Question

Draw all geometrical and linkage isomers of \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{NO}_{2}\right)_{2}\).

Short answer

The complex \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{NO}_{2}\right)_{2}\) can have a total of four possible isomers: cis-NN, cis-NO, trans-NN, and trans-NO. These isomers arise from the different arrangements of the \(\mathrm{NH}_3\) and \(\mathrm{NO}_2\) ligands around the cobalt ion (cis and trans geometrical isomers) as well as the different ways the \(\mathrm{NO}_2\) ligand can bind to the cobalt ion (through either nitrogen or oxygen, leading to linkage isomers).

Step-by-step solution

Identifying possible geometrical isomers

In an octahedral complex with the general formula \(\mathrm{MA_4B_2}\), there are two possibilities for geometrical isomers: cis and trans arrangements. The cis isomer has the two B ligands adjacent to each other, whereas the trans isomer has the two B ligands opposite each other.

Drawing cis and trans isomers

Now, let's draw the cis and trans isomer of the complex \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{NO}_{2}\right)_{2}\). Cis isomer: In this arrangement, the two \(\mathrm{NO}_2\) ligands are adjacent to each other. \( \require{AMScd} \begin{CD} \ @. \mathrm{NO}_2 @. \mathrm{NO}_2 \\ @. \ | \\ \mathrm{NH}_3 - \mathrm{Co} @{-}@ _{- \mathrm{NH}_3} \\ @. \ | \\ @. \mathrm{NH}_3 @. \mathrm{NH}_3 \end{CD} \) Trans isomer: In this arrangement, the two \(\mathrm{NO}_2\) ligands are opposite to each other. \( \require{AMScd} \begin{CD} \ @. \mathrm{NH}_3 @. \mathrm{NH}_3 \\ @. \ | \\ \mathrm{NO}_2 - \mathrm{Co} @{-}@ _{- \mathrm{NH}_3} \\ @. \ | \\ @. \mathrm{NH}_3 @. \mathrm{NO}_2 \end{CD} \)

Identifying possible linkage isomers

In the given complex, only the \(\mathrm{NO}_2\) ligand can exhibit linkage isomerism, as it can bind to the cobalt ion through either the nitrogen (N) or the oxygen (O) atom.

Drawing linkage isomers with \(\mathrm{NO}_2\) bonding through nitrogen and oxygen

Now, let's draw the linkage isomers for each geometrical isomer. Cis isomers: 1. Both \(\mathrm{NO}_2\) ligands bind through nitrogen (cis-NN isomer) 2. One \(\mathrm{NO}_2\) ligand binds through nitrogen, and the other binds through oxygen (cis-NO isomer) \( \require{AMScd} \begin{CD} \ @. \mathrm{N}<- \mathrm{O}_2 @. \mathrm{N}<- \mathrm{O}_2 \\ @. \ | \\ \mathrm{NH}_3 - \mathrm{Co} @{-}@ _{- \mathrm{NH}_3} \\ @. \ | \\ @. \mathrm{NH}_3 @. \mathrm{NH}_3 \end{CD} \qquad \require{AMScd} \begin{CD} \ @. \mathrm{N}<- \mathrm{O}_2 @. \mathrm{O}-> \mathrm{N}<- \mathrm{O} \\ @. \ | \\ \mathrm{NH}_3 - \mathrm{Co} @{-}@ _{- \mathrm{NH}_3} \\ @. \ | \\ @. \mathrm{NH}_3 @. \mathrm{NH}_3 \end{CD} \) Trans isomers: 1. Both \(\mathrm{NO}_2\) ligands bind through nitrogen (trans-NN isomer) 2. One \(\mathrm{NO}_2\) ligand binds through nitrogen, and the other binds through oxygen (trans-NO isomer) \( \require{AMScd} \begin{CD} \ @. \mathrm{NH}_3 @. \mathrm{NH}_3 \\ @. \ | \\ \mathrm{N}<- \mathrm{O}_2 - \mathrm{Co} @{-}@ _{- \mathrm{NH}_3} \\ @. \ | \\ @. \mathrm{NH}_3 @. \mathrm{N}<- \mathrm{O}_2 \end{CD} \qquad \require{AMScd} \begin{CD} \ @. \mathrm{NH}_3 @. \mathrm{NH}_3 \\ @. \ | \\ \mathrm{N}<- \mathrm{O}_2 - \mathrm{Co} @{-}@ _{- \mathrm{NH}_3} \\ @. \ | \\ @. \mathrm{NH}_3 @. \mathrm{O}-> \mathrm{N}<- \mathrm{O} \end{CD} \) In total, there are four possible isomers for the complex \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{NO}_{2}\right)_{2}\): cis-NN, cis-NO, trans-NN, and trans-NO.