Question
The correct order of increasing $$C - O$$ bond length of $$CO,\,CO_3^{2 - },C{O_2},$$ is
A.
$$C0_3^{2 - } < C{O_2} < CO$$
B.
$$C{O_2} < CO_3^{2 - } < CO$$
C.
$$CO < CO_3^{2 - } < C{O_2}$$
D.
$$CO < C{O_2} < CO_3^{2 - }$$
Answer :
$$CO < C{O_2} < CO_3^{2 - }$$
Solution :
KEYCONCEPT
(i) Bond length $$ \propto \frac{1}{{{\text{Bond}}\,{\text{order}}}}$$
(ii) Bond order is calculated by either the help of molecular orbital theory or by resonance.
(i) Bond order of $$CO$$ as calculated by molecular orbital
theory = $$3\left\{ {b.o. = \frac{1}{2}\left[ {{N_b} - {N_a}} \right]} \right\}$$
(ii) Bond order of $$C{O_2}$$ (by resonance method)
$$\eqalign{
& = \frac{{{\text{No}}{\text{. of bonds in all possible sides}}}}{{{\text{No}}{\text{. of resonating structure }}}} \cr
& = \frac{4}{2} \cr
& = 2 \cr} $$
(iii) Bond order in $$CO_3^{2 - }$$ (by resonance method)
$$ = \frac{4}{3} = 1.33$$
∴ Order of bond length of $$C - O$$ is $$CO < C{O_2} < CO_3^{2 - }$$