Theories of Covalent Bonding

What type of central-atom orbital hybridization corresponds to each electron-group arrangement:

(a) trigonal planar

(b) octahedral

(c) linear

(d) tetrahedral

(e) trigonal bipyramidal?

How do carbon and silicon differ with regard to the types of orbitals available forhybridization? Explain.

How many hybrid orbitals form when four atomic orbitals of a central atom mix? Explain

Give the number and type of hybrid orbital that forms when each set of atomic orbitals mixes:

(a) two d, one s, and one p

(b) three p and one s

Give the number and type of hybrid orbital that forms when each set of atomic orbitals mixes:

(a) one p and one s       

(b) three p, one d, and one s

What is the orbital hybridization of a central atom that has one lone pair and bonds to

1. two other atoms;
2.  three other atoms;
3.  four other atoms;
4.  five other atoms?

What is the hybridization of nitrogen in each of the following: (a) NO; (b) ${\mathbf{NO}}_{\mathbf{2}}$ ; (c) ${{\mathbf{NO}}^{\mathbf{.}}}_{\mathbf{2}}$ ?

What is the hybridization of carbon in each of the following: (a) ${\mathbf{CO}}_{\mathbf{3}}^{\mathbf{2}\mathbf{-}}$ ; (b) ${\mathbf{C}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{4}}^{\mathbf{2}\mathbf{-}}$ ;(c) ${\mathbf{NCO}}^{\mathbf{-}}$ ?

What is the hybridization of bromine in each of the following: (a) BrF₂ ; (b) BrO₂ ; (c) BrF₅ ?

Which types of atomic orbitals of the central atom mix to form hybrid orbitals in 

(a) SiCIH₃ ; (b) CS₂ ; (c) SCI₃F ; (d) NF₃ ?

2-Butene ($\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathit{C}\mathit{H}\mathbf{=}\mathit{C}\mathit{H}\mathit{C}{\mathit{H}}_{\mathbf{3}}$) is a starting material in the manufacture of lubricating oils and many other compounds. Draw two different structures for 2-butene, indicating the sigma and pi bonds in each.

Describe the hybrid orbitals used by the central atom(s) and the type(s) of bonds formed in 

(a) $\mathit{B}\mathit{r}{\mathit{F}}_{\mathbf{3}}$;     (b) $\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathit{C}\mathbf{=}\mathit{C}\mathit{H}$;     (c)  $\mathit{S}{\mathit{O}}_{\mathbf{2}}$

Describe the hybrid orbitals used by the central atom(s) and the type(s) of bonds formed in

1. $\mathit{F}\mathit{N}\mathit{O}$;

2. ${\mathit{C}}_{\mathbf{2}}{\mathit{F}}_{\mathbf{4}}$;

3. ${\mathbf{\left(}\mathbf{CN}\mathbf{\right)}}_{\mathbf{2}}$

Describe the hybrid orbitals used by the central atom and the type(s) of bonds formed in

(a) ${\mathit{O}}_{\mathbf{3}}$

(b) ${{\mathit{I}}_{\mathbf{3}}}^{\mathbf{-}}$

(c) $\mathit{C}\mathit{O}\mathit{C}{\mathit{I}}_{\mathbf{2}}$ (C is central)

Describe the hybrid orbitals used by the central atom and the type(s) of bonds formed in

(a) $\mathit{N}{{\mathit{O}}_{\mathbf{3}}}^{\mathbf{-}}$

(b) $\mathit{C}{\mathit{S}}_{\mathbf{2}}$

(c) $\mathit{C}{\mathit{H}}_{\mathbf{2}}\mathit{O}$

What is the hybridization of chlorine in each of the following: (a) ${{\mathbf{CO}}_{\mathbf{2}}}^{\mathbf{-}}$; (b) ${{\mathbf{ClO}}_{\mathbf{3}}}^{\mathbf{-}}$ ; (c) ${{\mathbf{ClO}}_{\mathbf{4}}}^{\mathbf{-}}$ ?

Methyl isocyanate, is an intermediate in the manufacture of many pesticides. It received notoriety in 1984 when a leak from a manufacturing plant resulted in the death of more than 2000 people in Bhopal, India. What are the hybridizations of the N atom and the two C atoms in methyl isocyanate? Sketch the molecular shape.

How do the bonding and antibonding MOs formed from a given pair of AOs compare to each other with respect to

(a) Energy

(b) Presence of nodes

(c) Inter-nuclear electron density

Question: The molecular orbitals depicted below are derived from $\mathbf{n}\mathbf{=}\mathbf{2}$ atomic orbitals.

(a) Give the orbital designations. 

(b) Which is highest in energy? 

(c) Lowest in energy? 

(d) Rank the MO’s in order of increasing energy for  ${\mathbf{B}}_{\mathbf{2}}$. 

Use partial orbital diagrams to show how the atomic orbitals of the central atom lead to hybrid orbitals in

(a)  ${\mathbf{GeCl}}_4$

(b)  ${\mathbf{BCl}}_3$

(c)  ${{\mathbf{CH}}_3}^{+}$

Which types of atomic orbitals of the central atom mix to form hybrid orbitals in 

(a) CI₂O ; (b) BrCI₃ ; (c) PF₅ ; (d) SO₃²?

Phosphine ( PH₃ )reacts with borane ( BH₃ ) as follows:

$\mathit{P}{\mathit{H}}_{\mathbf{3}}\mathbf{+}\mathit{B}{\mathit{H}}_{\mathbf{3}}\mathbf{\to }\mathit{P}{\mathit{H}}_{\mathbf{3}}\mathbf{-}\mathit{B}{\mathit{H}}_{\mathbf{3}}$

The illustrations below depict differences in orbital hybridization of some tellurium ( Te ) fluorides.

(a) Which depicts the difference, if any, between TeF₆ (left) and TeF₅ (right)? (b) Which depicts the difference, if any, between TeF₄ (left) and TeF₆ (right)?

Use partial orbital diagrams to show how the atomic orbitals of the central atom lead to hybrid orbitals in

(a) BF₄^- 

(b) PO₄^3-

(c) SO₃

Use partial orbital diagrams to show how the atomic orbitals of the central atom lead to hybrid orbitals in

(a) ${\mathbf{SeCI}}_{\mathbf{2}}$

(b) ${\mathbf{H}}_{\mathbf{3}}{\mathbf{O}}^{\mathbf{+}}$

(c) ${\mathbf{IF}}_{\mathbf{4}}^{\mathbf{-}}$

Use partial orbital diagrams to show how the atomic orbitals of the central atom lead to hybrid orbitals in

(a) AsCI₃

(b) SnCI₂

(c) PF₆^-

Are these statements true or false? Correct any that are false. 

1. Two $\mathit{\sigma }$bonds comprise a double bond.
2. A triple bond consists of one $\mathbf{\tau \tau }$ bond and two $\mathbf{\sigma }$bonds.
3. Bonds formed from atomic s orbitals are always $\mathbf{\sigma }$bonds.
4. A  $\mathbf{\tau \tau }$bond restricts rotation about the $\mathbf{\sigma }$-bond axis.
5. A $\mathbf{\tau \tau }$bond consists of two pairs of electrons.
6. End-to-end overlap results in a bond with electron density above and below the bond axis.

Certain atomic orbitals on two atoms were combined to form the following MO’s. Name the atomic orbitals used and the MO’s formed, and explain which MO has higher energy:

How do the bonding and antibonding MOs formed from a given pair of AOs compare to each other with respect to

1. energy;
2.  presence of nodes;
3.  inter-nuclear electron density?

Antibonding MOs always have at least one node. Can a bonding MO have a node? If so, draw an example.

The hydrocarbon allene, ${\mathbf{H}}_{\mathbf{2}}\mathbf{C}\mathbf{=}\mathbf{C}\mathbf{=}{\mathbf{CH}}_{\mathbf{2}}$ , is obtained indirectly from petroleum and used as a precursor for several types of plastics. What is the hybridization of each C atom in allene? Draw a bonding picture for allene with lines for sigma bonds, and show the arrangement of the pi bonds. Be sure to represent the geometry of the molecule in three dimensions.

Some species with two oxygen atoms only are the oxygen molecule ${\mathbf{O}}_{\mathbf{2}}$, the peroxide ion,  ${\mathbf{O}}_{\mathbf{2}}^{\mathbf{2}\mathbf{-}}$, the superoxide ion, ${\mathbf{O}}_{\mathbf{2}}^{\mathbf{-}}$ , and the dioxygenyl ion, ${\mathbf{O}}_{\mathbf{2}}^{\mathbf{+}}$ Draw an MO diagram for each, rank them in order of increasing bond length, and find the number of unpaired electrons in each.

Isoniazid (below) is an antibacterial agent that is very useful against many common strains of tuberculosis. 

1. How many sigma bonds are in the molecule?
2. What is the hybridization of each C and N atom?

Use partial orbital diagrams to show how the atomic orbitals of the central atom lead to the hybrid orbitals in: 

$$\begin{gathered} \mathbf{a}\mathbf{.}\mathbf{ }{{\mathbf{IF}}_{\mathbf{2}}}^{\mathbf{-}} \\ \mathbf{b}\mathbf{.}\mathbf{ }{\mathbf{ICI}}_{\mathbf{3}} \\ \mathbf{c}\mathbf{.}\mathbf{ }{\mathbf{XeOF}}_{\mathbf{4}} \\ \mathbf{d}\mathbf{.}\mathbf{ }{\mathbf{BHF}}_{\mathbf{2}} \end{gathered}$$

Epinephrine (or adrenaline; see structure) is a naturally occurring hormone that is also manufactured commercially for use as a heart stimulant, a nasal decongestant, and to treat glaucoma. 

1. What is the hybridization of each C, O, and N atom? 
2. How many sigma bonds does the molecule have? 
3. How many pi electrons are delocalized in the ring?

Butadiene is a colourless gas used to make synthetic rubber and many other compounds. 

1. How many sigma bonds and pi bonds does the molecule have?
2. Are cis-trans arrangements about the double bonds possible? Explain.

Predict the shape, state the hybridization of the central atom, and give the ideal bond angle(s) and any expected deviations for:

 $$\begin{gathered} \mathbf{\left(}\mathbf{a}\mathbf{\right)}\mathbf{ }{\mathbf{BrO}}_{\mathbf{3}}\mathbf{ } \\ \mathbf{\left(}\mathbf{b}\mathbf{\right)}\mathbf{ }\mathbf{AsC}{{\mathbf{l}}_{\mathbf{4}}}^{\mathbf{-}}\mathbf{ } \\ \mathbf{\left(}\mathbf{c}\mathbf{\right)}\mathbf{ }\mathbf{Se}{{\mathbf{O}}_{\mathbf{4}}}^{\mathbf{2}\mathbf{-}}\mathbf{ } \\ \mathbf{\left(}\mathbf{d}\mathbf{\right)}\mathbf{ }\mathbf{Bi}{{\mathbf{F}}_{\mathbf{5}}}^{\mathbf{2}\mathbf{-}}\mathbf{ } \\ \mathbf{\left(}\mathbf{e}\mathbf{\right)}\mathbf{ }\mathbf{Sb}{{\mathbf{F}}_{\mathbf{4}}}^{\mathbf{+}\mathbf{ }} \\ \mathbf{\left(}\mathbf{f}\mathbf{\right)}\mathbf{ }\mathbf{AI}{{\mathbf{F}}_{\mathbf{6}}}^{\mathbf{3}\mathbf{-}}\mathbf{ } \\ \mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{ }{{\mathbf{IF}}_{\mathbf{4}}}^{\mathbf{+}} \end{gathered}$$

Use MO diagrams to place${{\mathbf{B}}_{\mathbf{2}}}^{\mathbf{+}\mathbf{ }}\mathbf{,}{\mathbf{B}}_{\mathbf{2}}\mathbf{,}$and ${{\mathbf{B}}_{\mathbf{2}}}^{\mathbf{-}}$in order of 

b. Decreasing bond length

How many electrons does it take to fill

1. a  $\mathbf{\sigma }$  bonding MO;
2. a $\mathbf{\pi }$  antibonding MO;
3. the MO’s formed from combination of the 1s orbitals of two atoms?

How many electrons does it take to fill

1. the MOs formed from combination of the 2p orbitals of two atoms;
2.  a ${\mathbf{\sigma }}_{2p}^{\ast }$  MO;
3. The MO’s formed from combination of the 2s orbitals of two atoms?

Predict the shape, state the hybridization of the central atom, and give the ideal bond angle(s) and any expected deviations for:

1.  ${{\mathbf{BrO}}_3}^{-}$
2.  ${{\mathbf{AsCl}}_4}^{-}$
3.  ${{\mathbf{SeO}}_4}^{2-}$
4.  ${{\mathbf{BiF}}_5}^{2-}$
5.  ${{\mathbf{SbF}}_4}^{+}$
6.  ${{\mathbf{AlF}}_6}^{3-}$
7.  ${{\mathbf{IF}}_4}^{+}$

Hydrazine, ${\mathbf{N}}_2{\mathbf{H}}_4$ , and carbon disulfide, ${\mathbf{CS}}_2$ , form a cyclic molecule (right). 

1. Draw Lewis structures for ${\mathbf{N}}_2{\mathbf{H}}_4$ and  ${\mathbf{CS}}_2$.
2. How do electron-group arrangement, molecular shape, and hybridization of N change when ${\mathbf{N}}_2{\mathbf{H}}_4$ reacts to form the product?
3. How do electron-group arrangement, molecular shape, and hybridization of C change when ${\mathbf{CS}}_2$ reacts to form the product?

In each of the following equations, what hybridization change, if any, occurs for the underlined atom?

The ionosphere lies about 100 km above Earth’s surface. This layer consists mostly of $\mathbf{NO}$ ,  ${\mathbf{O}}_2$ , and ${\mathbf{N}}_2$ , and photoionization creates ${\mathbf{NO}}^{+}$  , ${{\mathbf{O}}_2}^{+}$  , and  ${{\mathbf{N}}_2}^{+}$. 

(a) Use MO theory to compare the bond orders of the molecules and ions.

(b) Does the magnetic behaviour of each species change when its ion forms?

The sulfate ion can be represented with four S—O bonds or with two S-O and two S=O bonds. 

1. Which representation is better from the standpoint of formal charges? 
2. What is the shape of the sulfate ion, and what hybrid orbitals of S are postulated for the sigma bonding?
3. In view of the answer to part (b), what orbitals of S must be used for the pi bonds? What orbitals of O?
4. Draw a diagram to show how one atomic orbital from S and one from O overlap to form a pi bond.

Sulfur forms oxides, oxoanions, and halides. What is the hybridization of the central S in ${\mathbf{SO}}_2$ ,${\mathbf{SO}}_3$  , ${{\mathbf{SO}}_3}^{2-}$  , ${\mathbf{SCl}}_4$ ,  ${\mathbf{SCl}}_6$, and  ${\mathbf{S}}_2{\mathbf{Cl}}_2$ (atom sequence Cl—S—S—Cl)?

Question: The molecular orbitals depicted below are derived from 2p atomic orbitals in ${{\mathbf{F}}_{\mathbf{2}}}^{\mathbf{+}}$ .

1. Give the orbital designations.
2. Which is occupied by at least one electron in  ${{\mathbf{F}}_{\mathbf{2}}}^{\mathbf{+}}$?
3. Which is occupied by only one electron in  ${{\mathbf{F}}_{\mathbf{2}}}^{\mathbf{+}}$?

Use MO diagrams and the bond orders you obtain from them to answer: 

(a) Is $\mathbf{B}{{\mathbf{e}}_{\mathbf{2}}}^{\mathbf{+}}$ stable? 

(b) Is  $\mathbf{B}{{\mathbf{e}}_{\mathbf{2}}}^{\mathbf{+}}$ diamagnetic? 

(c) What is the outer (valence) electron configuration of  $\mathbf{B}{{\mathbf{e}}_{\mathbf{2}}}^{\mathbf{+}}$?

Question: Use MO diagrams to place  ${{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{-}}$, ${\mathbf{C}}_{\mathbf{2}}$ , ${{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{+}}$and  in order of 

(a) Increasing bond energy; 

(b) Increasing bond length.        

Simple proteins consist of amino acids linked together in long chain; a small portion of such a chain 

Experiment shows that rotation about the C—N bond (indicated by the arrow) is somewhat restricted. Explain with resonance structures, and show the types of bonding involved.