Question

The correct option(s) regarding the complex [Co(en) \(\left.\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{3+}\) \(\left(\right.\) en \(\left.=\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)\) 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 [Co(en)(NH3)4] \(^{3+}\)

Short answer

The correct options are (B) It will have three geometrical isomers if bidentate 'en' is replaced by two cyanide ligands, and (D) It absorbs light at longer wavelength as compared to [Co(en)(NH3)4]^(3+).

Step-by-step solution

- Determine Coordination Number and Geometry

The coordination number of a complex is the number of ligand donor atoms that are bonded to the central metal ion. In this complex, Co has a coordination number of 6, bonded with two nitrogen atoms from one ethylenediamine (en) molecule and three ammonia (NH3) molecules along with one water molecule (H2O), making a total of six ligands. Hence, the complex has an octahedral geometry.

- Analyze Geometrical Isomers

Geometrical isomers occur in octahedral complexes usually with bidentate ligands and when there's a cis-trans configuration possibility. In the given complex, due to the presence of a symmetrical bidentate ligand (en) and three unidentate ligands of one type (NH3) and one of another (H2O), there are no cis-trans isomers possible. Hence, the complex cannot have two geometrical isomers.

- Predict Geometrical Isomers upon Ligand Replacement

If the bidentate 'en' ligand is replaced by two monodentate cyanide ligands, the number of different types of ligands increases to three (three NH3, two CN, and one H2O). This allows for three possible isomers, where the CN ligands can be adjacent (cis) or opposite (trans) to each other, and the water molecule can be either cis or trans to the CN ligands. Hence, three geometrical isomers are possible.

- Determine Magnetic Properties

The oxidation state of Co in the complex can be determined by assuming a charge of +1 for each NH3 and H2O ligands and +2 for the en ligand. Since the overall charge of the complex is +3, and the charges on the ligands add up to +3, Co must be in the +3 oxidation state. Cobalt(III) typically forms low-spin d6 complexes, which are diamagnetic. Therefore, this complex is not paramagnetic.

- Analyze Light Absorption

The absorption of light in a complex depends largely on the ligand field strength. The 'en' ligand is a stronger field ligand than NH3, so it will cause a larger splitting in the d-orbitals of Co(III). Thus, the complex [Co(en)(NH3)4]^(3+) will have a higher energy gap between the d-orbitals than [Co(en)(NH3)3(H2O)]^(3+), and will therefore absorb light at a shorter wavelength (higher energy). Contrary to the claim in option D, the complex [Co(en)(NH3)3(H2O)]^(3+) will absorb light at a longer wavelength.

Key concepts

Coordination Number

In coordination chemistry, the coordination number is a fundamental concept referring to the number of points around a central metal atom where ligands (atoms, ions, or molecules that donate electrons to the metal) are attached. This number is crucially linked with the overall geometry and stability of the complex.

For instance, the complex in the exercise, [Co(en)(NH₃)₃(H₂O)]³⁺, has a coordination number of six. This number is derived from the following attachments to the metal center: two nitrogens from one bidentate ethylenediamine (en) ligand and one nitrogen each from three ammonia (NH₃) ligands, in addition to one oxygen from a water molecule. When counting coordination number, both unidentate ligands such as NH₃ and H₂O, which occupy one coordination site each, and bidentate ligands like en, which occupy two sites, are considered.

An accurate determination of coordination number is vital as it directly impacts the molecular geometry and the potential for isomerism, as seen in the step-by-step solution provided in the textbook exercise.

Geometrical Isomers

Geometrical isomers about coordination complexes arise from the spatial arrangement of ligands attached to the central metal atom. These isomers have the same molecular formula but with different geometrical configurations, often referred to as cis (same side) and trans (across from each other) isomers.

In the given exercise, the key to understanding isomerism lies in recognizing that certain ligand arrangements permit isomerism, while others do not. The complex [Co(en)(NH₃)₃(H₂O)]³⁺ cannot display geometrical isomerism due to its symmetrical bidentate ligand (en) and the identical nature of the three NH₃ ligands, which leads to a uniform octahedral structure. However, if we replace the 'en' with two cyanide ligands, the resulting increase in the diversity of ligands allows for different arrangements — enabling the formation of geometrical isomers.

Ligand Field Theory

Ligand Field Theory (LFT) is an extension of crystal field theory, providing a more detailed account of the bonding in transition metal complexes. Using the principles of molecular orbital theory, it accounts for the nature of metal-ligand interactions and how these interactions influence the energy levels (orbitals) of the metal ions.

In our exercise, LFT explains why the complex [Co(en)(NH₃)₃(H₂O)]³⁺ absorbs light at a longer wavelength compared to [Co(en)(NH₃)₄]³⁺. Due to the strength of the ligand field created by 'en,' it results in a larger gap between the metal's d-orbitals compared to complexes with weaker ligands. A greater splitting leads to higher energy differences that are overcome when the complex absorbs light. Consequently, complexes with strong-field ligands like 'en' absorb light of shorter wavelengths, which aligns with the fact that light of longer wavelengths has lower energy.