Problem 82 - Chemistry: The Central Science in SI Units, Global Edition

Question

Solutions of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+},\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (both octahedral), and \(\left[\mathrm{CoCl}_{4}\right]^{2-}(\) tetrahedral) are colored. One is pink, one is blue, and one is yellow. Based on the spectrochemical series and remembering that the energy splitting in tetrahedral complexes is normally much less than that in octahedral ones, assign a color to each complex.

Step-by-Step Solution

Answer

The color assignment for the given coordination complexes based on the spectrochemical series and their coordination geometry is: \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\): Pink \(\left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\): Blue \(\left[\mathrm{CoCl}_{4}\right]^{2-}\): Yellow

Step 1: Understand the energy splitting in octahedral and tetrahedral complexes

In an octahedral complex, the energy of the d orbitals splits into two levels: the lower energy t2g level (consisting of dxy, dxz, and dyz orbitals) and the higher energy eg level (consisting of dx^2-y^2 and dz^2 orbitals). The energy difference between these two levels is called ∆o. In a tetrahedral complex, the energy splitting of d orbitals is inverted compared to octahedral complexes, with the higher energy level being t2 and the lower energy level being e; this energy difference is called ∆t. It is important to note that ∆t is usually much smaller than ∆o.

Step 2: Understand the spectrochemical series

The spectrochemical series is a ranking of ligands based on their ability to split the d orbitals. Ligands that cause a large splitting are called strong-field ligands, and those that cause a small splitting are called weak-field ligands. The series is as follows: I- < Br- < Cl- < F- < OH- < H2O < NH3 < en < bipy < phen < CN- < CO Here, NH3 (ammine) and H2O (aqua) are both moderate-field ligands, while Cl- (chloride) is a weak-field ligand.

Step 3: Estimate the energy splitting for the given complexes

For the two octahedral complexes: 1. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) - Coordination geometry: Octahedral - Ligand: NH3 (moderate-field) - Energy splitting: Moderate ∆o 2. \(\left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\) - Coordination geometry: Octahedral - Ligand: H2O (moderate-field) - Energy splitting: Moderate ∆o For the tetrahedral complex: 3. \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) - Coordination geometry: Tetrahedral - Ligand: Cl- (weak-field) - Energy splitting: Small ∆t

Step 4: Relate energy splitting to absorbed/observed color

The absorbed photon's energy determines the electron's transition between the split d orbitals, which also determines the color of light absorbed. Based on the relationship between energy and wavelength (E = hν = hc/λ), a shorter wavelength corresponds to a higher energy, and vice versa. The complementary color of the absorbed light is the observed color, which is the color we associate with the complex. Thus, the complex absorbing the lowest-energy light will appear with the highest-energy complementary color, and vice versa. The energy of absorbed light in the visible spectrum follows the order: Red < Orange < Yellow < Green < Blue < Violet The corresponding complementary colors, which are the observed colors, follow the reverseorder: Violet < Blue < Green < Yellow < Orange < Red

Step 5: Assign the color to each complex

Comparing the energy splitting of the complexes, we can order them as follows: Small ∆t: \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) (tetrahedral) Moderate ∆o: \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+},\left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\) (both octahedral) Since there are three colors given in the problem (pink, blue, and yellow), we can assign the colors based on the energy order for complementary colors: - \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\): Pink (lower energy absorption compared to the other octahedral complex due to slightly stronger field ligand) - \(\left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\): Blue (higher energy absorption compared to pink) - \(\left[\mathrm{CoCl}_{4}\right]^{2-}\): Yellow (highest energy complementary color due to the smallest energy splitting) Thus, the color assignment is: \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\): Pink \(\left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\): Blue \(\left[\mathrm{CoCl}_{4}\right]^{2-}\): Yellow

Key Concepts

Spectrochemical Series

The spectrochemical series is a vital tool in understanding transition metal complexes. It ranks ligands based on their ability to split the d orbitals of metal ions. This splitting results from the different electric field strengths exerted by ligands when they approach the metal center.
The variation in the electrostatic field strength arises due to differences in the electron donation or withdrawal capability of the ligands.
This creates distinct levels of d orbital splitting, known as "ligand field strength." The spectrochemical series places ligands in order of increasing field strength:

• Weak-field ligands: Such as I-, Br-, and Cl-, have a minimal effect in splitting the d orbitals.
• Moderate-field ligands: H2O and NH3 fall into this category, inducing moderate energy separation.
• Strong-field ligands: Include ligands like CN- and CO, which cause the greatest splitting in d orbitals.

This ordering allows chemists to predict the relative energy difference and optical properties of complexes.

Energy Splitting

Energy splitting is a central concept when analyzing the colorations of metal complexes. In these complexes, the ligands cause the degenerate d orbitals of the metal ion to split into two distinct energy levels.
For octahedral complexes, this energy difference, denoted as \(\Delta_o\), causes three lower energy orbitals \((t_{2g})\) and two higher energy orbitals \((e_g)\).
In tetrahedral complexes, the pattern is reversed, creating a smaller energy difference, \(\Delta_t\). Due to the geometric configuration, \(\Delta_t\) is generally less than \(\Delta_o\).

• Octahedral splitting: This usually involves moderate differences, especially when bounded with moderate-field ligands like \(NH_3\) and \(H_2O\).
• Tetrahedral splitting: Results in lower energy differences due to both geometry and weak-field ligands like \(Cl^-\).

The size of the energy gap determines the wavelength of light absorbed, directly influencing the color observed in transition metal complexes.

Complementary Colors

The concept of complementary colors is intrinsic to the study of how and why certain transition metal complexes exhibit particular colors.
When light strikes a complex, certain wavelengths are absorbed; the light's energy facilitates electron transitions between the split d orbitals.
The color that we observe is the sum of the wavelengths that are not absorbed and instead reflected or transmitted.

• An absorbed wavelength near red (lower energy) results in the complex appearing green (its complementary color).
• Conversely, if a complex absorbs blue light (higher energy), it tends to appear yellow.

Using the complementarity guide, we infer that a complex with a higher split (like octahedral complexes) absorbs longer wavelengths and exhibits colors like pink or red. Tetrahedral complexes with small energy gaps may appear yellow as they reflect complementary colors of higher energy absorptions.

Ligand Field Theory

Ligand Field Theory (LFT) extends Crystal Field Theory by considering the covalent character in interactions between metal ions and surrounding ligands.
This more sophisticated approach explains the magnetic, optical, and electronic properties of complexes.

• Electrostatic Interactions: Initial views under Crystal Field Theory primarily focus on how these interactions cause d-orbital splitting.
• Covalency Effects: LFT incorporates overlaps between ligand orbitals and metal d orbitals, influencing energy levels.
• Predictive Insights: While addressing both bonding types, the theory helps to predict the possible electronic transitions, influencing color perception.
• Analysis Extension: LFT explains changes in properties when ligands or metal ion charges differ, aligning with observations in complex colorations.

This theory aids in understanding not just spectral properties but the bond strengths, reactivity, and stability of complexes, revealing why certain ligands cause greater energy differences than others.