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Chapter 23: Problem 100

The value of \(\Delta\) for the \(\left[\mathrm{MoI}_{6}\right]^{3-}\) complex is \(198.58 \mathrm{~kJ} / \mathrm{mol}\). 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?

Short Answer

Expert verified
The calculated wavelength of absorption for the \(\left[\text{MoI}_{6}\right]^{3-}\) complex is approximately 1.00 nm, which is not within the visible range (400 nm to 700 nm). Therefore, the complex should not absorb in the visible range.

Step by step solution

01

1. Convert energy from kJ/mol to J

Given Δ = 198.58 kJ/mol, we can convert it to J/mol by multiplying with 1000: Δ = 198.58 × 1000 = 198,580 J/mol
02

2. Calculate the frequency of light absorbed using Planck's equation

Planck's equation relates the energy of a photon (E) to its frequency (ν) as follows: E = hν where h is Planck's constant (6.626 × 10^{-34} Js). We know the energy needed for the electron transition in the complex is Δ. So, we can express the frequency as: ν = Δ / h Plug in the Δ value (198,580 J/mol) and Planck's constant. ν = (198,580 J/mol) / (6.626 × 10^{-34} Js) ν ≈ 2.996 × 10^{20} Hz
03

3. Calculate the wavelength using the speed of light

The frequency (ν) and wavelength (λ) of light are related by the speed of light (c) as follows: c = νλ where c is the speed of light (2.998 × 10^{8} m/s). Rearrange the equation to solve for λ: λ = c / ν Plug in the values of c and ν. λ = (2.998 × 10^{8} m/s) / (2.996 × 10^{20} Hz) λ ≈ 1.00 × 10^{-12} m
04

4. Determine if the complex absorbs in the visible range

In general, the visible range of light spans wavelengths from about 400 nm to 700 nm. Our calculated wavelength is 1.00 × 10^{-12} m, which can be converted to nm: λ = (1.00 × 10^{-12} m) × (1 × 10^9 nm/m) λ ≈ 1.00 nm Since 1.00 nm is much shorter than the wavelengths in the visible range, the complex should not absorb in the visible range.

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Most popular questions from this chapter

A classmate says, “A weak-field ligand usually means the complex is high spin." Is your classmate correct? Explain.

Draw the crystal-field energy-level diagrams and show the placement of electrons for the following complexes: (a) \(\left[\mathrm{VCl}_{6}\right]^{3-},(\mathbf{b})\left[\mathrm{FeF}_{6}\right]^{3-}\) (a high-spin complex), (c) \(\left[\mathrm{Ru}(\text { bipy })_{3}\right]^{3+}\) (a low-spin complex), (d) \(\left[\mathrm{NiCl}_{4}\right]^{2-}\) (tetrahedral), (e) \(\left[\mathrm{PtBr}_{6}\right]^{2-},(\mathbf{f})\left[\mathrm{Ti}(\mathrm{en})_{3}\right]^{2+}\).

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