Question

Consider the complex ions \(\mathrm{Co}\left(\mathrm{NH}_{3}\right) 6^{3+}, \mathrm{Co}(\mathrm{CN})_{6}^{3-},\) and \(\mathrm{CoF}_{6}^{3-} .\) The wavelengths of absorbed electromagnetic radiation for these compounds (in no specific order) are \(770 \mathrm{nm},\) \(440 \mathrm{nm},\) and 290 \(\mathrm{nm} .\) Match the complex ion to the wave- length of absorbed electromagnetic radiation.

Short answer

The complex ions can be matched with the absorbed wavelengths as follows: - Co(NH3)6^3+ (moderate field ligand) absorbs 440 nm - Co(CN)6^3- (strong field ligand) absorbs 770 nm - CoF6^3- (weak field ligand) absorbs 290 nm

Step-by-step solution

Remember the spectrochemical series and its relationship to the absorbed wavelength

The spectrochemical series is an ordering of ligands based on their ability to cause a splitting in the d-orbitals of the central metal atom in a complex. The series is as follows (increasing order): I- < Br- < S^2- < SCN- < Cl- < NO3- < N3- < F- < OH- < C2O4^2- < H2O < NCS- < CH3CN < py < NH3 < en < bipy < phen < NO2- < PPh3 < CN- < CO < C2O2- < bpy < tpy As the strength of the crystal field splitting increases, the energy difference between the split d-orbitals increases, meaning that the energy (and therefore absorbed wavelength) of the complex will change.

Identify the position of each ligand in the spectrochemical series

In the given complexes, the ligands are: - NH3 (ammonia) - CN- (cyanide) - F- (fluoride) Now locate their positions in the spectrochemical series: - NH3 is moderately strong field ligand. - CN- is a strong field ligand as it is near the end of the series. - F- is a weak field ligand as it is closer to the beginning of the series.

Match each complex ion to the absorbed wavelength based on the strength of the ligands

Since the strength of the ligands affects the energy difference between the split d-orbitals, we can match each complex ion to the absorbed wavelength based on their ligands strength. - Co(NH3)6^3+: has a moderate field ligand (NH3), so it should be associated with an intermediate absorbed wavelength, which is 440 nm. - Co(CN)6^3-: has a strong field ligand (CN-), so it should be associated with the highest absorbed wavelength, which is 770 nm. - CoF6^3-: has a weak field ligand (F-), so it should be associated with the lowest absorbed wavelength, which is 290 nm. #Conclusion#: Therefore, the complex ions can be matched with the absorbed wavelengths as follows: - Co(NH3)6^3+ absorbs 440 nm - Co(CN)6^3- absorbs 770 nm - CoF6^3- absorbs 290 nm

Key concepts

Crystal Field Theory

Crystal Field Theory (CFT) is a model that helps explain the electronic structure of complex ions. Simply put, CFT describes how metal ions inside a complex interact with surrounding ligands. These interactions are primarily electrostatic. Ligands, which act as negative point charges, approach the metal ion (which is positively charged). This causes the d-orbitals of the central metal ion to split into different energy levels. The interaction changes the energy levels depending upon the geometry of the complex and nature of ligands.

The d-orbitals, which are usually degenerate (of equal energy), split into different sets of orbitals, like the higher-energy and lower-energy levels. The difference in energy between these levels is called crystal field splitting energy. This energy gap is symbolized as Δ. The size of Δ affects the color of the complex. Complexes with large Δ absorb light of shorter wavelength, while those with small Δ absorb longer wavelength light.

• This theory helps in predicting the electronic configuration of the metal ions in a complex.
• It also aids in determining the magnetic properties (paramagnetic or diamagnetic) of the complex.

Understanding Crystal Field Theory provides valuable insight into the nature of complex compounds and their properties.

Ligand Field Strength

Ligand Field Strength is an essential idea related to how much a ligand can cause d-orbital splitting in a metal ion in a complex. The strength is determined by the ligand's position in the spectrochemical series. This series orders ligands from those causing the least splitting to those causing the most.

A stronger field ligand will induce a greater splitting or a larger energy gap (\( \Delta\)). This can have significant effects on the properties of the complex, including its color and stability. There are several key points to keep in mind about ligand field strength:

• Weak field ligands, like F-, generally cause smaller splitting, resulting in complexes that are often high spin.
• Strong field ligands, such as CN-, cause more significant splitting that can lead to low-spin configurations of electrons.
• The ligands NH3, C2O42-, and CO also play a critical role in the magnitude of d-orbital splitting, located at different points in the spectrochemical series.

The concept of ligand field strength is crucial for predicting the properties and behavior of a complex. It helps understand why different complexes absorb different wavelengths of light, contributing to their unique colors.

d-Orbital Splitting

In a transition metal complex, the d-orbitals of the central metal ion are affected by surrounding ligands, leading to d-orbital splitting. Whenever ligands approach a metal ion, the incoming electric field from the ligands affects the d-electrons differently in the metal's orbitals.

For an octahedral complex, which is one of the most common geometries, the d-orbitals split into two groups: t2g and eg. The t2g orbitals (dxy, dxz, dyz) are lower in energy, while the eg orbitals (dx2-y2, dz2) possess higher energy levels.

• t2g orbitals have less energy since they are oriented between the axes where maximum electron density is avoided.
• eg orbitals have higher energy as they lie directly along the axes facing the ligands, causing more repulsion.

The amount of energy difference between these two sets, Δ, affects both the spectroscopic and magnetic properties of the complex.

Different ligand field strengths, based on their positioning in the spectrochemical series, determine the extent of d-orbital splitting. This plays a critical role in predicting the color due to the absorption of visible light and the spin state of the electrons, which can determine if a compound is paramagnetic (unpaired electrons) or diamagnetic (paired electrons). Understanding d-orbital splitting is pivotal in the study of transition metal chemistry.