Chapter 20, Problem 20.31QP

1. a)

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 20.31QP

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.

1. b)

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 20.31QP

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