Problem 161 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

[Co(CN)_6]^{3-} exhibits the lowest paramagnetic behavior as it has zero unpaired electrons.

Step 1: Understanding Paramagnetism

Paramagnetic behavior arises from unpaired electrons in the d orbitals of transition metals. The fewer the unpaired electrons, the lower the paramagnetic behavior. Hence, to identify which complex has the lowest paramagnetic behavior, we must find which has the fewest unpaired electrons.

Step 2: Determining Electron Configuration

For each metal complex, determine the oxidation state of the metal and its electron configuration. Consider that CN- is a strong field ligand, which often causes pairing of electrons in the d orbitals due to a large crystal field splitting energy.

Step 3: Evaluating [Cr(CN)6]^{3-}

In \([Cr(CN)6]^{3-}\), the oxidation state of Cr is +3. Cr^{3+} has an electron configuration of \[\text{3d}^3\text{4s}^0\text{4p}^0\] . With the 3 strong field CN^- ligands, all 3 electrons remain unpaired.

Step 4: Evaluating [Mn(CN)6]^{3-}

For \([Mn(CN)6]^{3-}\), Mn is in the oxidation state of +3. Mn^{3+} has a configuration of \[\text{3d}^4\text{4s}^0\text{4p}^0\] . With strong field CN^-, these electrons fill to have 2 unpaired electrons.

Step 5: Evaluating [Fe(CN)6]^{3-}

In \([Fe(CN)6]^{3-}\), Fe is +3. Fe^{3+} has \[\text{3d}^5\text{4s}^0\text{4p}^0\] . With strong field CN^- ligands, all electrons pair up resulting in 1 unpaired electron.

Step 6: Evaluating [Co(CN)6]^{3-}

\([Co(CN)6]^{3-}\), Co is +3. Co^{3+} has \[\text{3d}^6\text{4s}^0\text{4p}^0\] . Due to strong field CN^- ligands, all electrons are paired, resulting in zero unpaired electrons.

Step 7: Conclusion: Determining Lowest Paramagnetism

Among the complexes, [Co(CN)6]^{3-} has zero unpaired electrons, resulting in the lowest paramagnetic behavior.

Key Concepts

Crystal Field Theory

Crystal Field Theory (CFT) is a crucial model that helps us understand the behavior of transition metal complexes. It mainly focuses on the interaction between the central metal ion and the ligands surrounding it. When ligands approach a metal ion, they create an electric field that affects the metal's d orbitals. These orbitals, which usually have the same energy, split into different energy levels due to this interaction. The degree of splitting depends on various factors but is most significantly influenced by the strength of the ligands.

Ligands are classified as either strong or weak field, based on their ability to cause the splitting of metal d orbitals. Strong field ligands like cyanide (\(\text{CN}^-\)) lead to a large gap in energy, often resulting in paired electrons within these orbitals. This leads to lower paramagnetic behavior because fewer or no unpaired electrons remain. In the context of transition metal complexes:

• Strong field ligands can force electrons to pair up, reducing the number of unpaired ones.
• Weak field ligands lead to less pairing, leaving more unpaired electrons.

Understanding these interactions is key in predicting the magnetic properties of metal complexes.

Electron Configuration in Coordination Compounds

The electron configuration of transition metals in coordination compounds plays a vital role in determining their magnetic properties. Transition metal ions typically contain unfilled d orbitals, and their electron arrangements can vary based on ligand interaction.

When considering coordination compounds, it is essential to determine the oxidation state of the metal ion to establish the correct electron configuration. For instance:

• Chromium in \([Cr(CN)_6]^{3-}\) has an oxidation state of +3, leading to an electron configuration of \([Ar] 3d^3\).
• Manganese in \([Mn(CN)_6]^{3-}\) is also +3, resulting in \([Ar] 3d^4\).
• Similarly, iron and cobalt in their respective complexes are in the +3 oxidation state, with configurations \([Ar] 3d^5\) for iron and \([Ar] 3d^6\) for cobalt.

Cyanide ligands, being strong field, cause significant splitting, which drives electrons to pair up in the lower energy orbitals, affecting the overall magnetic properties. In contrast, compounds with weak field ligands behave differently, resulting in more unpaired electrons and higher paramagnetism.

Transition Metal Complexes

Transition metal complexes are fascinating chemical entities comprising a central metal atom or ion surrounded by molecules or ions, known as ligands. These complexes exhibit a range of interesting properties due to the unique behavior of transition metals, principally their variable oxidation states and ability to form colored compounds.

The property of paramagnetism in transition metal complexes arises from unpaired electrons in the metal's d orbitals. The number of unpaired electrons is influenced by the ligand field strength. Cyanide (\(\text{CN}^-\)) is notable for being a strong field ligand in these contexts, which usually results in fewer unpaired electrons:

• In the discussed complexes, cobalt forms \([Co(CN)_6]^{3-}\) with no unpaired electrons, hence exhibiting the least paramagnetism.
• Other metals like chromium, manganese, and iron in similar complexes retain more unpaired electrons, contributing to their paramagnetic behavior.

Transition metal complexes' ability to showcase behaviors like paramagnetism is influenced significantly by their electron arrangement, dictated by both the metal's inherent properties and the nature of the surrounding ligands.