Question

In ${{P}_{4}}{{O}_{10}}$ molecule, bridging P-O bond length is:
A. Larger than that of in ${{P}_{4}}{{O}_{6}}$
B. lesser than that of in ${{P}_{4}}{{O}_{6}}$
C. equal to that of in ${{P}_{4}}{{O}_{6}}$
D. cannot be compared

Answer 1

Hint: The presence of double and single bonds leads to the bond length and orientation of bonds in a molecule. ${{P}_{4}}{{O}_{10}} $is tetra phosphorus decaoxide. This molecule consists of a double bond character in the oxygen bond.

Complete answer:
We have to find about the P-O bond length in ${{P}_{4}}{{O}_{10}}$ molecule and compare it with the P-O bond in ${{P}_{4}}{{O}_{6}}$ molecule.
As we know that the multiplicity of bonds affects the bond length. Double bonds and triple bonds tend to be of lesser length than single bonds. This is the reason why some bonds have more bond length and some bonds have less bond length. The presence of any double bond in the oxygen atom in both the oxides of phosphorus will tell us the information about the P-O bridge.
The molecule of ${{P}_{4}}{{O}_{10}}$ is as follows:

We can see the presence of 4 P-O bonds here. These bonds are double bonds (4) and others single bonds.
Now here is the ${{P}_{4}}{{O}_{6}}$ molecule:

This molecule consists of a network of only single bonds in the P-O bonds.
Clearly, from the nature of P-O bonds present in both the molecules, it can be inferred that P-O bond length in ${{P}_{4}}{{O}_{10}}$ is lesser than that of in ${{P}_{4}}{{O}_{6}}$ molecule, due to the presence of double bonds.
Hence, P-O bond in ${{P}_{4}}{{O}_{10}}$ is lesser than P-O bond in ${{P}_{4}}{{O}_{6}}$.

Thus option B is correct.

Note:
From the observed measurements of the P-O bonds in ${{P}_{4}}{{O}_{6}}$ and ${{P}_{4}}{{O}_{10}}$, the value of P-O bond in ${{P}_{4}}{{O}_{6}}$ is 166 pm, while that of this bond in ${{P}_{4}}{{O}_{10}}$ is 143 pm. This also proves that P-O bond in ${{P}_{4}}{{O}_{6}}$ is larger than P-O bond in ${{P}_{4}}{{O}_{10}}$.