Question

Which of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour? (a) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) (b) \([\mathrm{Co}(\mathrm{CN})]^{3-}\) (c) \([\mathrm{Mn}(\mathrm{CN})]^{3-}\) (d) \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{3}\)

Short answer

\([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\) and \([\mathrm{Co}(\mathrm{CN})]^{3-}\) exhibit low paramagnetic behavior, but are actually diamagnetic.

Step-by-step solution

Identify the Metal and Its Oxidation State

For each complex, identify the metal ion involved and determine its oxidation state. The anion cyanide (CN\(^-\)) has a charge of -1. - For \( \left[ \mathrm{Fe} ( \mathrm{CN} )_{6} \right]^{3-} \), the oxidation state of Fe is +3 (6 times -1 from CN plus 3 gives +3). - For \( [ \mathrm{Co} ( \mathrm{CN} )]^{3-} \), the oxidation state of Co is +3. - For \( [ \mathrm{Mn} ( \mathrm{CN} )]^{3-} \), the oxidation state of Mn is +3.- For \( \left[ \mathrm{Cr} ( \mathrm{CN} )_{6} \right]^{3} \), the oxidation state of Cr is +6.

Analyze the Electron Configuration

Determine the electron configuration for each metal ion with its given oxidation state:- For Fe\(^{3+}\): [Ar] 3d\(^5\).- For Co\(^{3+}\): [Ar] 3d\(^6\).- For Mn\(^{3+}\): [Ar] 3d\(^4\).- For Cr\(^{6+}\): [Ar]. (Since all 3d and 4s electrons are removed).

Evaluate the Ligand Field

Cyanide (CN\(^-\)) is a strong field ligand, which means it causes pairing of electrons and can lead to low-spin complexes.Assess which of the complexes could become low spin due to this pairing. A low-spin configuration is often associated with lower paramagnetism.

Check for Unpaired Electrons

Count unpaired electrons in each complex:- \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\) in low-spin would have no unpaired electrons.- \([\mathrm{Co}(\mathrm{CN})]^{3-}\) in low-spin would have no unpaired electrons.- \([\mathrm{Mn}(\mathrm{CN})]^{3-}\) low-spin would be unlikely due to fewer electrons and would still have 2 unpaired electrons.- \([\mathrm{Cr}(\mathrm{CN})_{6}]^{3}\), since it is already empty, has no unpaired electrons.

Determine the Complex with Lowest Paramagnetism

The lowest amount of magnetic behaviour coincides with the complex that has the fewest or no unpaired electrons. Therefore, - \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\), \([\mathrm{Co}(\mathrm{CN})]^{3-}\), and \([\mathrm{Cr}(\mathrm{CN})_{6}]^{3}\) have no unpaired electrons in their low-spin state, making them diamagnetic.

Key concepts

Electronic Configuration

In coordination chemistry, understanding electronic configuration is crucial when examining metal complexes. Electronic configuration provides insight into how electrons are distributed in the orbitals of an atom or ion. For transition metals, it's especially important to note how these electrons are arranged in the d-orbitals, as this affects the chemical behavior.
For the cyano complexes in this exercise, we analyze the electronic configuration for each metal in its specific oxidation state:

• Iron (Fe) in \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\), has an oxidation state of +3, leading to an electron configuration of \([\mathrm{Ar}] 3d^{5}\).
• Cobalt (Co) in \([\mathrm{Co}(\mathrm{CN})]^{3-}\), also at a +3 oxidation state, has an electron configuration of \([\mathrm{Ar}] 3d^{6}\).
• Manganese (Mn) in \([\mathrm{Mn}(\mathrm{CN})]^{3-}\) has a +3 oxidation state, resulting in \([\mathrm{Ar}] 3d^{4}\).
• Chromium (Cr) in \([\mathrm{Cr}(\mathrm{CN})_{6}]^{3}\) at a +6 oxidation state, leaves us with \([\mathrm{Ar}]\) since all 3d and 4s electrons are removed.

The electronic configuration assists us in predicting the behavior of these metal complexes when interacting with ligands like cyanide.

Cyano Complexes

Cyano complexes refer to coordination compounds where the ligand is the cyanide ion (CN^{−}). Cyanide is a well-known ligand in coordination chemistry due to its strong ability to bind to metal ions, forming stable complexes. It is particularly known for being a strong field ligand.
The implication of having cyanide as a ligand is that it can significantly influence the metal ion’s electronic structure.

• The cyanide ligand causes a substantial increase in energy splitting in the metal d-orbitals.
• It often leads to the pairing of electrons in lower energy orbitals, leading to low-spin configurations.
• This property makes cyano complexes particularly interesting to study in terms of their magnetic and spectroscopic properties.

Understanding how the cyanide ligand interacts with different metal ions can explain why some complexes exhibit particular magnetic and electronic properties.

Paramagnetic Behaviour

Paramagnetism arises in substances that have unpaired electrons. The presence or absence of unpaired electrons is a key factor determining if a substance exhibits magnetic behavior. In coordination compounds, the ligand field strength and the specific metal ion are critical in influencing whether a complex is paramagnetic or diamagnetic.
For example, consider the cyano complexes:

• \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\) can be diamagnetic in a low-spin state because of complete electron pairing.
• \([\mathrm{Co}(\mathrm{CN})]^{3-}\) is also diamagnetic when paired by the strong-field ligand cyanide.
• In contrast, \([\mathrm{Mn}(\mathrm{CN})]^{3-}\) may remain paramagnetic due to the presence of two unpaired electrons.
• \([\mathrm{Cr}(\mathrm{CN})_{6}]^{3}\) has no unpaired electrons and is thus diamagnetic in its empty 3d configuration.

Thus, assessing paramagnetic behavior helps determine how electron pairing in complexes influences their magnetic properties.

Ligand Field Theory

Ligand Field Theory is an extension of Crystal Field Theory, aimed at describing the effect of ligands on the metal ion’s d-orbitals. In essence, it addresses how the interactions between ligands and metal ions modify the energy levels, shapes, and occupancy of these d-orbitals.
Key features of Ligand Field Theory include:

• Strong field ligands like cyanide cause a large splitting in d-orbital energies, known as ligand field splitting.
• This often results in low-spin complexes as it forces electrons to pair up in lower energy orbitals.
• These low-spin states are typically experience reduced paramagnetism due to fewer unpaired electrons.
• The ligand field also affects other properties such as color and stability of the metal complexes.

Understanding Ligand Field Theory helps predict and explain the magnetic and electronic behavior of coordination complexes, such as the variability seen in cyano complexes.