/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 80 The value of \(\Delta\) for the ... [FREE SOLUTION] | 91影视

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Chapter 24: Problem 80

The value of \(\Delta\) for the \(\left[\mathrm{CrF}_{6}\right]^{3-}\) complex is \(182 \mathrm{~kJ} / \mathrm{mol}\). Calculate the expected wavelength of the absorption corresponding to promotion of an electron from the lower-energy to the higher-energy \(d\) -orbital set in this complex. Should the complex absorb in the visible range? (You may need to review Sample Exercise 6.3; remember to divide by Avogadro's number.)

Short Answer

Expert verified
The expected wavelength of absorption for the \(\left[\mathrm{CrF}_{6}\right]^{3-}\) complex is \(657 \mathrm{~nm}\), which falls within the visible range (400 to 700 nm). Therefore, the complex should absorb in the visible range.

Step by step solution

01

Convert energy to joules per particle

First, let's convert the given value of \(\Delta\) to joules per particle by dividing by Avogadro's number (\(6.022 \times 10^{23} \mathrm{~particles} / \mathrm{mol}\)): \[\frac{182 \mathrm{~kJ}}{\mathrm{mol}} \times \frac{1000 \mathrm{~J}}{1 \mathrm{~kJ}} \times \frac{1 \mathrm{~mol}}{6.022 \times 10^{23} \mathrm{~particles}} = 3.018 \times 10^{-19} \mathrm{~J} / \mathrm{particle} \]
02

Use the energy-wavelength relationship

Next, we will use the energy-wavelength relationship from the Planck equation: \[E = h\nu = \frac{hc}{\lambda}\] Where \(E\) is the energy, \(h\) is the Planck constant (\(6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\)), \(c\) is the speed of light (\(2.998 \times 10^{8} \mathrm{~m} / \mathrm{s}\)), and \(\lambda\) is the wavelength. We will solve for \(\lambda\): \[\lambda = \frac{hc}{E}\]
03

Calculate the expected wavelength

Substitute the values of \(h, c,\) and \(E\) that we derived and calculated in Steps 1 and 2 and solve for the wavelength \(\lambda\): \[\lambda = \frac{(6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s})(2.998 \times 10^{8} \mathrm{~m} / \mathrm{s})}{3.018 \times 10^{-19} \mathrm{~J} / \mathrm{particle}} = 657 \mathrm{~nm}\]
04

Determine if the complex absorbs in the visible range

The visible range of the electromagnetic spectrum is typically between 400 nm and 700 nm. Since the calculated expected wavelength of absorption of the complex \(\left[\mathrm{CrF}_{6}\right]^{3-}\) is 657 nm, we can conclude that the complex should absorb in the visible range.

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Most popular questions from this chapter

Indicate the coordination number of the metal and the oxidation number of the metal in each of the following complexes: (a) \(\mathrm{Na}_{2}\left[\mathrm{CdCl}_{4}\right]\) (b) \(\mathrm{K}_{2}\left[\mathrm{MoOCl}_{4}\right]\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (d) \(\left[\mathrm{Ni}(\mathrm{CN})_{5}\right]^{3-}\) (e) \(\mathrm{K}_{3}\left[\mathrm{~V}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\) (f) \(\left[\mathrm{Zn}(\mathrm{en})_{2}\right] \mathrm{Br}_{2}\)

(a) What is the difference between Werner's concepts of primary valence and secondary valence? What terms do we now use for these concepts? (b) Why can the \(\mathrm{NH}_{3}\) molecule serve as a ligand but the \(\mathrm{BH}_{3}\) molecule cannot?

Polydentate ligands can vary in the number of coordination positions they occupy. In each of the following, identify the polydentate ligand present and indicate the probable number of coordination positions it occupies: (a) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}(0-\mathrm{phen})\right] \mathrm{Cl}_{3}\) (b) \(\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right] \mathrm{Br}\) (c) \(\left[\mathrm{Cr}(\mathrm{EDTA})\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{-}\) (d) \(\left[\mathrm{Zn}(\mathrm{en})_{2}\right]\left(\mathrm{ClO}_{4}\right)_{2}\)

The complexes \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) and \(\left[\mathrm{VF}_{6}\right]^{3-}\) are both known. (a) Draw the \(d\) -orbital energy-level diagram for \(\mathrm{V}(\mathrm{III})\) octahedral complexes. (b) What gives rise to the colors of these complexes? (c) Which of the two complexes would you expect to absorb light of higher energy? Explain.

A Cu electrode is immersed in a solution that is \(1.00 \mathrm{M}\) in \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) and \(1.00 \mathrm{M}\) in \(\mathrm{NH}_{3} .\) When the cathode is a standard hydrogen electrode, the emf of the cell is found to be \(+0.08 \mathrm{~V}\). What is the formation constant for \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} ?\)
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