Chapter 22, Problem 22.33QP

The absorption maximum for the complex ion [Co(NH₃)₆]³⁺ occurs at 470 nm. (a) Predict the color of the complex, and (b) calculate the crystal field splitting in kJ/mol.

Interpretation Introduction

Interpretation: The color of the complex is predicted and the crystal field splitting to be calculated.

Concept Introduction:

Crystal field splitting: The splitting of d-orbitals in the presence of ligands is known as crystal field splitting.

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

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

Crystal field splitting: The energy gap between the splitting of d-orbitals of the metal ion in presence of ligands is known as the crystal field splitting $\text{(Δ)}$. The magnitude of $\text{(Δ)}$ is depends on the nature of metal ions and the ligands.

To Identify: The color of the complex is predicted and the crystal field splitting to be calculated.

Answer to Problem 22.33QP

The observed color of the complex ${{\text{[Co(NH}}_{\text{3}}{\text{)}}_{\text{6}}\text{]}}^{\text{3+}}$ is orange.

Explanation of Solution

Predict the color of the complex ${{\text{[Co(NH}}_{\text{3}}{\text{)}}_{\text{6}}\text{]}}^{\text{3+}}$.

Given information: Wavelength of the incident light is $\text{470 nm}$.

In complex ion ${{\text{[Cr(CN)}}_{\text{6}}\text{]}}^{\text{4-}}$ , the wavelength of the incident light is $\text{470 nm}$ which fall between blue and blue-green in the visible region of the electromagnetic radiation and transmits the complementary color orange (color wheel). Thus, the observed color of the complex ion is orange.

Interpretation Introduction

Interpretation: The color of the complex is predicted and the crystal field splitting to be calculated.

Concept Introduction:

Crystal field splitting: The splitting of d-orbitals in the presence of ligands is known as crystal field splitting.

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

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

Crystal field splitting: The energy gap between the splitting of d-orbitals of the metal ion in presence of ligands is known as the crystal field splitting $\text{(Δ)}$. The magnitude of $\text{(Δ)}$ is depends on the nature of metal ions and the ligands.

To Identify: The color of the complex is predicted and the crystal field splitting to be calculated.

Answer to Problem 22.33QP

The calculated value of crystal field splitting is $\text{255 }\text{kJ/mol}$.

Explanation of Solution

Calculate value of crystal field splitting.

$\begin{array}{l}\text{λ=470 nm}\\ \text{E= hν}\\ \text{where,}\\ \text{ν=}\frac{\text{c}}{\text{λ}}\text{,}\text{h=6}{\text{.626×10}}^{\text{-34}}\text{J}\text{.s}\text{,}\text{c=}{\text{3×10}}^{\text{8}}\text{m/s}\\ \text{E (Δ)= }\frac{\text{hc}}{\text{λ}}\text{=}\frac{\text{(6}{\text{.626×10}}^{\text{-34}}\text{J}\text{.s)}{\text{(3×10}}^{\text{8}}\text{m/s)}}{{\text{470×10}}^{\text{-9}}\text{ m}}\text{ = 4}{\text{.23×10}}^{\text{-19}}\text{J}\text{.}\\ \text{Conversion}\text{of}\text{unit:}\\ \frac{\text{4}{\text{.23×10}}^{\text{-19}}\text{J}}{\text{1photon}}\text{×}\frac{\text{6}{\text{.626×10}}^{\text{23}}\text{photons}}{\text{1}\text{mol}}\text{×}\frac{\text{1}\text{kJ}}{\text{1000}\text{J}}\text{=}\text{255}\text{kJ/mol}\end{array}$

In complex ion ${{\text{[Co(NH}}_{\text{3}}{\text{)}}_{\text{6}}\text{]}}^{\text{3+}}$ , the crystal field splitting is calculated as shown above followed by the conversion of unit