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Chapter 24: Problem 64

A structure that Werner examined as a possible alternative to the octahedron is the trigonal prism. (a) Does this structure predict the correct number of isomers for the complex ion \(\left[\mathrm{CoCl}_{2}\left(\mathrm{NH}_{3}\right)_{4}\right]^{+} ?\) If not, why not? (b) Does this structure account for optical isomerism in \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+} ?\) Explain.

Short Answer

Expert verified
The trigonal prism structure does not predict the correct number of geometric isomers for the complex ion \(\left[\mathrm{CoCl}_{2}\left(\mathrm{NH}_{3}\right)_{4}\right]^{+}\) because it only accounts for one isomer, not two. However, it does account for optical isomerism in the complex ion \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) because it enables the formation of two non-superimposable mirror images.

Step by step solution

01

determining isomers

The complex ion \(\left[\mathrm{CoCl}_{2}\left(\mathrm{NH}_{3}\right)_{4}\right]^{+}\) has two Chlorine ligands and four Ammonia ligands in coordination with Cobalt. A trigonal prism structure would place two sets of three ligands on opposite triangular faces. Because the Chlorine ligands are identical to each other and the Ammonia ligands are identical to each other, this arrangement produces only one geometric isomer, regardless of where the Chlorine and Ammonia groups are placed.
02

explaining missing isomers

The trigonal prism structure does not account for all possible geometric isomers. The octahedral structure, in contrast, predicts two isomers because the Chlorine ligands can either be adjacent to each other (cis arrangement) or opposite to each other (trans arrangement). Therefore, the trigonal prism structure fails to predict the correct number of isomers for this complex ion.
03

addressing optical isomerism

In the case of the complex ion \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\), where en refers to ethylenediamine, a different type of isomerism—optical isomerism—must be considered. A molecule is optically active if it is not superimposable on its mirror image. The en ligands are bidentate, meaning they each bind to cobalt at two points, forming a composed lattice of triangles. In the trigonal prism arrangement, two possible configurations (mirror images of each other) can be formed, which represents an instance of optical isomerism. Therefore, the trigonal prism structure does correctly predict optical isomerism in this complex ion.

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Most popular questions from this chapter

Explain the following observations in terms of complex-ion formation. (a) \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) is soluble in \(\mathrm{NaOH}(\mathrm{aq})\) but insoluble in \(\mathrm{NH}_{3}(\mathrm{aq})\) (b) \(\mathrm{ZnCO}_{3}(\mathrm{s})\) is soluble in \(\mathrm{NH}_{3}(\mathrm{aq}),\) but \(\mathrm{ZnS}(\mathrm{s})\) is not. (c) The molar solubility of AgCl in pure water is about \(1 \times 10^{-5} \mathrm{M} ;\) in \(0.04 \mathrm{M} \mathrm{NaCl}(\mathrm{aq}),\) it is about \(2 \times 10^{-6}; \mathrm{M}\) but in \(1 \mathrm{M} \mathrm{NaCl}(\mathrm{aq}),\) it is about \(8 \times 10^{-5} \mathrm{M}\).

Indicate what type of isomerism may be found in each of the following cases. If no isomerism is possible, so indicate. (a) \(\left[\mathrm{Cr}(\mathrm{en})_{2} \mathrm{Br}_{2}\right]^{+}\) (b) \(\left[\operatorname{Co}(\text { ox })_{2} \operatorname{Br}(\text { SCN })\right]^{3-}\) (c) \(\left[\mathrm{NiCl}_{4}(\mathrm{en})\right]^{2-}\) (d) \([\mathrm{PtBrCl}(\text { ox })]^{-}\) (e) \(\left[\operatorname{Cr}(\text { Cl })_{3}(\text { det })\right],\) det is \(\mathrm{H}_{2} \mathrm{N}\left(\mathrm{CH}_{2}\right)_{2} \mathrm{NH}\left(\mathrm{CH}_{2}\right)_{2} \mathrm{NH}_{2}\)

Of the following complex ions, the one that is optically active is (a) \(\operatorname{cis}-\left[\operatorname{CoCl}_{2}(\text { en })_{2}\right]^{+} ;\) (b) \(\left[\operatorname{CoCl}_{2}\left(\mathrm{NH}_{3}\right)_{4}\right]^{+}\) (c) \(\left[\mathrm{CoCl}_{4}\left(\mathrm{NH}_{3}\right)_{2}\right]^{-} ;(\mathrm{d})\left[\mathrm{CuCl}_{4}\right]^{-}\).

Draw structures to represent these four complex ions: (a) \(\left[\mathrm{PtCl}_{4}\right]^{2-} ;\) (b) \(\left[\mathrm{FeCl}_{4}(\mathrm{en})\right]^{-} ;\) (c) \(\operatorname{cis}-\left[\mathrm{FeCl}_{2}(\mathrm{ox})(\mathrm{en})\right]^{-}\) (d) trans- \(\left[\mathrm{CrCl}(\mathrm{OH})\left(\mathrm{NH}_{3}\right)_{4}\right]^{+}\).

In Example \(24-5,\) we chose between a tetrahedral and a square-planar structure for \(\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}\) based on magnetic properties. Could we similarly use magnetic properties to establish whether the ammine complex of \(\mathrm{Ni}(\mathrm{II})\) is octahedral \(\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) or tetrahedral \(\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} ?\) Explain.
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