Problem 10 - Chemistry The Central Science

Question

Two Fe(II) complexes are both low spin but have different ligands. A solution of one is green and a solution of the other is red. Which solution is likely to contain the complex that has the stronger-field ligand? [Section 23.6\(]\)

Step-by-Step Solution

Answer

The red solution is likely to contain the complex with the stronger-field ligand because it absorbs green light, which has higher energy than the red light absorbed by the green solution. The energy of absorbed light is directly related to the crystal-field splitting energy in the complex, so a higher energy absorbed light indicates a larger crystal-field splitting energy associated with a stronger-field ligand.

Step 1: Determine the color of absorbed light

First, we need to determine the color of the light that is absorbed by each complex based on the color of their respective solutions. Colors that are observed result from the transmission of light in the complementary color of the absorbed light. The complementary color of green is red, meaning the green solution absorbs red light. And the complementary color of red is green, meaning the red solution absorbs green light.

Step 2: Compare the energy of absorbed light

Based on the color wheel, the energy of the light increases from red to green. The equation connecting energy (E) and wavelength (λ) is given by the Planck's constant (h) and the speed of light (c): \[E = \dfrac{hc}{\lambda}\] Since the green solution absorbs red light, and the red solution absorbs green light, we can say that the green solution absorbs lower energy light and the red solution absorbs higher energy light.

Step 3: Determine the stronger-field ligand

A stronger-field ligand will lead to a larger crystal-field splitting energy in the complex. Given that the energy of the absorbed light is directly related to the crystal-field splitting energy, we can conclude that the complex with the red solution (absorbing green, higher energy light) has the stronger-field ligand. So, the solution that contains the complex with the stronger-field ligand is the red solution.

Key Concepts

Ligand Field Strength

The concept of ligand field strength is crucial in understanding how different ligands affect the properties of transition metal complexes. In simple terms, a ligand is an ion or molecule that binds to a central metal atom to form a coordination complex. The strength of the ligand field refers to the ability of these ligands to split the d-orbitals in the metal atom.

This field strength can influence various properties, such as the color of the complexes and their magnetic behaviors. Ligands can be classified as strong-field or weak-field based on their influence:

• **Strong-field ligands**: Cause large splittings in the d-orbitals, possibly leading to low-spin complexes.
• **Weak-field ligands**: Cause smaller splittings and often result in high-spin complexes.

Knowing whether a ligand is strong or weak is essential for predicting the number of unpaired electrons, the magnetic properties, and the overall stability of the complex. This also helps in identifying specific properties of the coordination compounds in different chemical solutions and conditions.

Complementary Colors in Chemistry

In chemistry, especially when dealing with transition metal complexes, understanding complementary colors is vital for interpreting the visible spectrum results of these compounds. The complementary color concept involves how the color observed is due to the absorption of its opposite on the color wheel.

When we see a color, we are seeing the light that is not absorbed by the compound. For example:

• A green solution absorbs red light, which is its complementary color.
• A red solution absorbs green light, its complementary counterpart.

These observed colors help chemists infer the energy of light absorbed, which is directly related to the behavior and arrangement of electrons in the metal complex. This absorption of light is not random but is closely linked to crystal field splitting, giving chemists clues about the electronic transitions occurring within the complex.

Crystal Field Splitting Energy

Crystal field splitting energy (\(Δ\)) arises when ligands approach the metal ion, causing a difference in energy between sets of d-orbitals. This energy depends on the type and arrangement of the ligands, as well as the geometry of the complex.

When these ligands approach, they distort the electron cloud around the metal ion, causing some d-orbitals to be at a higher energy level compared to others. This splitting is quantitatively described by the splitting energy, \(Δ\).

• High \(Δ\) values indicate strong-field ligands and are often associated with low-spin configurations.
• Low \(Δ\) values are indicative of weak-field ligands, generally leading to high-spin configurations.

Predicting \(Δ\) is pivotal in coordination chemistry as it helps to explain properties such as magnetism, color, and overall stability of the metal complexes. Understanding these concepts allows chemists to design new materials and catalysts with specific properties tailored for various industrial and research applications.