Problem 52 - Chemistry: Principles and Reactions

Question

WEB 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 \(\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{4}(\mathrm{en})^{3+}\) is 5 . (b) \(\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\) is expected to absorb at a longer wavelength than \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}{\underline{\phantom{xx}}}^{2+}\)

Step-by-Step Solution

Answer

Question: Determine the coordination number of iron(III) in the complex \(\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{4}(\mathrm{en})^{3+}\) and compare the absorption wavelengths of \(\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\) and \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}{\underline{\phantom{xx}}}^{2+}\). Answer: The coordination number of iron(III) in the complex \(\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{4}(\mathrm{en})^{3+}\) is 6. The complex \(\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\) is expected to absorb at a shorter wavelength than \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}{\underline{\phantom{xx}}}^{2+}\).

Step 1: (a) Determining the coordination number of iron(III)

The coordination number of a metal ion in a complex is determined by the number of ligand donor atoms directly bonded to it. In the complex \(\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{4}(\mathrm{en})^{3+}\), there are 4 ammonia ligands (\(\mathrm{NH}_{3}\)) and 1 ethylenediamine ligand (en). Each ammonia ligand provides 1 donor atom (N), while the ethylenediamine ligand (en) provides 2 donor atoms (2 N). To find the coordination number, sum up the number of donor atoms provided by all ligands: \(\text{Coordination number} = 4(\text{from } \mathrm{NH}_{3}s) + 2(\text{from } \mathrm{en}) = 6\) Thus, the statement is false, since the actual coordination number of iron(III) ion in the complex is 6.

Step 2: (b) Comparing the absorption wavelengths of given complexes

To determine which complex has a longer absorption wavelength, we need to understand crystal field theory. The magnitude of the crystal field splitting parameter, \(\Delta_{o}\), affects the wavelength of light absorbed in a d-d transition. Complexes with stronger ligands (ligands that cause a larger splitting) will have a higher \(\Delta_{o}\) and will, therefore, absorb light at a lower wavelength according to the approximate relation \(\Delta_{o} = h\frac{c}{\lambda}\). Hence, the complex with a larger \(\Delta_{o}\) will have a shorter wavelength of absorption. The spectrochemical series orders ligands depending on their ability to split the d orbitals of a transition metal. Based on the spectrochemical series, the cyanide ligand (CN-) is a stronger field ligand compared to ammonia (NH3). Thus, the \(\Delta_{o}\) for \(\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\) will be larger than that of \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}{\underline{\phantom{xx}}}^{2+}\), resulting in the \(\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\) complex absorbing light at a shorter wavelength than \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}{\underline{\phantom{xx}}}^{2+}\). The statement is false. The correct statement is: \(\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\) is expected to absorb at a shorter wavelength than \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}{\underline{\phantom{xx}}}^{2+}\).

Key Concepts

Coordination Number

In coordination chemistry, the coordination number is a fundamental concept. It refers to the number of donor atoms that are directly bonded to the central metal ion in a complex. This is determined by counting the number of ligand atoms that can form a coordinate bond with the metal ion.
For example, in the complex \((\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{4}(\mathrm{en})^{3+}\), the coordination number is not simply the count of ligands, but the total number of donor atoms. Ammonia (\(\mathrm{NH}_{3}\)) acts as a monodentate ligand, contributing one nitrogen atom each.
The ligand ethylenediamine (\(\mathrm{en}\)) is bidentate, which means it can attach at two sites via its nitrogen atoms, providing two donor atoms. Consequently, the coordination number is the sum of donor atoms: 4 from ammonia and 2 from ethylenediamine, totaling 6. Remember, the number of coordination sites is determined by counting these atoms, not the ligands themselves.

Crystal Field Theory

Crystal Field Theory (CFT) is a model that describes the electronic structure of transition metal complexes. It focuses on the interaction between the metal ion's d-orbitals and the electrons from the ligands.
When ligands approach a metal ion, they can cause the d-orbitals of the metal to split into different energy levels. This is due to the electrostatic interactions between the ligand's negative charge and the d-electrons.
The degree of this split is represented by the crystal field splitting parameter \(\Delta_o\). Stronger ligands cause a larger \(\Delta_o\), meaning a greater energy difference between the d-orbitals. This dictates the color and absorption properties of the complex as light absorbed promotes d-electron excitation from a lower to a higher energy state. \[ \Delta_o = \frac{hc}{\lambda} \] If a complex absorbs light at longer wavelengths, it indicates a smaller \(\Delta_o\), while absorption at shorter wavelengths indicates a larger \(\Delta_o\). This is crucial to understanding the optical properties of transition metal complexes.

Spectrochemical Series

The spectrochemical series is an ordered list of ligands based on their ability to split the d-orbitals of the metal center, which directly affects \(\Delta_o\). Ligands that cause a large splitting are termed strong-field ligands, while those causing smaller splits are weak-field ligands.
A key insight of the series is that it provides a comparative understanding of ligand strength in metal complexes. For example, typical strong-field ligands include cyanide (\(\mathrm{CN}^-\)), while ammonia (\(\mathrm{NH}_{3}\)) ranks as a weaker field ligand.
This ordering helps predict the electronic configuration of complexes. For instance, knowing that cyanide is stronger than ammonia lets us predict that the complex \(\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\) has a larger \(\Delta_o\) compared to \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}{\underline{\phantom{xx}}}^{2+}\), resulting in \(\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\) absorbing light at shorter wavelengths. Such concepts are essential to both predicting and understanding the behavior of transition metal complexes in various chemical environments.