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Chapter 23: Problem 46

(a) A complex absorbs light in the range of \(200-300 \mathrm{nm} . \mathrm{Do}\) you expect it to have visible 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 an absorption at \(440 \mathrm{nm}\) in \(\mathrm{kJ} / \mathrm{mol} ?\)

Short Answer

Expert verified
(a) We cannot determine its visible color since the complex absorbs light in the 200-300 nm range, which is outside the range of visible light (380-750 nm). (b) A green-colored solution does not necessarily mean that all colors other than green are absorbed by the solution; other colors might still be partially transmitted or reflected but to a much lesser extent. (c) A visible absorption spectrum usually presents the absorption bands, peak wavelengths, and molar absorptivity of a compound. (d) The energy associated with an absorption at 440 nm is approximately 272.7 kJ/mol.

Step by step solution

01

Visible Light Range

Visible light has a wavelength range of approximately 380-750 nm. Any color we can see falls within this range.
02

Determining the Visible Color

The compound absorbs light in the range of 200-300 nm, which is outside the range of visible light (380-750 nm). Therefore, we cannot determine its visible color based on this information. #Part (b)#
03

Color Perception

A compound appears green if it reflects or transmits green light and absorbs most of the other colors in the visible spectrum.
04

Conclusion

The observation of a green-colored solution does not necessarily mean that all colors other than green are absorbed by the solution. Some of the other colors might still be partially transmitted or reflected, but to a much lesser extent than the green light. #Part (c)#
05

Visible Absorption Spectrum

In a visible absorption spectrum, the following information is usually presented: 1. The absorption bands of the compound, 2. The peak wavelengths where maximum absorption occurs, 3. The molar absorptivity (a measure of the compound's ability to absorb light) associated with each peak. #Part (d)#
06

Formula for Energy

To calculate the energy associated with light absorption at 440 nm, we use the formula: \[E = \frac{hc}{\lambda}\] Where E is energy, h is Planck's constant (6.63 x 10^{-34} Js), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the light (in meters).
07

Convert Wavelength

Convert the given wavelength (440 nm) to meters: \[\lambda = 440 \,\text{nm} \cdot \frac{1 \,\text{m}}{10^9\, \text{nm}} = 4.40 \times 10^{-7}\, \text{m}\]
08

Calculate Energy per Photon

Use the formula to calculate the energy per photon: \[E = \frac{(6.63 \times 10^{-34}\, \text{Js})(3.00 \times 10^8\, \text{m/s})}{4.40 \times 10^{-7}\, \text{m}} = 4.53 \times 10^{-19}\,\text{J}\]
09

Calculate Energy per Mole of Photons

Multiply the energy per photon by Avogadro's number (6.022 x 10^23 mol^{-1}) to find the energy per mole of photons: \[E_\text{mol} = (4.53 \times 10^{-19}\,\text{J}) \cdot (6.022 \times 10^{23}\, \text{mol}^{-1}) = 272.7\, \text{kJ mol}^{-1}\] The energy associated with an absorption at 440 nm is approximately 272.7 kJ/mol.

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Most popular questions from this chapter

A four-coordinate complex \(\mathrm{MA}_{2} \mathrm{~B}_{2}\) is prepared and found to have two different isomers. Is it possible to determine from this information whether the complex is square planar or tetrahedral? If so, which is it?

Write the names of the following compounds, using the standard nomenclature rules for coordination complexes: (a) \(\left[\mathrm{Rh}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (b) \(\mathrm{K}_{2}\left[\mathrm{TiCl}_{6}\right]\) (c) \(\mathrm{MoOCl}_{4}\) (d) \(\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\right] \mathrm{Br}_{2}\)

The molecule methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\) can act as a monodentate ligand. The following are equilibrium reactions and the thermochemical data at \(298 \mathrm{~K}\) for reactions of methylamine and en with \(\mathrm{Cd}^{2+}(a q):\) $$ \begin{array}{c} \mathrm{Cd}^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) \rightleftharpoons\left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q) \\ \Delta H^{\circ}=-57.3 \mathrm{~kJ} ; \quad \Delta S^{\circ}=-67.3 \mathrm{~J} / \mathrm{K} ; \quad \Delta G^{\circ}=-37.2 \mathrm{~kJ} \\\ \mathrm{Cd}^{2+}(a q)+2 \mathrm{en}(a q) \rightleftharpoons\left[\mathrm{Cd}(\mathrm{en})_{2}\right]^{2+}(a q) \\ \Delta H^{\circ}=-56.5 \mathrm{~kJ} ; \quad \Delta S^{\circ}=+14.1 \mathrm{~J} / \mathrm{K} ; \quad \Delta G^{\circ}=-60.7 \mathrm{~kJ} \end{array} $$ (a) Calculate \(\Delta G^{\circ}\) and the equilibrium constant \(K\) for the following ligand exchange reaction: \(\left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q)+2 \operatorname{en}(a q) \rightleftharpoons\) $$ \left[\mathrm{Cd}(\mathrm{en})_{2}\right]^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) $$ Based on the value of \(K\) in part (a), what would you conclude about this reaction? What concept is demonstrated? (b) Determine the magnitudes of the enthalpic \(\left(\Delta H^{\circ}\right)\) and the entropic \(\left(-T \Delta S^{\circ}\right)\) contributions to \(\Delta G^{\circ}\) for the ligand exchange reaction. Explain the relative magnitudes. (c) Based on information in this exercise and in the "A Closer Look" box on the chelate effect, predict the sign of \(\Delta H^{\circ}\) for the following hypothetical reaction: $$ \begin{aligned} \left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q) &+4 \mathrm{NH}_{3}(a q) \rightleftharpoons \\ \left[\mathrm{Cd}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) \end{aligned} $$

Give the number of (valence) \(d\) electrons associated with the central metal ion in each of the following complexes: (a) \(\mathrm{K}_{3}\left[\mathrm{TiCl}_{6}\right]\) (b) \(\mathrm{Na}_{3}\left[\mathrm{Co}\left(\mathrm{NO}_{2}\right)_{6}\right],\) (c) \(\left[\mathrm{Ru}(\mathrm{en})_{3}\right] \mathrm{Br}_{3},\) (d) \([\mathrm{Mo}(\mathrm{EDTA})] \mathrm{ClO}_{4},(\mathrm{e}) \mathrm{K}_{3}\left[\mathrm{ReCl}_{6}\right] .\)

Explain why the \(d_{x y}, d_{x z}\), and \(d_{y z}\) orbitals lie lower in energy than the \(d_{z}^{2}\) and \(d_{x^{2}-y^{2}}\) orbitals in the presence of an octahedral arrangement of ligands about the central metal ion.
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