Chapter 22.6, Problem 1RC

Interpretation Introduction

Interpretation: The complex that absorbs light of the longest wavelength is to be determined from the given option.

Concept introduction:

Spectrochemical series: The list of ligands arranged in an ascending order of $\text{(Δ)}$(the splitting of d-orbitals in presence of various ligands).

$\begin{array}{l}\stackrel{{}^{{\text{I}}^{\text{-}}\text{<}{\text{Br}}^{\text{-}}\text{<}{\text{SCN}}^{\text{-}}\text{<}{\text{Cl}}^{\text{-}}\text{<}{\text{S}}^{\text{2-}}\text{<}{\text{F}}^{\text{-}}\text{<}{\text{OH}}^{\text{-}}\text{<}{\text{O}}^{\text{2-}}\text{<}{\text{H}}_{\text{2}}\text{O}\text{<}{\text{NCS}}^{\text{-}}\text{<}{\text{edta}}^{\text{4-}}\text{<}{\text{NH}}_{\text{3}}\text{< en}\text{<}{\text{NO}}^{\text{2-}}\text{<}{\text{CN}}^{\text{-}}\text{<}\text{CO}}}{\to }\\ {}_{{}^{{}^{\begin{array}{l}\text{weak-field}\text{increasing(Δ)}\text{strong-field}\\ \text{ligands}\text{ligands}\end{array}}}}\end{array}$

The energy increases as the wavelength of the light decreases.

$\begin{array}{c}\text{E}\text{=}\text{hν}\text{=}\frac{\text{hc}}{\text{λ}}\\ \text{where, ν}=\text{frequency}\\ \text{λ}=\text{wavelength}\end{array}$

Visible region: The electromagnetic radiation in range of $400-700nm$ is regarded as visible region which is actually visible to human eyes.

d-to-d transition: d orbitals in a metal split into higher and lower energy orbitals by absorbing energies.

Answer to Problem 1RC

Correct answer:

1. c) ${\left[Cr{F}_6\right]}^{3-}$

Explanation of Solution

Reason for correct option

d orbitals in a metal splits into higher and lower energy orbitals by absorbing energies. The energy separation depends on the ligand. Ligand with weak-field has low energy and thus has higher wavelength. Thus metal complex with weak-field ligand absorbs light in the longest wavelength. Comparing to other ligands given, $F^{-}$ is the weak-ligand. Therefore, ${\left[Cr{F}_6\right]}^{3-}$ absorb light of the longest wavelength.

Hence the correct option for the complex that absorbs light of the longest wavelength is option c.

Reasons for incorrect options:

Write all the complexes in the options except option c.

1. a) ${\left[Cr{\left(H_{2}O\right)}_6\right]}^{3+}$
2. b) ${\left[Cr{\left(N{H}_3\right)}_6\right]}^{3-}$
3. d) ${\left[Cr{\left(CN\right)}_6\right]}^{3-}$

Comparing to other ligands given, $F^{-}$ is the weak-ligand. So the complex that absorbs light of the longest wavelength is ${\left[Cr{F}_6\right]}^{3-}$.

Hence the incorrect options are a, b and d.

Conclusion

The correct option for the complex that absorbs light of the longest wavelength is identified from the given options. The complex that absorbs light of the longest wavelength is ${\left[Cr{F}_6\right]}^{3-}$.