Problem 58 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The correct option(s) regarding the complex \(\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{3+}\) \(\left(\right.\) en \(=\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\) ) is (are) (a) It has two geometrical isomers (b) It will have three geometrical isomers if bidentate 'en' is replaced by two cyanide ligands (c) It is paramagnetic (d) It absorbs light at longer wavelength as compared to \(\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{4}\right]^{3+}\)

Step-by-Step Solution

Answer

(a), (b), (d) are correct options.

Step 1: Identify the Complex Geometry

The complex given is \( \left[\mathrm{Co}(\mathrm{en})(\mathrm{NH}_{3})_{3}(\mathrm{H}_{2}\mathrm{O})\right]^{3+} \). This is a coordination compound with one bidentate ligand (en) and three monodentate ligands (NH3, NH3, NH3, H2O). Since cobalt in +3 oxidation state typically forms octahedral complexes, we expect this complex to have an octahedral geometry.

Step 2: Determine Geometrical Isomerism

In an octahedral complex with a bidentate ligand and three different monodentate ligands, geometrical isomers are possible. The ligands can occupy different positions around the octahedral metal center. Here, two possible geometrical isomers exist depending on the arrangement of the ligands: trans (bidentate ligand opposite) and cis (bidentate ligand adjacent). So, option (a) is true.

Step 3: Replace Bidentate Ligand and Analyze isomerism

Replacing bidentate 'en' with two monodentate cyanide ligands cn to form \(\left[\text{Co}(\text{CN})_{2}(\text{NH}_{3})_{3}(\text{H}_{2}\text{O})\right]^{3+}\). This complex can have three possible isomers by varying the position of the monodentate ligands: one with all cyanides cis, one with one cyanide cis and one trans, and all cyanides trans. Thus, option (b) is true.

Step 4: Check Paramagnetism

Cobalt in the +3 state (\(\text{Co}^{3+}\)) with strong field ligands (such as en and \(\text{NH}_{3}\)) tends to form low-spin complexes. Low-spin \(\text{Co}^{3+}\) has no unpaired electrons, making the complex diamagnetic. Therefore, option (c) is false.

Step 5: Compare Light Absorption with another Complex

The complex \(\left[\mathrm{Co}( ext{en})(\mathrm{NH}_{3})_{4}\right]^{3+}\) has stronger ligand field strength than water (\(\text{H}_2\text{O}\)). A stronger field results in a larger difference in energy levels, absorbing light at shorter wavelengths. As such, the original complex with water should absorb light at a longer wavelength compared to the comparison complex. Option (d) is true.

Key Concepts

Geometrical Isomerism

Geometrical isomerism, also known as cis-trans isomerism, is a form of stereoisomerism, where the relative positions of ligand atoms bonded to a central atom or ion can lead to different arrangements in space. This can occur in coordination compounds like octahedral complexes, where the ligands can either be adjacent (cis) or opposite (trans) to each other. In the complex \( \left[\text{Co}(\text{en})(\text{NH}_3)_3(\text{H}_2\text{O})\right]^{3+} \), the geometrical isomerism arises because of its octahedral shape, where a bidentate ligand (en) and three different monodentate ligands (\( \text{NH}_3 \) and \( \text{H}_2\text{O} \)) can arrange in more than one distinct way.
Geometrical isomers have significance in chemistry due to their different chemical and physical properties. For example, their reactivity can differ, affecting how they interact with other molecules. These differences can be critical in fields like biochemistry and pharmacology, where the shape of a molecule can influence its function or how it is processed in the body.
When the bidentate ligand 'en' is replaced by two cyanide ions in \( \left[\text{Co}(\text{CN})_2(\text{NH}_3)_3(\text{H}_2\text{O})\right]^{3+} \), more geometrical isomers can form because the monodentate ligands add flexibility to the arrangement. Consequently, the complex can adopt three different isomeric forms based on ligand positioning.

Paramagnetism

Paramagnetism is a form of magnetism that arises from the presence of unpaired electrons in an atom or molecule. Compounds with one or more unpaired electrons are drawn to magnetic fields. In coordination chemistry, whether a complex is paramagnetic or diamagnetic depends on the arrangement of electrons in the metal center's d-orbitals, which is influenced by ligand field strength.
In the complex \( \left[\text{Co}(\text{en})(\text{NH}_3)_3(\text{H}_2\text{O})\right]^{3+} \), cobalt is in the +3 oxidation state. With strong field ligands like 'en' and \( \text{NH}_3 \), the electrons usually pair up in low-spin configurations, resulting in no unpaired electrons. Thus, this specific complex is diamagnetic.
However, not all cobalt(III) complexes are diamagnetic. The spin state depends on the specific ligands attached to the metal and their ability to split d-orbital energies. High-spin complexes, with weak field ligands, typically have unpaired electrons, making them paramagnetic. Understanding whether a complex is paramagnetic or diamagnetic is essential for predicting its reactivity and behavior in magnetic fields, which is useful in catalysis and material science.

Octahedral Complexes

Octahedral complexes are a common type of coordination compound where six ligands are symmetrically arranged around a central metal ion. This geometry is prevalent in compounds with metal ions that have a coordination number of six, such as cobalt in its +3 oxidation state. The spatial arrangement of ligands in an octahedral complex can significantly influence the chemical properties and reactivity of the compound.
In the complex \( \left[\text{Co}(\text{en})(\text{NH}_3)_3(\text{H}_2\text{O})\right]^{3+} \), the octahedral structure allows for different configurations of ligands, leading to potential geometrical isomers. The octahedral geometry also affects the electronic transitions within the metal ion, influencing properties such as color and magnetic behavior.
One notable aspect of octahedral complexes is their ligand field strength, which impacts the splitting of the d-orbitals in the metal ion. For instance, strong field ligands like 'en' and \( \text{NH}_3 \) lead to larger d-orbital splitting and tend to result in low-spin complexes. This property is crucial in determining the electronic structure, magnetic properties, and spectroscopic behavior of the complex.
Understanding octahedral complexes and their characteristics is vital in fields like inorganic chemistry and material science, where the design of specific geometries can lead to new materials with tailored properties.