question_answer

The correct arrangement of the species in the decreasing order of the bond length between carbon and oxygen in them is

A)  \[CO,C{{O}_{2}},HCO_{2}^{-},CO_{3}^{2-}\]

B)  \[C{{O}_{2}},HCO_{2}^{-},CO,CO_{3}^{2-}\]

C)  \[CO_{3}^{2-},HCO_{2}^{-},C{{O}_{2}},CO\]

D)  \[CO,CO_{3}^{2-},C{{O}_{2}},HCO_{2}^{-}\]

Correct Answer: C

Solution :

: Bond order \[\propto \frac{1}{Bond\,length}\] Bond length   \[=\frac{Bond\,order\,of\,each\,C-O\,bond}{Total\,no.\,of\,resontating\,structures}\] [a] \[CO\to C\overset{\leftarrow }{\mathop{=}}\,O\] \[\Rightarrow \] \[\frac{2+1}{1}=3.0\] [b] \[C{{O}_{2}}\to O=C=O\] \[\Rightarrow \] \[\frac{2+2}{2}=2.0\] [c]     \[\Rightarrow \] \[\frac{2+1}{2}=1.5\] [d]  \[\Rightarrow \] \[\frac{1+1+2}{3}=1.33\] Hence, the decreasing order of bond length is \[CO_{3}^{2-}>HCO_{2}^{-}>C{{O}_{2}}>CO.\]