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Chapter 24: Problem 24

In both \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) and \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) ions, the iron is present as \(\mathrm{Fe}(\mathrm{II}) ;\) however, \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) is paramagnetic, whereas \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) is diamagnetic. Explain this difference.

Short Answer

Expert verified
The difference in magnetic behavior of the two complexes is due to the nature of the ligands attached to the metal center. In \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\), water is a weak field ligand, leading to unpaired electrons and therefore a paramagnetic complex. In contrast, in \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\), the cyanide is a strong field ligand that causes pairing of electrons, resulting in a diamagnetic complex.

Step by step solution

01

- Understanding Complex Ions and Ligands

The first step is understanding the nature of the two complex ions. A complex ion has a metal center surrounded by ligands. Here, \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) has water (\(\mathrm{H}_{2} \mathrm{O}\)) as ligands, while \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) has cyanide (\(\mathrm{CN}^{-}\)) as ligands. Despite both having the same metal center (\(\mathrm{Fe}^{2+}\)), the ligand difference suggests they may interact with the iron differently, affecting its electron configuration and thus its magnetic properties.
02

- Understanding Magnetism in Coordination Complexes

Paramagnetism arises from the presence of unpaired electrons, while diamagnetism is a property of substances with no unpaired electrons. In other words, if a metal ion in a complex ion has any unpaired electrons, it will be paramagnetic; if all electrons are paired, it will be diamagnetic. The difference in ligands and their electron-pairing behavior will determine the type of magnetism.
03

- Analyzing the Electron Configurations

In the octahedral field as seen in both complexes, the energy levels split into two sets - the lower energy level called t2g and the higher energy level called eg. Now let's look at each complex individually.
04

- Understanding the \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) Complex

For the \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) complex, the \(\mathrm{Fe}^{2+}\) ion has the electron configuration 3d6, because the ligand is a weak field ligand, it doesn't cause pairing of the electrons. Therefore, four of the six electrons fill the t2g level and the remaining two electrons partially fill the eg level. The presence of these unpaired electrons results in the complex being paramagnetic.
05

- Understanding the \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) Complex

In the \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) complex, the \(\mathrm{Fe}^{2+}\) ion also has the electron configuration 3d6, but since cyanide (\(\mathrm{CN}^{-}\)) is a strong field ligand, it forces the electrons to pair up. In this case, all six electrons fill the lower energy t2g level and the higher energy eg level remains vacant, indicating no unpaired electrons. This makes the complex ion diamagnetic.

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Most popular questions from this chapter

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.

Cyano complexes of transition metal ions (such as \(\mathrm{Fe}^{2+}\) and \(\mathrm{Cu}^{2+}\) ) are often yellow, whereas aqua complexes are often green or blue. Explain the basis for this difference in color.

Explain the following observations in terms of complex-ion formation. (a) \(\mathrm{CoCl}_{3}\) is unstable in aqueous solution, being reduced to \(\mathrm{CoCl}_{2}\) and liberating \(\mathrm{O}_{2}(\mathrm{g}) .\) Yet, \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}\) can be easily maintained in aqueous solution. (b) AgI is insoluble in water and in dilute \(\mathrm{NH}_{3}(\mathrm{aq})\) but AgI will dissolve in an aqueous solution of sodium thiosulfate.

A tabulation of formation constant data lists the following log \(K\) values for the formation of \(\left[\mathrm{CuCl}_{4}\right]^{2-}\): \(\log K_{1}=2.80, \quad \log K_{2}=1.60, \quad \log K_{3}=0.49, \quad\) and \(\log K_{4}=0.73 .\) What is the overall formation constant \(\beta_{4}=K_{\mathrm{f}}\) for \(\left[\mathrm{CuCl}_{4}\right]^{2-} ?\)

Write the names and formulas of three coordination isomers of \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]\left[\mathrm{Cr}(\mathrm{ox})_{3}\right]\).
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