Question

Which of the following has p${}_{\pi }-d_{\pi }$ bonding?

• A. ${N{O}_3}^{-}$
• B. $S{O}_3^{-2}$
• C. $B{O}_3^{-3}$
• D. $C{O}_3^{-2}$

Answer 1

Answer: (B)

$S{O}_3^{-2}$

To find the no. of $d_{\pi }-p_{\pi }$ Bonding in a molecule follow the sequence:-

$a.$Total no. of Bonded and free electron pairs in the molecule has to be calculated.

$b.$ Then find out the no. of $\pi$ bonds and lone pairs of electrons.

$c.$ Now calculate the no. of $\pi$ bonds. You could do that either by drawing the structure of the molecule from the above data; or refer to the formula;

$\pi$Bonds= (No. of oxygen atoms)$-$(No. of negative charge)

$\to$ Now, No. of $p_{\pi }-p_{\pi }$ Bonds$=$ No. of unhybridized $p-$orbitals left

$\to p_{\pi }-d_{\pi }$ Bonds will be formed when $\pi$ bonds are formed more than the no. of unhybridized $p-$orbitals left.

$\to$First $p_{\pi }-p_{\pi }$ Bonds are formed;after that $p_{\pi }-d_{\pi }$ bonds are formed if there are not enough $p-$orbitals left for multiple bond formation.

A. $N{O}_3^{-}=(5+6(3)+1)=24$ electrons

$\frac{-24}{0lonepairs}$

(Subtract the total no. of electrons with the highest multiple of $8$ to find out the no. of lone pairs )

Lone pairs$=0$

$\sigma =3$

$\pi =1$

(Image 1)

$p_{\pi }-p_{\pi }=1$

$p_{\pi }-d_{\pi }=0$

$\therefore N{O}_3^{-}$ does not have any $p_{\pi }-d_{\pi }$ Bonds.

B. $S{O}_3^{-2}=(6+6(3)+2)=26$ electrons

$\frac{-24\overline{e}}{2\overline{e}=1lonepair}$

Lone pair$=1$

$\sigma =3$

$\pi =1$

(Image 2)

$\to$The lone pair of electrons on Sulphur is back donated to the vacant $p-$orbital of oxygen

$\to$Hence, the unhybrid electron of the d orbital of Sulphur forms a $\pi$ bond with the unhybrid $p-$orbital of oxygen

(image 3)

$\therefore S{O}_3^{-2}$ has a $d_{\pi }-p_{\pi }$ bond.

C. $B{O}_3^{3-}=[3+6(3)+3]=24$ electrons

Lone pair$=0$

$\sigma =3$

$\pi =1$

(Image 4)

This $\pi$ bond is a $p_{\pi }-p_{\pi }$ bond; as explained previously. (First $p_{\pi }-p_{\pi }$ bonds are formed, followed by $p_{\pi }-d_{\pi }$ bonds)

Hence $B{O}_3^{3-}$ does not have any $p_{\pi }-d_{\pi }$ bonds.

D.$C{O}_3^{-2}=[4+6(3)+2]=24$

Lone pairs$=0$

$\sigma =3$

$\pi =1$

(Image 5)

Again the only $\pi$ bond that is present is a $p_{\pi }-p_{\pi }$ Bond.

Again, $C{O}_3^{-2}$ does not have a $p_{\pi }-d_{\pi }$ bond

Correct answer:- The only molecule that has a $d_{\pi }-d_{\pi }$ bond is $S{O}_3^{-2}$