Question

An aqueous solution of \(\left[\mathrm{Rh}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\) is yellow. Predict the approximate wavelength and predominant color of light absorbed by the complex.

Short answer

The complex absorbs light in the violet range, around 380-450 nm.

Step-by-step solution

Understand the Color of the Complex

The given complex \([\mathrm{Rh}(\mathrm{C}_{2}\mathrm{O}_{4})_{3}]^{3-}\) is yellow. Yellow is seen because the complementary color is absorbed. To find the absorbed color, we need to figure out the complementary color on the color wheel.

Determine the Complementary Color

The complementary color to yellow is violet/purple. This indicates the complex absorbs light in the violet/purple range.

Identify Wavelength Range for Absorbed Color

Violet light has wavelengths approximately between 380 nm to 450 nm.

Formulate the Prediction

Given that the solution absorbs violet light, which has a wavelength range of about 380 nm - 450 nm, we predict that the complex primarily absorbs light around these wavelengths.

Key concepts

Color of Complexes

The color of a coordination complex in solution results from its interaction with visible light. A coordination complex consists of a central metal atom or ion bonded to surrounding molecules or ions known as ligands. The complex's electronic configuration influences how light is absorbed and reflected. For instance, the complex \( [\mathrm{Rh}(\mathrm{C}_{2}\mathrm{O}_{4})_{3}]^{3-} \) appears yellow to our eyes.

Yellow is not a primary color reflected by the complex, but the resulting color after certain wavelengths are absorbed. Understanding the specific absorbing color involves using a color wheel, which visually represents complementary colors that absorb and reflect light to produce the observed color.

• Complexes often show a color opposite to the absorbed color on the color wheel.
• For this complex, the absorption of violet light results in a yellow appearance.

By understanding the fundamental interactions of light and electrons in complexes, we can predict their colors based on absorbed wavelengths.

Wavelength and Light Absorption

Wavelength is a key concept in understanding the light absorption properties of coordination complexes. Each color within the visible spectrum corresponds to specific wavelengths measured in nanometers (nm). Light absorption happens when a complex's electrons absorb photons, moving from a lower energy state to a higher one. This energy transition correlates directly with the wavelength of light absorbed.

In our specific example of \( [\mathrm{Rh}(\mathrm{C}_{2}\mathrm{O}_{4})_{3}]^{3-} \), yellow light is observed as violet light is absorbed. Violet light encompasses wavelengths between approximately 380 nm and 450 nm.

• As a result, the complex's absorbed color falls within this "violet region" of the spectrum.
• The shorter the wavelength absorbed, the higher the energy transition.

Comprehending this principle allows us to predict the color properties of various metal-ligand complexes.

Color Wheel and Complementary Colors

A color wheel is an essential tool for identifying the complementary color relationships involved in the color properties of chemical complexes. By understanding these relationships, students can predict what color will be absorbed leading to the observed color. Colors that are opposite each other on the wheel are known as complementary colors. When a compound absorbs a certain color, we see its complementary color.

For a yellow complex like \( [\mathrm{Rh}(\mathrm{C}_{2}\mathrm{O}_{4})_{3}]^{3-} \), the absorbed color is violet, located directly opposite yellow on the color wheel. This relationship is crucial in spectroscopy, where complementary colors play a fundamental role:

• The visible color of a substance comes from the light it doesn't absorb.
• Predicting the absorbed color helps in assigning specific electronic transitions within the complex.

Utilizing the color wheel aids in visualizing and understanding how substances interact with light to display their characteristic colors.