Problem 45 - Chemistry The Central Science

Question

(a) Can we see light that is \(300 \mathrm{nm}\) in wavelength? \(500 \mathrm{nm}\) in wavelength? (b) What is meant by the term complementary color? (c) What is the significance of complementary colors in understanding the colors of metal complexes? (d) If a complex absorbs light at \(610 \mathrm{nm},\) what is the energy of this absorption in \(\mathrm{kJ} / \mathrm{mol}\) ?

Step-by-Step Solution

Answer

We cannot see light with a wavelength of 300nm as it falls in the ultraviolet spectrum, but we can see light with a wavelength of 500nm, which corresponds to the color green. Complementary colors are those that create a neutral color when combined, and they help predict the color of metal complexes based on light absorption properties. The energy of absorption for a complex that absorbs light at 610nm is approximately 196 kJ/mol.

Step 1: a) Visible Light Wavelengths

Visible light lies within a certain range of wavelengths. This range is typically between 380nm (violet) and 700nm (red). To determine if we can see light of 300nm and 500nm, let's compare them against this range. Wavelength 1: 300nm - This wavelength is outside the visible light region (less than 380nm) and falls in the ultraviolet spectrum. Therefore, we cannot see light with a wavelength of 300nm. Wavelength 2: 500nm - This wavelength is within the visible light region and corresponds to the color green. Therefore, we can see light with a wavelength of _revision_df3674675560424dab75830017bdf278_500nm.

Step 2: b) Complementary Color Definition

A complementary color is a color that, when combined with another color, creates a neutral color (white, gray, or black). In additive color combinations (e.g., light), the complementary color pairs are red-cyan, green-magenta, and blue-yellow.

Step 3: c) Significance of Complementary Colors in Metal Complexes

Complementary colors play an important role in understanding the colors of metal complexes. When a metal complex absorbs light of one color, it generally reflects or transmits the complementary color of that absorbed light. This reflected or transmitted complementary color is what we perceive as the color of the metal complex. Therefore, understanding complementary colors helps us predict the color of a metal complex based on its light absorption properties.

Step 4: d) Energy of absorption calculation

To calculate the energy (E) of absorption in kJ/mol for a complex that absorbs light at 610nm, we can use the following formula: E(hv) = \( (h \times c) / \lambda \) Where h is Planck's constant (\( 6.626 \times 10^{-34} \,\mathrm{Js} \)), c is the speed of light (\( 2.998 \times 10^{8}\, \mathrm{m/s} \)), and λ is the wavelength of light absorbed (610nm or \( 6.10 \times 10^{-7}\, \mathrm{m} \)). First, we will calculate the energy in joules: \( E = (6.626 \times 10^{-34} \,\mathrm{Js}) \times (2.998 \times 10^{8}\, \mathrm{m/s}) / (6.10 \times 10^{-7}\, \mathrm{m}) \) \( E \approx 3.25 \times 10^{-19}\, \mathrm{J} \) To convert the energy from joules to kJ/mol, we can use the Avogadro constant (N) (\( 6.022 \times 10^{23}\, \mathrm{mol^{-1}} \)) and convert the energy to kJ: \( E_{\mathrm{kJ/mol}} = E_{\mathrm{J}} \times N \times 10^{-3} \) \( E_{\mathrm{kJ/mol}} = (3.25 \times 10^{-19}\, \mathrm{J}) \times (6.022 \times 10^{23}\, \mathrm{mol^{-1}} ) \times 10^{-3} \) \( E_{\mathrm{kJ/mol}} \approx 196\, \mathrm{kJ/mol} \)

Key Concepts

Wavelength

The concept of wavelength is crucial when we discuss visible light. Wavelength is the distance between consecutive peaks in a wave and is typically measured in nanometers (nm) for light.

• Visible light waves are the ones our eyes can detect, ranging from 380 nm (violet) to 700 nm (red).
• Wavelengths shorter than 380 nm fall into the ultraviolet region, while those longer than 700 nm extend into the infrared region. These are not visible to the human eye.

In the given exercise, light at 500 nm is mentioned, which lies well within the visible spectrum, appearing green to us. On the other hand, 300 nm is ultraviolet and invisible to us. It's fascinating to note how these electromagnetic waves affect our perception, showing us different colors based strictly on their wavelengths.

Complementary Colors

Complementary colors are essential in understanding the interplay of light and color.

• When combined, complementary colors produce a neutral color such as white, gray, or black. This is due to the nature of additive color mixing.
• These colors are pairs, like red-cyan, green-magenta, and blue-yellow, where each color in the pair complements the other to create a color balance.

In applications such as art and design, complementary colors are used to create contrast and emphasis. The concept is especially useful in visual media, where color harmony is required. Understanding these pairs helps us anticipate which hues will appear when certain wavelengths are absorbed or emitted.

Metal Complexes

In chemistry, metal complexes are fascinating structures where metal ions are bonded to other molecules or ions. Their colors, which often seem vibrant, are due to the specific wavelengths of light they absorb.

• When a metal complex absorbs a specific color, it typically reflects or transmits the complementary color.
• This reflection or transmission is the color that we perceive when looking at the complex.

Understanding metal complexes in terms of complementary colors allows chemists to predict their appearance based on the light they absorb. Such knowledge can be particularly useful in fields like material science and chemistry, where the visual identification of compounds can be crucial. Knowing this relationship helps us decide how these complexes can be applied, for example, in dyes and pigments.