Question

(a) A complex absorbs light with wavelength of \(530 \mathrm{~nm}\). Do you expect it to have color? (b) A solution of a compound appears green. Does this observation necessarily mean that all colors of visible light other than green are absorbed by the solution? Explain. (c) What information is usually presented in a visible absorption spectrum of a compound? (d) What energy is associated with the absorption at \(530 \mathrm{~nm}\) in \(\mathrm{kJ} / \mathrm{mol}\) ?

Short answer

(a) Yes, the complex will have color since it absorbs light within the visible light spectrum (530 nm). (b) No, it doesn't necessarily mean all colors other than green are absorbed. Some might be partially absorbed or not absorbed at all. (c) A visible absorption spectrum presents the absorption of light as a function of wavelength, showing absorption peaks, wavelengths, and intensities. (d) The energy associated with the absorption at 530 nm is 226 kJ/mol.

Step-by-step solution

Question (a)

To answer whether a complex that absorbs light with a wavelength of 530 nm will have color, we need to consider the visible light spectrum. The visible light spectrum ranges from 400 nm (violet) to 700 nm (red). As 530 nm is within this range, the complex will have a color.

Question (b)

If a solution of a compound appears green, this means that it reflects or transmits green light (wavelengths around 495-570 nm) while absorbing other wavelengths in the visible light spectrum. It does not necessarily mean that all colors other than green are absorbed by the solution. Some colors might be partially absorbed or not absorbed at all, resulting in the green color perceived.

Question (c)

A visible absorption spectrum of a compound presents the absorption of light in the visible light spectrum range (400 nm to 700 nm) as a function of wavelength. It usually shows the absorption peaks and their corresponding wavelengths, which can be related to the colors absorbed by the compound. Additionally, the intensity of these peaks represents the relative efficiency of the light absorption at specific wavelengths.

Question (d)

To calculate the energy associated with the absorption at 530 nm in kJ/mol, we can use the formula: \( E = \frac{hc}{\lambda} \) Where: E is the energy, h is the Planck's constant (h = 6.626 × 10^{-34} J s), c is the speed of light (c = 2.998 × 10^{8} m/s), λ is the wavelength (530 nm = 5.30 × 10 ^{-7} m). First, calculate the energy per photon by plugging in the values into the formula: \( E_{photon} = \frac{(6.626 \times 10^{-34} \mathrm{J~s})(2.998 \times 10^8 \mathrm{m/s})}{(5.30 \times 10^{-7} \mathrm{m})} \) \( E_{photon} = 3.754 \times 10^{-19} \mathrm{J} \) Now, we convert this energy to kJ per mole of photons. 1 mol of photons = Avogadro's number = 6.022 × 10^{23} photons \( E_{mol} = E_{photon} \times 6.022 \times 10^{23} \) \( E_{mol} = 3.754 \times 10^{-19} \mathrm{J} \times 6.022 \times 10^{23} \) \( E_{mol} = 2.26 \times 10^{5} \mathrm{J/mol} \) Finally, convert J/mol to kJ/mol: \( E_{mol} = \frac{2.26 \times 10^{5} \mathrm{J/mol}}{1000} \) \( E_{mol} = 226 \mathrm{kJ/mol} \) The energy associated with the absorption at 530 nm is 226 kJ/mol.

Key concepts

Wavelength and Color

When we talk about wavelength and color, we are discussing how different wavelengths of light correspond to different colors we perceive. Visible light is a small portion of the electromagnetic spectrum with wavelengths ranging between 400 nm (nanometers) and 700 nm. This range includes all the colors visible to the human eye, from violet at the shorter wavelengths to red at the longer wavelengths.

- Wavelengths around 400 nm correspond to violet.
- Wavelengths near 700 nm appear red.
- In between, we have colors like blue, green, yellow, and orange.

When a substance absorbs a specific wavelength, it can change the color of the material as viewed by our eyes. For example, if a compound absorbs light at around 530 nm, a wavelength in the visible spectrum associated with green light, then the complex might appear red because it reflects the colors that are not absorbed.

The appearance of color arises because our eyes see the light that is reflected or transmitted by the material. So when something absorbs green light, the remaining colors (mix of red and blue light) combine to create a different perceived color, which in many cases is red or purple. This is due to the complementary nature of light colors.

Absorption Spectrum

An absorption spectrum is a form of fingerprint for a substance, detailing which wavelengths of light a substance absorbs. It is usually plotted with the wavelength on the x-axis and the degree of light absorption on the y-axis.

Here’s what you might discover in an absorption spectrum:

• Peaks: These show where light is absorbed most strongly, indicating the wavelengths the compound absorbs.
• Troughs or valleys: These areas occur where light is not absorbed and hence is either reflected or transmitted.

The absorption spectrum provides essential information about the electronic transitions occurring in the compound's molecules. This is incredibly useful for physicists and chemists as it helps determine the structure and behavior of the compound upon interaction with light. Each unique spectrum can provide clues about the identity of unknown substances or confirm the presence of known ones. Importantly, the absorption spectrum not only tells which wavelengths are absorbed but also hints at what colors will likely be visible, which is vital for understanding color changes in chemical processes.

Energy Calculation

Understanding how to calculate the energy associated with light absorption is crucial in chemistry and physics. The energy of absorbed light depends directly on its wavelength and can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
Here:

• \( E \) is the energy of the light.
  
• \( h \) is Planck’s constant, valued at \( 6.626 \times 10^{-34} \) J·s.
  
• \( c \) is the speed of light, approximately \( 2.998 \times 10^{8} \) m/s.
  
• \( \lambda \) is the wavelength in meters.
  

To find the energy associated with a 530 nm absorption, convert 530 nm to meters, which is \( 5.30 \times 10^{-7} \) meters, and substitute into the formula:
\[ E_{photon} = \frac{(6.626 \times 10^{-34} \mathrm{J~s})(2.998 \times 10^8 \mathrm{m/s})}{5.30 \times 10^{-7} \mathrm{m}} \]The resulting energy per photon is \( 3.754 \times 10^{-19} \) J. But usually, we're interested in the energy per mole, so we multiply this by Avogadro's number \( 6.022 \times 10^{23} \), yielding \( 226 \) kJ/mol. This calculation is fundamental to quantify the energy shifts when molecules absorb light, an essential piece in understanding chemical reactions and material properties in relation to light.