Question

Part A 

How many \(\sigma\) and \(\pi\) bonds are present in a molecule of cumulene? (Part A 1 figure) Enter the number of \(\sigma\) bonds followed by the number of \(\pi\) bonds separated by a comma. 

Part B What types of orbital overlap occur incumulene? Check all that apply. \(s p^{2} / s p^{2}\) overlap

\(s p / s p^{2}\) overlap

\(s p / s p\) overlap

\(s / s\) overlap

\(s / s p^{2}\) overlap

\(p / p\) overlap \(s / s p\) overlap

In cumulene, what are the \(\mathrm{C}=\mathrm{C}=\mathrm{C}\) and \(\mathrm{H}-\mathrm{C}-\mathrm{H}\) bond angles, respectively? Enter the \(\mathrm{C}=\mathrm{C}=\mathrm{C}\) bond angle followed by the \(\mathrm{H}-\mathrm{C}-\mathrm{H}\) bond angle separated by a comma.

Answer 1

Concepts and reason

The chemical bond is formed by the attraction of atom or ions. Due to electronegativity, the atoms can attract the electrons in a chemical bond. Chemical bond is also formed with the help of valance electrons in an atom and should obey octet rule.

The chemical bonding is formed with the help of overlapping of atomic orbitals.

There are two types of bond. They are sigma bond $\left( \sigma \right)$ and pi bond $\left( {\rm{\pi }} \right)$ .

Fundamentals

Sigma bond:

The head – on overlapping of atomic orbitals which leads to covalent bond formation is represented as sigma bond.

Pi bond:

A side wise overlapping of atomic orbitals which leads to the formation of bond is represented as pi bond.

Example:

The double bond in ethene contains 1 sigma bond and 1 pi bond. The 4 electrons of each carbon forms a bond with 2 hydrogen, 1 carbon – carbon bond and 1 pi bond with carbon.

The double bond in ethene includes 1 ${\rm{\sigma }}\,{\rm{(s}}{{\rm{p}}^{\rm{2}}}{\rm{ - s}}{{\rm{p}}^{\rm{2}}}{\rm{ overlap)}}$ and 1 ${\rm{\pi }}\,{\rm{(p}}\,{\rm{ - }}\,{\rm{p overlap)}}$ bonds. Each carbon – hydrogen bond shows ${\rm{\sigma }}\,{\rm{(s}}{{\rm{p}}^{\rm{2}}}{\rm{ - s overlap)}}$ .The bond angle is 120⁰ and shows Trigonal planar geometry.

(A)

(B.1)

The corner carbon (red) shows ${\rm{s}}{{\rm{p}}^{\rm{2}}}$ hybridization and the two carbons present in the center (blue) shows ${\rm{sp}}$ hybridization. Each hydrogen contains ${\rm{s}}$ orbital which undergoes head – on overlapping with carbon atom.

The two carbons in the corner that shows ${\rm{s}}{{\rm{p}}^{\rm{2}}}$ hybridization and bonds with carbons are ${\rm{sp}}$ hybridized. Therefore, there is no ${\rm{s}}{{\rm{p}}^{\rm{2}}}{\rm{/s}}{{\rm{p}}^{\rm{2}}}$ overlap in this molecule.

The hydrogen present in this molecule has ${\rm{s}}$ orbital which bonds with ${\rm{s}}{{\rm{p}}^{\rm{2}}}$ carbon. Therefore, there is no ${\rm{s/s}}$ overlap in this molecule.

The hydrogen present in this molecule has ${\rm{s}}$ orbital which is bonded with ${\rm{s}}{{\rm{p}}^{\rm{2}}}$ carbon. There is no ${\rm{s}}$ orbital overlap with ${\rm{sp}}$ carbon. Therefore, there is no ${\rm{s/sp}}$ overlap present in this molecule.

The carbon present in the center shows ${\rm{sp}}$ hybridization and the carbon present in the corner shows ${\rm{s}}{{\rm{p}}^{\rm{2}}}$ hybridization. Therefore, the molecule has ${\rm{sp /s}}{{\rm{p}}^{\rm{2}}}$ overlap.

(B.2)

${\rm{sp/sp overlap}}$

(B.3)

Cumulene molecule shows ${\rm{s /s}}{{\rm{p}}^2}$ overlap.

(B.4)

Cumulene molecule shows ${\rm{p / p}}$ overlap.

Ans: Part A

Cumulene contains 7 sigma bond and 3 pi bonds.

Part B.1

O	${\rm{s}}{{\rm{p}}^2}{\rm{ /s}}{{\rm{p}}^{\rm{2}}}$ overlap
O	${\rm{sp /s}}{{\rm{p}}^{\rm{2}}}$ overlap
O	${\rm{sp /sp}}$ overlap
O	${\rm{s /s}}$ overlap
O	${\rm{s /s}}{{\rm{p}}^{\rm{2}}}$ overlap
O	${\rm{p /p}}$ overlap
O	${\rm{s /sp}}$ overlap

Part B.2

O	${\rm{s}}{{\rm{p}}^2}{\rm{ /s}}{{\rm{p}}^{\rm{2}}}$ overlap
O	${\rm{sp /s}}{{\rm{p}}^{\rm{2}}}$ overlap
O	${\rm{sp /sp}}$ overlap
O	${\rm{s /s}}$ overlap
O	${\rm{s /s}}{{\rm{p}}^{\rm{2}}}$ overlap
O	${\rm{p /p}}$ overlap
O	${\rm{s /sp}}$ overlap

Part B.3

O	${\rm{s}}{{\rm{p}}^2}{\rm{ /s}}{{\rm{p}}^{\rm{2}}}$ overlap
O	${\rm{sp /s}}{{\rm{p}}^{\rm{2}}}$ overlap
O	${\rm{sp /sp}}$ overlap
O	${\rm{s /s}}$ overlap
O	${\rm{s /s}}{{\rm{p}}^{\rm{2}}}$ overlap
O	${\rm{p /p}}$ overlap
O	${\rm{s /sp}}$ overlap

Part B.4

O	${\rm{s}}{{\rm{p}}^2}{\rm{ /s}}{{\rm{p}}^{\rm{2}}}$ overlap
O	${\rm{sp /s}}{{\rm{p}}^{\rm{2}}}$ overlap
O	${\rm{sp /sp}}$ overlap
O	${\rm{s /s}}$ overlap
O	${\rm{s /s}}{{\rm{p}}^{\rm{2}}}$ overlap
O	${\rm{p /p}}$ overlap
O	${\rm{s /sp}}$ overlap

,

The bond angle is ${180^0}\,,\,{120^0}.$