# Determine the bond order of the "C"-"O" bond in the following molecules, and then arrange the "C"-"O" bond lengths in increasing order? "CO", "CO"^(+), "CO"^(2+), "CO"_2, "CO"_3^(2-)

Apr 30, 2017

Bond length increases from left to right on your list, i.e.

${r}_{C O} < {r}_{C {O}^{+}} < \left[{r}_{C {O}^{2 +}} = {r}_{C {O}_{2}}\right] < {r}_{C {O}_{3}^{2 -}}$

• $\text{CO}$: $3$
• ${\text{CO}}^{+}$: $2.5$
• ${\text{CO}}^{2 +}$: $2$
• ${\text{CO}}_{2}$: $2$
• ${\text{CO}}_{3}^{2 -}$: $1. \overline{33}$

In order to determine this, we should reference an MO diagram.

We can see that the highest occupied molecular orbital (HOMO) is fully occupied, but the next-highest MOs are the ${\pi}^{\text{*}}$ antibonding lowest unoccupied molecular orbitals (LUMOs). Keep this in mind.

CO MOLECULE

$\text{CO}$ by default has a triple bond, so by chemical intuition, its bond order is $3$. This can be verified by the usual equation:

"BO" = 1/2("Bonding - Antibonding")

$= \frac{1}{2} \left(\left[\stackrel{2 \sigma}{\overbrace{2}} + \stackrel{1 \pi}{\overbrace{2 \left(2\right)}} + \stackrel{3 \sigma}{\overbrace{2}}\right] - \left[\stackrel{2 {\sigma}^{\text{*}}}{\overbrace{2}}\right]\right) = 3$

CO+ CATION

${\text{CO}}^{+}$ has one electron removed from a bonding MO, so its bond order decreases by $\frac{1}{2}$ to become $2.5$. Use the example above to verify via the equation.

CO""^(bb(2+)) DICATION

${\text{CO}}^{2 +}$ has an additional bonding electron removed relative to ${\text{CO}}^{+}$, so it has a bond order of $2$.

CO2 MOLECULE

${\text{CO}}_{2}$ looks like this:

:stackrel(..)("O")="C"=stackrel(..)"O":

So, its double bonds suggest a bond order of $2$.

CARBONATE ANION

By considering its resonance delocalization, the bond order on this molecular ion can be determined.

We should notice that for the $\pi$ bond order, there will be $2$ $\pi$ electrons delocalized onto three bonds, making each bond on average having $\frac{2}{3}$ of a $\pi$ electron, thereby giving a $\pi$ bond order of $\frac{1}{3}$.

Since perfect single bonds have a bond order of $1$, the total bond order on ${\text{CO}}_{3}^{2 -}$ is $\boldsymbol{1. \overline{33}}$.

OVERALL

Overall, we have the bond orders:

• $\text{CO}$: $3$
• ${\text{CO}}^{+}$: $2.5$
• ${\text{CO}}^{2 +}$: $2$
• ${\text{CO}}_{2}$: $2$
• ${\text{CO}}_{3}^{2 -}$: $1. \overline{33}$

You can choose how to order ${\text{CO}}^{2 +}$ and ${\text{CO}}_{2}$ however you like, but the rest is already in order. The shortest bond corresponds to the strongest bond.

Hence, bond length increases down this list.