Question

Which has the shortest C-C bond length?
A)\[{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{5}}}{\rm{OH}}\]
B) \[{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{6}}}\]
C) \[{{\rm{C}}_{\rm{2}}}{{\rm{H}}_2}\]
D) \[{{\rm{C}}_{\rm{2}}}{{\rm{H}}_4}\]

Answer 1

Hint: The bond length defines a distance of two bonded atoms nuclei. There is a relation between bond length and bond order. The more the bond order, the less the bond length is.

Complete Step by Step Answer:
Let’s understand what a bond order is. The bond order defines the number of bonds between two atoms. Bond order 1 indicates that there is one bond between the atoms, bond order 2 indicates a double bond and bond order 3 indicates 1 triple bond.

As we mentioned above, the relation between bond order and bond length is inversely proportional. So, we will discuss all the options one by one.
Option A is \[{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{5}}}{\rm{OH}}\]. Its structure is \[{\rm{C}}{{\rm{H}}_{\rm{3}}} - {\rm{C}}{{\rm{H}}_{\rm{2}}} - {\rm{OH}}\] . So, we find that only single bonds are present in the compound, which means the bond order is 1.

Option B is \[{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{6}}}\]. Its structure is \[{\rm{C}}{{\rm{H}}_{\rm{3}}} - {\rm{C}}{{\rm{H}}_3}\] . Here also, only single bonds are present. So, the bond order is 1.

Option C is \[{{\rm{C}}_{\rm{2}}}{{\rm{H}}_2}\]. Its structure is \[{\rm{CH}} \equiv {\rm{CH}}\] . Here, the bond order is 3.

Option D is \[{{\rm{C}}_{\rm{2}}}{{\rm{H}}_4}\]. Its structure is \[{\rm{C}}{{\rm{H}}_2} = {\rm{C}}{{\rm{H}}_2}\]. Here, the bond order is 2. So, we find that bond order is highest in \[{{\rm{C}}_{\rm{2}}}{{\rm{H}}_2}\]. Therefore, the bond length of ethyne is the lowest.
Hence, option C is right.

Note: It is to be noted that, the increasing order bond lengths of different types of hydrocarbons are alkanes < alkenes < alkynes. Therefore, any alkyne has the lowest bond length and any alkane has the highest bond length.