Problem 51 - Chemistry and Chemical Reactivity

Question

In water, the titanium(III) ion, \(\left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+},\) has a broad absorption band centered at about \(500 \mathrm{nm}\) What color light is absorbed by the ion?

Step-by-Step Solution

Answer

The ion absorbs blue-green light around 500 nm.

Step 1: Understanding Light Absorption and Color

When a substance absorbs certain wavelengths of light, it reflects or transmits the complementary color. To determine what color is absorbed, we need to consider the complementary relationship between absorbed light and perceived color.

Step 2: Identifying the Absorbed Light Wavelength

The problem states that the titanium(III) ion absorbs light centered at approximately 500 nm. Light at 500 nm falls in the visible spectrum between blue and green colors.

Step 3: Determining the Complementary Color

The complementary color of blue-green light is red-orange. Therefore, when the ion absorbs blue-green light at 500 nm, the color we perceive is the complementary color.

Key Concepts

Titanium(III) ion

Titanium(III) ion, \([\mathrm{Ti}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}]^{3+}\), is a complex ion found in aqueous solutions. It is notable for its unique light absorption properties. This ion is surrounded by six water molecules, forming an octahedral geometry. The oxidation state of titanium here is +3, which gives it distinct electronic and chemical characteristics.
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• The +3 oxidation state means the titanium atom has lost three electrons.
• This alters how it interacts with light, leading to specific absorption of wavelengths in the visible spectrum.

When titanium(III) ions are in solution, they can absorb light at specific wavelengths. This property is crucial in understanding light absorption and color, forming the basis for techniques such as colorimetry in chemistry, where measuring absorbed wavelengths helps identify substances or determine concentrations.

Visible Spectrum

The visible spectrum represents the portion of the electromagnetic spectrum that is visible to the human eye. It ranges from approximately 380 nm to 750 nm in wavelength. Light in this range forms the various colors that we can perceive.
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• Violet light is at the short-wavelength end, around 380 nm.
• Red light is at the long-wavelength end, about 750 nm.

Within this range, the wavelength at 500 nm falls between the blue and green portions of the visible spectrum. Titanium(III) ions absorb light primarily at this wavelength, meaning they predominantly absorb light between these two colors. Knowing where a specific wavelength falls in this spectrum helps determine the corresponding color absorbed and the complementary color perceived.

Complementary Colors

Complementary colors are pairs of colors that, when combined, cancel each other out. This means they produce a grayscale shade like white or grey, rather than a distinct hue. In the context of light absorption, when a substance like the titanium(III) ion absorbs a certain color, we perceive the complementary color.
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• For example, if blue-green light around 500 nm is absorbed, the complementary color is red-orange.
• This principle is why titanium(III) solutions appear red-orange when they are actually absorbing blue-green light.

By understanding complementary colors, we can anticipate the change in color perception based on the absorbed light. This concept is essential not just in chemistry, but also in areas like design and art, where color theory plays a vital role in blending or contrasting colors for visual effects.