Chapter 20, Problem 20.104SP

Interpretation Introduction

Interpretation:

The crystal field splitting energy of ${\left[\text{Ti}{\left(\text{NCS}\right)}_{\text{6}}\right]}^{3-}$ has to be determined and also have to give whether ${\text{NCS}}^{-}$ is a stronger or weaker ligand than water and also have to predict the color of ${\left[\text{Ti}{\left(\text{NCS}\right)}_{\text{6}}\right]}^{3-}$.

Concept Introduction:

Crystal field theory: Bonding in coordination compounds accounts for the magnetic property and color of the complex ion. Crystal field theory is explained in terms of electrostatic interaction of between metal ion and ligands.

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.

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

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

Plank-Einstein relation:

The relationship between $\text{E}\text{,}\text{h}\text{and}\text{ν}$ is given by Plank-Einstein equation

$\begin{array}{l}\text{E}\text{=}\text{hν}\text{=}\frac{\text{hc}}{\text{λ}}\\ \text{where,}\\ \text{E}\text{-}\text{energy}\\ \text{h}\text{-}\text{Plank}\text{constant}\\ \text{ν}\text{-}\text{frequency}\\ \text{C}\text{-}\text{speed}\text{of}\text{light}\text{and}\text{λ}\text{-}\text{wavelength}\text{.}\end{array}$