Question

Bond order in $S{{O}_{4}}^{2-}$ = X and in $P{{O}_{4}}^{3-}$= Y. The value of X + Y = ?

Answer 1

Bond order of any molecule is the number of bonds between the atoms in that molecule. Greater the bond order, more is the bond energy, and less is the bond length. Bond order depends on the number of bonding electrons and the number of bonded atoms.

Formula used: Bond order = $\dfrac{No.of\,bonding\,electron\,pairs}{No.\,of\,bonded\,atoms}$

Complete step-by-step answer: Bond order of any molecule is taken in the bonded state. It is the measure of bonded pairs. We have been given, sulphate $S{{O}_{4}}^{2-}$, and phosphate $P{{O}_{4}}^{3-}$ions. We have to find the sum of their bond orders. Assuming the bond order of $S{{O}_{4}}^{2-}$ as X and that of $P{{O}_{4}}^{3-}$as Y.
For $S{{O}_{4}}^{2-}$ion, the structure of sulphate consist of bonded electron pairs of 6, 2 forming single bonds with 2 oxygen, while 2 oxygen having double bonds, that equals to 2 + 4 = 6 bond pairs. While the number of bonded oxygen atoms are 4. So, from the formula of bond order we have,
Bond order = $\dfrac{6}{4}$
Therefore, bond order = 1.5. So, X = 1.5
Now for $P{{O}_{4}}^{3-}$ion, we have the structure of phosphate having 5 bonded electron pairs, 3 forming single bonds with oxygen, and 1 forming a double bond with oxygen, that becomes 3 + 2 = 5. While the number of bonded atoms is 4 oxygen. So, from the given formula, the bond order will be,
Bond order = $\dfrac{5}{4}$
Therefore, bond order = 1.25. So, Y =1.25
Thus, the sum of X + Y = 1.5 + 1.25 = 1.75
Hence, the value of X + Y is 1.75.

Note: The bond order is observed from the structure of any compound. Bond order can also be calculated from number of electrons in bonding and anti bonding molecular orbital, as $BO=\dfrac{1}{2}({{N}_{b}}-{{N}_{a}})$ where ${{N}_{b}}$ is number of electron in bonding molecular orbital and ${{N}_{a}}$is number of electron in anti bonding molecular orbital.