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Question: The correct order of \(C-O\) bond length among \(CO\), \(CO_{3}^{-2}\) and \(C{{O}_{2}}\) is: A. \...

The correct order of C−OC-O bond length among COCO, CO3−2CO_{3}^{-2} and CO2C{{O}_{2}} is:
A. CO<CO32−<CO2CO < C{O_3}^{2 - } < C{O_2}
B. CO32−<CO2< COC{O_3}^{2 - } < C{O_2} < \,CO
C. CO<CO2<CO32−CO < C{O_2} < C{O_3}^{2 - }
D. CO2<CO<CO32−C{O_2} < CO < C{O_3}^{2 - }

Explanation

Solution

if bond order is smaller then the value of bond length will be higher. bond length is defined as the average between the nuclei of two bonded atoms in a molecule. Bond length is calculated by the number of bonded electrons.

Complete step by step answer:
If the value of bond order is smaller, then the value of bond length will be higher.
And as we know that,
Bond  order=Total  number  of  bonds  associated  between  two  atomsTotal  number  of  resonating  structureBond\;order=\dfrac{Total\;number\;of\;bonds\;associated\;between\;two\;atoms}{Total\;number\;of\;resonating\;structure}
For C≡OC\equiv O the bond order is:31=3\dfrac{3}{1}=3
For O=C=OO=C=O , the bond order is: 42=2\dfrac{4}{2}=2
For CO3−2CO_{3}^{-2} , bond order is: 43=1.33\dfrac{4}{3}=1.33
Therefore, the correct order of bond order is CO>CO2>CO32−CO > C{O_2} > C{O_3}^{2 - } and hence, the correct order of bond length is CO<CO2<CO32−CO < C{O_2} < C{O_3}^{2 - }

So, the correct answer is Option C.

Additional information:
Bond length is defined as the average distance between the nuclei of two bonded atoms in a molecule. When there are more number of electrons that get participated in the bond formation, the bond length is shorter. Bond length also depends upon the bond strength and bond dissociation energy. Bond length is inversely proportional to bond dissociation energy and bond strength. If a bond is stronger, it will be shorter.
Bond order is defined as the number of bonds between the two atoms in a molecule. For example, N≡NN\equiv N has the bond order equals to 33 , C−HC-H bond order is 11 .
If you want to find the bond order between atoms, then firstly, you have to draw the Lewis structure. After that, you should determine the type of bonds between the atoms, it can be a single bond, double bond or a triple bond. If you get a bond order equals to zero, then the molecule cannot be formed. If the bond order is high, then the molecule is stable.

Note: In case of COCO , we have to go through the molecular orbital theory. Here, the total number of electrons is 1414 (that is, carbon has six electrons and oxygen has eight electrons) which are known as isoelectronic species because they have 1414 electrons and hence its bond order is 33 .
Bond length is inversely proportional to bond order.
Bond  length∝1Bond  orderBond\;length\propto \dfrac{1}{Bond\;order}