Question

Which is predicted to have the shorter sulfur-oxygen bonds , $S{O_3}$ or $SO_3^{2 - }$ ?

Answer 1

The distance between the nuclei of two chemically bonded atoms in a molecule is measured by bond length. It is about equivalent to the sum of the two bound atoms' covalent radii. Bond length is inversely related to bond order in covalent bonds; greater bond orders result in stronger bonds, which are accompanied by stronger forces of attraction that hold the atoms together.

Complete answer:
$S{O_3}$ molecule contains $6$ $\sigma$ bonds and $\pi$ bonds to the three $O$ atoms. The average bond order of an $S - O$ bond becomes $\frac{6}{3} = 2$ .
In $SO_3^{2 - }$ ion, there are a total of $4$ $\sigma$ bonds and $\pi$ bonds to the three $O$ atoms. Therefore, the bond order of $S - O$ bond becomes $\frac{4}{3} = 1.33$ .
Since bond length decreases as bond order increases, $SO_3^{2 - }$ have a shorter bond length.

Additional Information:
The total number of covalently bound electron pairs between two atoms in a molecule is the bond order of a covalent bond. It can be discovered by drawing the molecule's Lewis structure and counting the total number of electron pairs between the atoms.
The bond order for single bonds is one.
The bond order of double bonds is two.
The bond order of triple bonds is three.

Note:
The atomic radii of the involved atoms are directly proportional to bond lengths. The periodic trends in element bond lengths are similar to the periodic trends in element atomic radii (decreases across the period, increases down the group).