Question

The X-X bond length is 1.00 $\overset{0}{\mathop{A}}\,$ and C-C bond length is 1.54$\overset{0}{\mathop{A}}\,$. the C-X bond length is likely to be:
a.) 0.80$\overset{0}{\mathop{A}}\,$
b.) 1.18$\overset{0}{\mathop{A}}\,$
c.) 1.57$\overset{0}{\mathop{A}}\,$
d.) 1.68$\overset{0}{\mathop{A}}\,$

Answer 1

Hint: Bond length is the average distance between the nuclei of two bonded atoms. Bond length is different for different bonding atoms. Bond length is related to bond order, bond strength and bond dissociation energy.


Complete step by step answer:
Given in the question:
The X-X bond length is 1.00 $\overset{0}{\mathop{A}}\,$
C-C bond length is 1.54$\overset{0}{\mathop{A}}\,$
The C-X bond length will be calculated as:
\[\begin{align}
 & C-X={{r}_{c}}-{{r}_{x}}-0.09({{X}_{c}}-{{X}_{x}}) \\
 & =\dfrac{1.54 + 1}{2} - 0.09(3-2) \\
 & =1.18\overset{0}{\mathop{A}}\, \\
\end{align}\]
Hence, the correct answer is option (B) i.e. the C-X bond length is likely to be 1.18$\overset{0}{\mathop{A}}\,$.

Additional Information .
- Bond length is the average distance between the nuclei of two bonded atoms. The bond length depends on the bond order. Bond order is calculated by dividing the number of bonds with the total number of bonding pair.The bond length is inversely proportional to the bond length. This means that more will be the bond order less will be the bond length. The bond order of triple bond is highest and similarly the bond length of triple bond is lowest.
- Ethane is an alkane which means that there is a single bond between two carbon atoms. Similarly, ethene is an alkene which means that there is a double bond between two carbon atoms and ethyne is an alkyne which means that there is a triple bond between two carbon atoms.

Note: Bond length is inversely proportional to the bond dissociation energy. This means that more will be the bond length less will be the bond dissociation energy. Triple bonds have the highest bond dissociation energy.