Chapter 22, Problem 22.32QP

1. a)

Interpretation Introduction

Interpretation: The number of unpaired electrons in the given complex ions to be predicted.

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 number of unpaired electrons in the given complex ions to be predicted.

Answer to Problem 22.32QP

The complex ion ${{\text{[Cr(CN)}}_{\text{6}}\text{]}}^{\text{4-}}$ has $2$ unpaired electrons.

Explanation of Solution

Interpret the complex ion ${{\text{[Cr(CN)}}_{\text{6}}\text{]}}^{\text{4-}}$.

In complex ion ${{\text{[Cr(CN)}}_{\text{6}}\text{]}}^{\text{4-}}$ , the oxidation state of chromium ion is $+2$. The electronic configuration of ${\text{Cr}}^{\text{2+}}$ ion is ${\text{4s}}^{\text{0}}{\text{3d}}^{\text{4}}$. The crystal field splitting is large because the cyanide ion is a strong field ligand which gives rise to low-spin complex with respect to Pauling’s exclusion principle. In octahedral splitting; the two $(2)$ number of unpaired electrons present.

1. b)

Interpretation Introduction

Interpretation: The number of unpaired electrons in the given complex ions to be predicted.

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 number of unpaired electrons in the given complex ions to be predicted.

Answer to Problem 22.32QP

The complex ion ${{\text{[Cr(H}}_2{\text{O)}}_{\text{6}}\text{]}}^{\text{2+}}$ has $4$ unpaired electrons.

Explanation of Solution

Interpret the complex ion ${{\text{[Cr(H}}_2{\text{O)}}_{\text{6}}\text{]}}^{\text{2+}}$.

In complex ion ${{\text{[Cr(H}}_2{\text{O)}}_{\text{6}}\text{]}}^{\text{2+}}$ , the oxidation state of chromium ion is $+2$. The electronic configuration of ${\text{Cr}}^{\text{2+}}$ ion is ${\text{4s}}^{\text{0}}{\text{3d}}^{\text{4}}$. The crystal field splitting is less because the aqua ligand is a weak field ligand which gives rise to high-spin complex with respect to Hund’s rule. In octahedral splitting; the four $(4)$ number of unpaired electrons present.