Question

Indicate whether each of the following is true or false. If the statement is false, correct it. (a) The coordination number of iron(III) in \(\left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{4}(e n)^{3+}\right]\) is \(5 .\) (b) \(\left[\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\right]\) is expected to absorb at a longer wavelength than \(\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}^{2+}\right]\) (c) Complexes of \(\mathrm{Cr}^{3+}\) are brightly colored, and those of \(\mathrm{Zn}^{2+}\) are colorless. (d) Ions with seven or more d electrons cannot form both high- and low-spin octahedral complexes.

Short answer

Question: Determine whether the following statement is true or false: The coordination number of iron(III) in \(\left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{4}(e n)^{3+}\right]\) is \(5\). Answer: False

Step-by-step solution

Statement (a) Analysis

The given complex is \(\left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{4}(e n)^{3+}\right]\). The coordination number is the number of ligands attached to the central metal ion, in this case, iron(III). We can count 4 ammonia ligands (\(\mathrm{NH}_{3}\)) and 1 ethylene diamine ligand (en) which has two donor atoms. Thus, the coordination number is 4 + 2 = 6, not 5.

Statement (a) Correction

The coordination number of iron(III) in \(\left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{4}(e n)^{3+}\right]\) is \(6\), not \(5\). So, the statement is false.

Statement (b) Analysis

The given complexes are \(\left[\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\right]\) and \(\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}^{2+}\right]\). According to crystal field theory, the stronger the ligand, the larger the splitting of d orbitals would be, resulting in a shorter wavelength absorption. Comparing the ligands \(\mathrm{CN}^{-}\) and \(\mathrm{NH}_{3}\), we can determine that \(\mathrm{CN}^{-}\) is a stronger ligand than \(\mathrm{NH}_{3}\), so the complex with cyanide ligands gives a larger splitting.

Statement (b) Correction

\(\left[\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\right]\) is expected to absorb at a shorter wavelength than \(\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}^{2+}\right]\). So, the statement is false.

Statement (c) Analysis

Complexes of \(\mathrm{Cr}^{3+}\) are indeed brightly colored due to the absorption of visible light, which leads to electronic transitions between their d orbitals. Complexes of \(\mathrm{Zn}^{2+}\) are colorless because \(\mathrm{Zn}^{2+}\) has a full d-orbital and therefore, it doesn't have any suitable electronic transitions that could absorb visible light.

Statement (c) Conclusion

Complexes of \(\mathrm{Cr}^{3+}\) are brightly colored, and those of \(\mathrm{Zn}^{2+}\) are colorless. The statement is true.

Statement (d) Analysis

Ions with seven or more d electrons can indeed only form low-spin octahedral complexes. With such a high number of d electrons, there aren't enough empty low-energy orbitals to adopt a high-spin configuration.

Statement (d) Conclusion

Ions with seven or more d electrons cannot form both high- and low-spin octahedral complexes. The statement is true.

Key concepts

Understanding Crystal Field Theory

Crystal Field Theory (CFT) is a model that describes the electronic structure of transition metal complexes. It is essential to grasp CFT to predict the properties such as colors and magnetism of coordination compounds.
CFT assumes that the interaction between the central metal ion and the ligands surrounding it can be thought of as purely electrostatic. Ligands are considered as point charges (if they are negatively charged) or dipoles (if they are neutral but polar). According to CFT, these negative charges or dipoles approach the metal ion and repel the electrons in the metal's d-orbitals, leading to a splitting into two energy levels: the lower-energy t_2g and the higher-energy e_g. This splitting of the d-orbitals is the central feature explained by CFT and affects many properties of coordination compounds.
Improvement advice on this concept would include discussing the factors that affect the magnitude of the splitting, such as the nature of the ligands and the oxidation state of the metal ion.

Factors Influencing Crystal Field Splitting

• The charge on the metal ion: A higher positive charge attracts ligands more strongly, resulting in greater splitting.
• The geometry of the complex: Different geometries can cause different degrees of splitting. For instance, octahedral complexes typically exhibit a larger split compared to tetrahedral ones.
• The nature of the ligand: Field strength of ligands, as documented in the spectrochemical series, dictates how strongly they can affect the orbitals' energy.

Ligand Field Strength and Its Impact

Ligand field strength is a vital concept when it comes to predicting the spectral and magnetic behaviors of transition metal complexes. The field strength is essentially how effectively a ligand can split the d orbital energies of the central metal ion.
Ligands can thus be organized into a 'spectrochemical series,' a ranking from weaker to stronger field ligands based on their ability to cause this splitting. For example, I⁻ ligands normally lie at the weak end of the series, whereas CN⁻ and CO are strong-field ligands.
Strong-field ligands can force the pairing of electrons in the lower-energy t_2g level, potentially leading to low-spin configurations in the case of octahedral complexes. This directly correlates to the compound's color and magnetism.

Interpreting Spectrochemical Series

• 'Spectrochemical series' helps predict the color and magnetic properties of complexes.
• Ligand field strength affects the possibility of high-spin versus low-spin configurations in octahedral complexes.
• Transition metals with weaker field ligands are often high-spin, making them more magnetic.

Electronic Transitions Within Complexes

Electronic transitions are changes in the energy state of an electron within a chemical species. In coordination chemistry, these transitions are responsible for the vivid colors we observe in certain metal complexes.
In an octahedral complex, for instance, electronic transitions can occur from the lower-energy t_2g level to the higher-energy e_g level. The energy required for such transitions falls in the visible spectrum, hence absorbing certain wavelengths and reflecting the complementary color.
The exercise provided indicates that Cr³⁺ complexes are colored because they have empty d orbitals that can absorb visible light. In contrast, Zn²⁺ complexes are colorless as Zn²⁺ has a completely filled d-shell, leaving no room for such electronic transitions.

Key Points About Electronic Transitions

• When an electron jumps to a higher orbital, the energy absorbed corresponds to a specific wavelength of light.
• The observed color of a complex is due to the wavelengths not absorbed (i.e., the light that is seen).
• Extensive ligand field splitting can lead to higher-energy electronic transitions, thereby absorbing lower wavelengths (higher frequency) of light.