Unequal bond lengths are present in : (1) \(\mathrm{BF}_{3}\) (2) \(\mathrm{CO}_{3}{ }^{2-}\) (present in \(\left.\mathrm{CaCO}_{3}\right)\) (3) \(\mathrm{HNO}_{3}\) (4) \(\mathrm{SO}_{4}^{2-}\)

Molecular geometry plays a crucial role in understanding a molecule's properties. It defines the arrangement of atoms in space around a central atom. For example, in \(\text{BF}_3\), boron forms three bonds with fluorine atoms. This arrangement causes \(\text{BF}_3\) to have a trigonal planar shape, with all bond angles being 120 degrees.
Since the geometry is symmetrical, all B-F bond lengths will be equal.
Similarly, \(\text{CO}_3^{2-}\) has a planar structure, which ensures that all carbon-oxygen bond lengths are the same due to resonance.
This is different from \(\text{HNO}_3\), where the nitrogen's bonds with oxygen atoms are not symmetrical due to the combination of double and single bonds. This asymmetric bond distribution creates unequal bond lengths.
Sulfate ion \(\text{SO}_4^{2-}\) also has a tetrahedral geometry, where the sulfur forms four equivalent bonds with oxygen, resulting in equal bond lengths. Understanding molecular geometry helps visualize the spatial arrangement and predict the lengths and strengths of bonds.

Resonance structures are essential to grasping how electrons are distributed in a molecule. They depict different possible configurations of electron pairs that a molecule can have.
For instance, the carbonate ion \(\text{CO}_3^{2-}\) has multiple resonance structures where the double bond 'jumps' between different oxygen atoms.
This delocalization causes each C-O bond to share the same characteristics, thus having the same bond length.
Sulfate ion \(\text{SO}_4^{2-}\) also benefits from resonance, where delocalized electrons make S-O bonds equivalent.
On the other hand, \(\text{HNO}_3\) has a resonance structure, but because it combines single and double bonds, the bond lengths vary. One nitrogen-oxygen bond is longer (single bond), while the others are shorter (double bonds).
Resonance stabilizes molecules, distributes charge, and affects bond lengths, making this concept vital in predicting molecular properties.

Bond length is the average distance between the nuclei of two bonded atoms. Different factors affect bond length, including bond order and resonance.
For example, in \(\text{BF}_3\), all B-F bonds are single bonds with equal lengths due to the symmetrical structure.
In \(\text{CO}_3^{2-}\) and \(\text{SO}_4^{2-}\), resonance leads to equal bond lengths by averaging the bond character across all atom pairs.
Nitric acid \(\text{HNO}_3\) offers a clear depiction of unequal bond lengths because it has a combination of single and double bonds. The single bond is longer because it involves fewer shared electrons, while double bonds are shorter due to a greater electron density between nuclei.
Resonance structures can explain why certain bonds in a molecule have equal lengths, while molecular geometry may show the spatial reasons behind bond length equality or inequality.