Chapter 2, Problem 2.46E

(a)

Interpretation Introduction

Interpretation:

Lewis structure of ${\text{H}}_2{\text{CCH}}_2$, ${\text{H}}_2{\text{CCCH}}_2$ and ${\text{H}}_2{\text{CCCCH}}_2$ has to be predicted.

Concept Introduction:

Lewis structures represent covalent bonds and describe valence electrons configuration of atoms. The covalent bonds are depicted by lines and unshared electron pairs by pairs of dots. The sequence to write Lewis structure of some molecule is given as follows:

• The central atom is identified and various other atoms are arranged around it. This central atom so chosen is often the least electronegative.
• Total valence electrons are estimated for each atom.
• single bond is first placed between each atom pair.
• The electrons left can be allocated as unshared electron pairs or as multiple bonds around the symbol of the element to satisfy the octet (or duplet) for each atom.
• Add charge on the overall structure in case of polyatomic cation or anion.

Explanation of Solution

${\text{H}}_2{\text{CCH}}_2$ consists of $\text{C}$ and $\text{H}$ atoms. $\text{C}$ possesses 4 valence electrons, $\text{H}$ possesses 1 valence electron. Thus total valence electrons is the sum of the valence electrons for each atom along with a charge in ${\text{H}}_2{\text{CCH}}_2$. It is calculated as follows:

  $\begin{array}{c}\text{Total valence electrons}=4\left(2\right)+1\left(4\right)\\ =12\end{array}$

Hence, 6 pairs are to be allocated to form the Lewis structure of ${\text{H}}_2{\text{CCH}}_2$. This can be done in the ethene molecule indicated as follows:

Similarly, total valence electrons is sum of the valence electrons for each atom along with a charge in ${\text{H}}_2{\text{CCCH}}_2$. It is calculated as follows:

  $\begin{array}{c}\text{Total valence electrons}=4\left(3\right)+1\left(4\right)\\ =16\end{array}$

Hence, 8 pairs are to be allocated to form the Lewis structure of ${\text{H}}_2{\text{CCCH}}_2$ . This can be done whether as two double bonds in allene indicated as follows:

Likewise, total valence electrons in ${\text{H}}_2{\text{CCCCH}}_2$ is calculated as follows:

  $\begin{array}{c}\text{Total valence electrons}=4\left(4\right)+1\left(4\right)\\ =20\end{array}$

Hence, 10 pairs are to be allocated to form the Lewis structure of ${\text{H}}_2{\text{CCCCH}}_2$. This can be done whether as two double bonds in allene indicated as follows:

(b)

Interpretation Introduction

Interpretation:

The hybridization at each carbon in ${\text{H}}_2{\text{CCH}}_2$, ${\text{H}}_2{\text{CCCH}}_2$ and ${\text{H}}_2{\text{CCCCH}}_2$ has to be assigned.

Concept Introduction:

The table that relates the steric number with hybridization is as follows:

$\begin{array}{cc}\text{Steric Number}& \text{Type of Hybridisation}\\ 2& \text{sp}\\ 3& {\text{sp}}^2\\ 4& {\text{sp}}^3\\ 5& {\text{sp}}^3\text{d}\\ 6& {\text{sp}}^3{\text{d}}^2\end{array}$

Explanation of Solution

In the structure of ${\text{H}}_2{\text{CCCCH}}_2$ the hybridization at each carbon is illustrated below.

The terminal carbon atoms at positions 1 and 2 are trigonal planar with 3 as steric number hence the hybridization of these carbon atoms is ${\text{sp}}^2$.

In the structure of ${\text{H}}_2{\text{CCCH}}_2$ the hybridization at each carbon is illustrated below.

Since the steric number around central carbon is 2 therefore, the hybridization of carbon atom located at positions 2 is $\text{sp}$. The terminal carbon atoms at positions 1 and 3 are trigonal planar with 3 as steric number hence the hybridization of carbon1 and 3  is ${\text{sp}}^2$.

In the structure of ${\text{H}}_2{\text{CCCCH}}_2$ the hybridization at each carbon is illustrated below.

Central carbon atoms have effectively two bond pairs as each double bond is regarded as one single bond pair. Since the steric number around central carbon atoms is 2 therefore, the hybridization of carbon atoms located at positions 2 and 3 is $\text{sp}$.

The terminal carbon atoms at positions 1 and 4 are trigonal planar with 3 as steric number hence the hybridization of this carbon is ${\text{sp}}^2$.

(c)

Interpretation Introduction

Interpretation:

The type of bonds that connect carbon atoms in ${\text{H}}_2{\text{CCH}}_2$, ${\text{H}}_2{\text{CCCH}}_2$ and ${\text{H}}_2{\text{CCCCH}}_2$ has to be identified.

Concept Introduction:

A single bond is always associated with sigma bonds. Molecules that have all atoms connected by sigma bond exclusively are stated to be in $s{p}^3$ hybridization. It has a bond angle of $109.5°$.

A double bond and carbocation are associated with $s{p}^2$ hybridization. It has a bond angle of $120°$.

A triple bond or central carbon structure similar to allene is always associated with $sp$ hybridization. It has a bond angle of $180°$.

Explanation of Solution

In ${\text{H}}_2{\text{CCCCH}}_2$ the hybridization at each carbon is ${\text{sp}}^2$ thus each carbon has a double bond.

In ${\text{H}}_2{\text{CCCH}}_2$ the hybridization at position 1 and 3 is ${\text{sp}}^2$ thus carbon at these positions have a double bond. Hybridization of carbon at position 2 is $\text{sp}$ and it has two double bonds.

In ${\text{H}}_2{\text{CCCCH}}_2$ the hybridization, terminal carbon is ${\text{sp}}^2$ so thus carbon at these positions has a double bond. The hybridization at the central two carbon atoms is $\text{sp}$. Theses have two double bonds on each side.

(d)

Interpretation Introduction

Interpretation:

The bond angles in ${\text{H}}_2{\text{CCH}}_2$, ${\text{H}}_2{\text{CCCH}}_2$ and ${\text{H}}_2{\text{CCCCH}}_2$ have to be determined.

Concept Introduction:

Refer to part (c).

Explanation of Solution

A single bond is always associated with sigma bonds. Molecules that have all atoms connected by sigma bond exclusively are stated to be in $s{p}^3$ hybridization. It has a bond angle of $109.5°$.

A double bond and carbocation are associated with $s{p}^2$ hybridization. It has a bond angle of $120°$.

A triple bond or central carbon structure similar to allene is always associated with $sp$ hybridization. It has a bond angle of $180°$.

Thus the bond angles can be illustrated as follows:

(e)

Interpretation Introduction

Interpretation:

Whether all hydrogen atoms lie in the same plane or not in ${\text{H}}_2{\text{CCH}}_2$, ${\text{H}}_2{\text{CCCH}}_2$ and ${\text{H}}_2{\text{CCCCH}}_2$ has to be determined.

Concept Introduction:

Refer to part (c).

Explanation of Solution

In allene, the central carbon that is double bonded to each carbon in different planes is $sp$ hybridized while the two terminal carbon atoms are $s{p}^2$ hybridized.

Thus the terminal hydrogen atom on carbon at position 1 is in a different plane than carbon at position 3 in case of ${\text{H}}_2{\text{CCCH}}_2$. However for structures with even number of carbon atoms as in ${\text{H}}_2{\text{CCCCH}}_2$ and ethane all four hydrogen atoms lie in the same plane.

(f)

Interpretation Introduction

Interpretation:

Orientation of hydrogen atoms at end of chain has to be determined.

Concept Introduction:

In allene, the central carbon that is double bonded to each carbon in different planes is $sp$ hybridized while the two terminal carbon atoms are $s{p}^2$ hybridized.

Explanation of Solution

For structures with even number of carbon atoms, for example, consider the structure:

  ${\text{H}}_{\text{2}}\text{C}{\left(\text{C}\right)}_x{\text{CH}}_{\text{2}}x=2,4,\mathrm{6...}$

Here, the relative position of the hydrogen atom is indicated as follows:

For structures with an odd number of carbon atoms, for example, consider the structure:

  ${\text{H}}_{\text{2}}\text{C}{\left(\text{C}\right)}_x{\text{CH}}_{\text{2}}x=1,3,\mathrm{5...}$

Here, the relative position of the hydrogen atom is indicated as follows:

Thus structures with even a number of carbon atoms as in ${\text{H}}_2{\text{CCCCH}}_2$ and ethane all four hydrogen atoms lie in the same plane while in allene with odd number of carbon atom, hydrogen atoms are oriented in a different plane.