells you \({{\rm{N}}_{\rm{2}}}\)has three \({\rm{\pi }}\)bonds due to overlap of the three p-orbitals on each N atom. Do you agree?

Draw the Lewis structures for \({\rm{C}}{{\rm{O}}_{\rm{2}}}\)and\({\rm{CO}}\), and predict the number of \({\rm{\sigma }}\) and \({\rm{\pi }}\) bonds for each molecule.

(a) \({\rm{C}}{{\rm{O}}_{\rm{2}}}\) 

(b) \({\rm{CO}}\)

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

Give the shape that describes each hybrid orbital set:

(a) \({\rm{s}}{{\rm{p}}^{\rm{2}}}\)

(b) \({\rm{s}}{{\rm{p}}^{\rm{3}}}{\rm{d}}\)

(c) sp

(d) \({\rm{s}}{{\rm{p}}^{\rm{3}}}{{\rm{d}}^{\rm{2}}}\)

What is the hybridization of the central atom in each of the following?

(a) \({\rm{Be}}{{\rm{H}}_{\rm{2}}}\)

(b) \({\rm{S}}{{\rm{F}}_{\rm{6}}}\)

(c) \({\rm{PO}}_{\rm{4}}^{{\rm{3 - }}}\)

(d) \({\rm{PC}}{{\rm{l}}_{\rm{5}}}\)

Methionine, \({\rm{C}}{{\rm{H}}_{\rm{3}}}{\rm{SC}}{{\rm{H}}_{\rm{2}}}{\rm{C}}{{\rm{H}}_{\rm{2}}}{\rm{CH}}\left( {{\rm{N}}{{\rm{H}}_{\rm{2}}}} \right){\rm{C}}{{\rm{O}}_{\rm{2}}}{\rm{H}}\), is an amino acid found in proteins. Draw a Lewis structure of this compound. What is the hybridization type of each carbon, oxygen, the nitrogen, and the sulfur?

Sulfuric acid is manufactured by a series of reactions represented by the following equations:

\(\begin{array}{l}{{\rm{S}}_{\rm{8}}}{\rm{(s) + 8}}{{\rm{O}}_{\rm{2}}}{\rm{(g)}} \to {\rm{8S}}{{\rm{O}}_{\rm{2}}}{\rm{(g)}}\\{\rm{2S}}{{\rm{O}}_{\rm{2}}}{\rm{(g) + }}{{\rm{O}}_{\rm{2}}}{\rm{(g)}} \to {\rm{2S}}{{\rm{O}}_{\rm{3}}}{\rm{(g)}}\\{\rm{S}}{{\rm{O}}_{\rm{3}}}{\rm{(g) + }}{{\rm{H}}_{\rm{2}}}{\rm{O(l)}} \to {{\rm{H}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}{\rm{(l)}}\end{array}\)

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

(a) circular \({{\rm{S}}_{\rm{8}}}\)molecule

(b) \({\rm{S}}{{\rm{O}}_{\rm{2}}}\)molecule

(c) \({\rm{S}}{{\rm{O}}_{\rm{3}}}\)molecule

(d) \({{\rm{H}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}\)molecule (the hydrogen atoms are bonded to oxygen atoms)

For many years after they were discovered, it was believed that the noble gases could not form compounds. Now we know that belief to be incorrect. A mixture of xenon and fluorine gases, confined in a quartz bulb and placed on a windowsill, is found to slowly produce a white solid. Analysis of the compound indicates that it contains \({\rm{77}}{\rm{.55\% }}\)Xe and \({\rm{22}}{\rm{.45\% \;F}}\)by mass.

(a) What is the formula of the compound?

(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?

For the carbonate ion, \({\rm{C}}{{\rm{O}}_{\rm{3}}}^{{\rm{2 - }}}\), draw all of the resonance structures. Identify which orbitals overlap to create each bond.

Consider nitrous acid, \({\rm{HN}}{{\rm{O}}_{\rm{2}}}{\rm{(HONO)}}\). (a) Write a Lewis structure. (b) What are the electron pair and molecular geometries of the internal oxygen and nitrogen atoms in the \({\rm{HN}}{{\rm{O}}_{\rm{2}}}\) molecule? (c) What is the hybridization on the internal oxygen and nitrogen atoms in \({\rm{HN}}{{\rm{O}}_{\rm{2}}}\)?

Strike-anywhere matches contain a layer of \({\rm{KCl}}{{\rm{O}}_{\rm{3}}}\) and a layer of \({{\rm{P}}_{\rm{4}}}{{\rm{S}}_{\rm{3}}}\). 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. \({\rm{KCl}}{{\rm{O}}_{\rm{3}}}\) contains the \({\rm{Cl}}{{\rm{O}}_{\rm{3}}}^{\rm{ - }}\) ion. \({{\rm{P}}_{\rm{4}}}{{\rm{S}}_{\rm{3}}}\) is an unusual molecule with the skeletal structure.

1. Write Lewis structures for \({{\rm{P}}_{\rm{4}}}{{\rm{S}}_{\rm{3}}}\) and the \({\rm{Cl}}{{\rm{O}}_{\rm{3}}}^{\rm{ - }}\) ion. 
2. Describe the geometry about the \({\rm{P}}\) atoms, the \({\rm{S}}\) atom, and the \({\rm{Cl}}\) atom in these species. 
3. Assign a hybridization to the \({\rm{P}}\) atoms, the  \({\rm{S}}\)atom, and the \({\rm{Cl}}\) atom in these species. 
4. Determine the oxidation states and formal charge of the atoms in \({{\rm{P}}_{\rm{4}}}{{\rm{S}}_{\rm{3}}}\) and the \({\rm{Cl}}{{\rm{O}}_{\rm{3}}}^{\rm{ - }}\) ion.

Identify the hybridization of each carbon atom in the following molecule. (The arrangement of atoms is given; you need to determine how many bonds connect each pair of atoms.)

Write Lewis structures for \({\rm{N}}{{\rm{F}}_{\rm{3}}}\) and \({\rm{P}}{{\rm{F}}_{\rm{5}}}\). On the basis of hybrid orbitals, explain the fact that \({\rm{N}}{{\rm{F}}_{\rm{3}}}\), \({\rm{P}}{{\rm{F}}_{\rm{3}}}\), and \({\rm{P}}{{\rm{F}}_{\rm{5}}}\) are stable molecules, but \({\rm{N}}{{\rm{F}}_{\rm{5}}}\) does not exist.

In addition to \({\rm{N}}{{\rm{F}}_{\rm{3}}}\), two other fluoro derivatives of nitrogen are known: \({{\rm{N}}_{\rm{2}}}{{\rm{F}}_{\rm{4}}}\) and \({{\rm{N}}_{\rm{2}}}{{\rm{F}}_{\rm{2}}}\). What shapes do you predict for these two molecules? What is the hybridization for the nitrogen in each molecule?

A useful solvent that will dissolve salts as well as organic compounds is the compound acetonitrile, \({{\rm{H}}_{\rm{3}}}{\rm{CCN}}\). 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 \({\rm{\sigma }}\) bonds. (c) Describe the atomic orbitals that form the   \({\rm{\pi }}\) bonds in the molecule. Note that it is not necessary to hybridize the nitrogen atom.

For the molecule allene, \({{\rm{H}}_{\rm{2}}}{\rm{C = C = C}}{{\rm{H}}_{\rm{2}}}\) , give the hybridization of each carbon atom. Will the hydrogen atoms be in the same plane or perpendicular planes?

The bond energy of a C–C single bond averages \({\rm{347 kJ mo}}{{\rm{l}}^{{\rm{ - 1}}}}\); that of a 

C ≡ C triple bond averages \({\rm{839 kJ mo}}{{\rm{l}}^{{\rm{ - 1}}}}\). Explain why the triple bond is not three times as strong as a single bond.

Identify the hybridization of the central atom in each of the following molecules and ions that contain multiple bonds: (a) \({\rm{ClNO}}\) (\({\rm{N}}\) is the central atom) (b) \({\rm{C}}{{\rm{S}}_{\rm{2}}}\) (c) \({\rm{C}}{{\rm{l}}_{\rm{2}}}{\rm{CO}}\) (\({\rm{C}}\) is the central atom) (d) \({\rm{C}}{{\rm{l}}_{\rm{2}}}{\rm{SO}}\) (\({\rm{S}}\) is the central atom) (e) \({\rm{S}}{{\rm{O}}_{\rm{2}}}{{\rm{F}}_{\rm{2}}}\) (\({\rm{S}}\) is the central atom) (f) \({\rm{Xe}}{{\rm{O}}_{\rm{2}}}{{\rm{F}}_{\rm{2}}}\) (\({\rm{Xe}}\) is the central atom) (g) \({\rm{ClO}}{{\rm{F}}_{\rm{2}}}^{\rm{ + }}\) (\({\rm{Cl}}\) is the central atom).

Describe the molecular geometry and hybridization of the N, P, or S atoms in each of the following compounds. (a) \({{\rm{H}}_{\rm{3}}}{\rm{P}}{{\rm{O}}_{\rm{4}}}\), phosphoric acid, used in cola soft drinks (b) \({\rm{N}}{{\rm{H}}_{\rm{4}}}{\rm{N}}{{\rm{O}}_{\rm{3}}}\) , ammonium nitrate, a fertilizer and explosive (c) \({{\rm{S}}_{\rm{2}}}{\rm{C}}{{\rm{l}}_{\rm{2}}}\), disulfur dichloride, used in vulcanizing rubber (d) \({{\rm{K}}_{\rm{4}}}{\rm{[}}{{\rm{O}}_{\rm{3}}}{\rm{POP}}{{\rm{O}}_{\rm{3}}}{\rm{]}}\), potassium pyrophosphate, an ingredient in some toothpastes

For each of the following molecules, indicate the hybridization requested and whether or not the electrons will be delocalized: (a) ozone (\({{\rm{O}}_{\rm{3}}}\)) central \({\rm{O}}\) hybridization (b) carbon dioxide (\({\rm{C}}{{\rm{O}}_{\rm{2}}}\)) central \({\rm{C}}\) hybridization (c) nitrogen dioxide (\({\rm{N}}{{\rm{O}}_{\rm{2}}}\)) central \({\rm{N}}\) hybridization (d) phosphate ion (\({\rm{P}}{{\rm{O}}_{\rm{4}}}^{{\rm{3 - }}}\)) central \({\rm{P}}\) hybridization.

For each of the following structures, determine the hybridization requested and whether the electrons will be delocalized:

(a)Hybridization of each carbon

(c)

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

Sketch the distribution of electron density in the bonding and antibonding molecular orbitals formed from two S orbitals and from two P orbitals.

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

If molecular orbitals are created by combining five atomic orbitals from atom A and five atomic orbitals from atom B combine, how many molecular orbitals will result?

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

Can a molecule with an even number of electrons ever be paramagnetic? Explain why or why not

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

Calculate the bond order for an ion with this configuration: \({\left( {{{\bf{\sigma }}_{{\bf{2s}}}}} \right)^{\bf{2}}}{\left( {{\bf{\sigma }}_{{\bf{2s}}}^{\bf{*}}} \right)^{\bf{2}}}{\left( {{{\bf{\sigma }}_{{\bf{2px}}}}} \right)^{\bf{2}}}{\left( {{{\bf{\pi }}_{{\bf{2py}}}}{\bf{,}}{{\bf{\pi }}_{{\bf{2pz}}}}} \right)^{\bf{4}}}{\left( {{\bf{\pi }}_{{\bf{2py}}}^{\bf{*}}{\bf{,\pi }}_{{\bf{2pz}}}^{\bf{*}}} \right)^{\bf{3}}}\).

The bonding molecular orbital in \({{\rm{H}}_2}\) is lower in energy than an electron in \({\rm{1s}}\) orbital because the bonding molecular is more stable.

Predict the valence electron molecular orbital configurations for the following, and state whether they will be stable or unstable ions.

(a) \({\rm{N}}{{\rm{a}}_{\rm{2}}}^{{\rm{2 + }}}\)

(b) \({\rm{M}}{{\rm{g}}_{\rm{2}}}^{{\rm{2 + }}}\)

(c) \({\rm{A}}{{\rm{l}}_{\rm{2}}}^{{\rm{2 + }}}\)

(d) \({\rm{S}}{{\rm{i}}_{\rm{2}}}^{{\rm{2 + }}}\)

(e) \({\rm{P}}_{\rm{2}}^{{\rm{2 + }}}\)

(f) \({{\rm{S}}_{\rm{2}}}^{{\rm{2 + }}}\)

(g) \({{\rm{F}}_{\rm{2}}}^{{\rm{2 + }}}\)

(h) \({\rm{A}}{{\rm{r}}_{\rm{2}}}^{{\rm{2 + }}}\)

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) \({{\rm{H}}_{\rm{2}}}{\rm{,}}{{\rm{H}}_{\rm{2}}}{\rm{ + ,H}}_{\rm{2}}^{\rm{ - }}\)

(b) \({{\rm{O}}_{\rm{2}}}{\rm{,O}}_{\rm{2}}^{{\rm{2 + }}}{\rm{,O}}_{\rm{2}}^{{\rm{2 - }}}\)

(c) \({\rm{L}}{{\rm{i}}_{\rm{2}}}{\rm{,B}}{{\rm{e}}_{\rm{2}}}{\rm{ + ,B}}{{\rm{e}}_{\rm{2}}}\)

(d) \({{\rm{F}}_{\rm{2}}}{\rm{,\;}}{{\rm{F}}_{\rm{2}}}{\rm{ + ,}}\;\;\;{\rm{F}}_{\rm{2}}^{\rm{ - }}\) 

(e) \({{\rm{N}}_{\rm{2}}}{\rm{,\;N}}_{\rm{2}}^{\rm{ + }}{\rm{,}}\;\;\;{\rm{N}}_{\rm{2}}^{\rm{ - }}\)

For the first ionization energy for an \({{\rm{N}}_2}\) molecule, what molecular orbital is the electron removed from?

A typical barometric pressure in Redding, California, is about 750mm Hg. Calculate this pressure in atm and kPa.

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) \({\rm{H}}\) and \({{\rm{H}}_{\rm{2}}}\)

(b) \({\rm{N}}\)and \({{\rm{N}}_{\rm{2}}}\) 

(c) \({\rm{O}}\)and \({{\rm{O}}_{\rm{2}}}\)

(d) \({\rm{C}}\)and \({{\rm{C}}_{\rm{2}}}\)

(e) \({\rm{B}}\)and \({{\rm{B}}_{\rm{2}}}\)

Which of the period 2 homonuclear diatomic molecules are predicted to be paramagnetic?

A friend tells you that the \({\rm{2s}}\)orbital for fluorine starts off at a much lower energy than the \({\rm{2s}}\) orbital for lithium, so the resulting \({{\rm{\sigma }}_{{\rm{2s}}}}\) molecular orbital in \({{\rm{F}}_{\rm{2}}}\) is more stable than in \({\rm{L}}{{\rm{i}}_{\rm{2}}}\). Do you agree?

True or false: Boron contains \({\rm{2}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{p}}^{\rm{1}}}\)valence electrons, so only one \({\rm{p}}\)- orbital is needed to form molecular orbitals.