Question

In water, the chromium(II) ion, \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) absorbs light with a wavelength of about \(700 \mathrm{nm}\). What color is the solution?

Short answer

The solution appears green.

Step-by-step solution

Understand the Absorption and Perception

The solution's color is determined by the wavelength of light it absorbs and the complementary color it reflects. When a solution absorbs light at a specific wavelength, it reflects or transmits its complementary color. The absorbed light has a wavelength of \(700 \: \mathrm{nm}\), which falls within the red region of the visible spectrum.

Identify the Complementary Color

The color wheel shows the relationship between colors. Since the \[ \mathrm{[Cr(H_{2}O)_{6}]^{2+}} \] ion absorbs red light around \(700 \: \mathrm{nm}\), its complementary color is the one directly across from red on the color wheel. The complementary color to red is green.

Conclusion - Solution Color

Given that the complex absorbs red light, it will appear as its complementary color, green, to the human eye. Thus, the solution of \[ \mathrm{[Cr(H_{2}O)_{6}]^{2+}} \] is perceived as green.

Key concepts

Absorption Spectrum

The absorption spectrum is a graph or range that represents the wavelengths of light a particular substance absorbs. These wavelengths correspond to specific colors that are absorbed when light passes through a solution. This is crucial in understanding the perceived color of a solution, because the colors absorbed are not visible to the human eye. Instead, we see the complementary color that is reflected or transmitted.

For chemical substances in solutions, such as ions, the absorbed light can indicate electronic transitions within the ions. For the chromium(II) ion, the specific light wavelength of about 700 nm is absorbed, which is part of the red region of the absorption spectrum. When this red light is absorbed, the perceptible color of the solution is not red, but rather the complementary color, which is green.

Visible Light Spectrum

The visible light spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. It ranges from approximately 400 nm (violet) to 700 nm (red). Each color within this spectrum has a distinct wavelength:

• Violet: 400-420 nm
• Blue: 420-490 nm
• Green: 490-570 nm
• Yellow: 570-590 nm
• Orange: 590-620 nm
• Red: 620-750 nm

Understanding how these wavelengths correlate with colors helps in determining complementary colors in chemistry. When a particular wavelength is absorbed, the human eye perceives the color of the complementary wavelength. For instance, if a chemical absorbs red light ( 700 nm), the complementary color observed will be green, which is crucial when considering the absorption behavior of chromium complex ions.

Chromium Complex Ions

Chromium complex ions are ions where chromium is bonded to other molecules or ions, often forming a coordination complex. A notable example is the aquo complex \(\left[\text{Cr}(\text{H}_2\text{O})_6\right]^{2+}\), where chromium is surrounded by water molecules. These complexes can absorb light at specific wavelengths due to electronic transitions between their energy levels.

Complex ions, like the \(\left[\text{Cr}(\text{H}_2\text{O})_6\right]^{2+}\) ion, exhibit unique absorption properties that influence their perceived color. The chromium ion's ability to absorb red light around 700 nm results in the solution appearing green. This property of absorbing one color and reflecting its complementary color is utilized in identifying and analyzing the presence and concentration of different ions in solutions. Understanding this concept not only aids in color perception but also in spectroscopic analysis in chemistry.