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Chapter 24: Problem 30

Consider an octahedral complex \(\mathrm{MA}_{3} \mathrm{~B}_{3}\). How many geometric isomers are expected for this compound? Will any of the isomers be optically active? If so, which ones?

Short Answer

Expert verified
There are two geometric isomers expected for the octahedral complex MA3B3: the fac isomer and the mer isomer. However, neither of these isomers will be optically active, as both possess planes of symmetry in their structures.

Step by step solution

01

Understand the Octahedral complex structure

An octahedral complex has six ligands surrounding the central metal atom. In this case, we have three A ligands and three B ligands. The arrangement of these ligands gives rise to different geometric isomers.
02

Draw the possible geometric isomers of the octahedral complex MA3B3

There are two possibilities for the arrangement of A and B ligands around the central metal atom: 1. All three A ligands can occupy a facial position (in a triangular face of the octahedron), while the B ligands occupy positions opposite to each A ligand, with two of them on the same face. This arrangement is called the fac isomer. 2. The second possibility is that A and B ligands can be in a meridional position with each A ligand having one B ligand occupying positions trans to it (also known as mer isomer).
03

Determine optical activity for each geometric isomer

To check for optical activity, we need to look for a plane of symmetry in the two isomers. If there is a plane of symmetry, the complex is not optically active. In the fac isomer, there are three planes of symmetry: Each plane passes through the central metal atom and is perpendicular to one of the triangular faces. Therefore, the fac isomer is NOT optically active. In the mer isomer, there is a single plane of symmetry: This plane passes through the central metal atom, dividing it into two equal halves. Because of this plane of symmetry, the mer isomer is also NOT optically active. So, in conclusion:
04

Summarize the results

There are two possible geometric isomers for the complex MA3B3: the fac isomer and the mer isomer. Neither of these isomers is optically active, as both have planes of symmetry.

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Most popular questions from this chapter

The molecule dimethylphosphinoethane \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{PCH}_{2}-\mathrm{CH}_{2} \mathrm{P}\left(\mathrm{CH}_{3}\right)_{2}\right.\), which is abbreviated \(\left.\mathrm{dmpe}\right]\) is used as a ligand for some complexes that serve as catalysts. A complex that contains this ligand is \(\mathrm{Mo}(\mathrm{CO})_{4}(\) dmpe \()\). (a) Draw the Lewis structure for dmpe, and compare it with ethylenediammine as a coordinating ligand. (b) What is the oxidation state of Mo in \(\mathrm{Na}_{2}\left[\mathrm{Mo}(\mathrm{CN})_{2}(\mathrm{CO})_{2}(\mathrm{dmpe})\right] ?\) (c) Sketch the structure of the \(\left[\mathrm{Mo}(\mathrm{CN})_{2}(\mathrm{CO})_{2}(\mathrm{dmpe})\right]^{2-}\) ion, including all the possible isomers.

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Carbon monoxide is toxic because it binds more strongly to the iron in hemoglobin (Hb) than does \(\mathrm{O}_{2}\), as indicated by these approximate standard free-energy changes in blood: $$ \begin{array}{clrl} \mathrm{Hb}+\mathrm{O}_{2} \longrightarrow \mathrm{HbO}_{2} & & \Delta G^{\circ}=-70 \mathrm{~kJ} \\ \mathrm{Hb}+\mathrm{CO} \longrightarrow \mathrm{HbCO} & \Delta G^{\circ}=-80 \mathrm{~kJ} \end{array} $$ Using these data, estimate the equilibrium constant at \(298 \mathrm{~K}\) for the equilibrium $$ \mathrm{HbO}_{2}+\mathrm{CO} \rightleftharpoons \mathrm{HbCO}+\mathrm{O}_{2} $$
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