Chapter 23, Problem 23.89P

(a)

Interpretation Introduction

Interpretation:

For the given complex the orbital splitting diagram has to be drawn using spectrochemial series.

  ${\left[Cr{(CN)}_6\right]}^{3-}$

Concept introduction:

The element in the periodic table and count its position in the respective transition series. These elements are in Periods 5 and 6, so the general configuration is

  $\left[noblegas\right]n{s}^2\left(n-1\right)d^x.$

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.

Splitting of five d-orbitals in an octahedral crystals field is as follows:

Figure 1

Explanation of Solution

Given,

  ${\left[Cr{(CN)}_6\right]}^{3-}$

Electron configuration of $Cr:\left[Ar\right]4s^{1}3d^5$

Charge on $Cr$: The aqua ligands are neutral, so the charge on $Cris+3.$

Electron configuration of $C{r}^{3+}:\left[Ar\right]3d^3$

Six ligands indicate an octahedral arrangement.  Using Hund’s rule, fill the lower energy

$t_{2}g$ orbitals first, filling empty orbitals before pairing electrons within an orbital.

(b)

Interpretation Introduction

Interpretation:

For the given complex the orbital splitting diagram has to be drawn using spectrochemial series.

  ${\left[Rh{(CO)}_6\right]}^{3+}$

Concept introduction:

The element in the periodic table and count its position in the respective transition series. These elements are in Periods 5 and 6, so the general configuration is

  $\left[noblegas\right]n{s}^2\left(n-1\right)d^x.$

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.

Splitting of five d-orbitals in an octahedral crystals field is as follows:

Figure 1

Explanation of Solution

Given,

  ${\left[Rh{(CO)}_6\right]}^{3+}$

Electron configuration of $Rh:\left[Ar\right]4s^{1}3d^8$

Charge on $Rh$: The carbonyl ligands are neutral, so $Rh$ has a +3 charge.

Electron configuration of $R{h}^{3+}:\left[Ar\right]3d^6$

Four ligands and a $d^6$ configuration indicate an octahedral geometry.  Use Hund’s rule to fill in the nine d electrons.  Thus, the carbonyl ligands is strong so the correct orbital-energy splitting diagram shows no unpaired electron.   

(c)

Interpretation Introduction

Interpretation:

For the given complex the orbital splitting diagram has to be drawn using spectrochemial series.

  ${\left[Co{(OH)}_6\right]}^{4-}$

Concept introduction:

The element in the periodic table and count its position in the respective transition series. These elements are in Periods 5 and 6, so the general configuration is

  $\left[noblegas\right]n{s}^2\left(n-1\right)d^x.$

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.

Splitting of five d-orbitals in an octahedral crystals field is as follows:

Figure 1

Explanation of Solution

Electron configuration of $Co:\left[Ar\right]4s^{2}3d^7$

Charge on $Co$: water is a neutral ligand so $Co$ has a +2 charge to make the overall complex charge equal to –4.

Electron configuration of $C{o}^{2+}:\left[Ar\right]3d^7$

Six ligands indicate an octahedral arrangement.  Use Hund’s rule to fill the orbitals.

Water – is a weak-field ligand, so the splitting energy, Δ, is not large enough to overcome the resistance to electron pairing. The electrons remain unpaired, and the complex is called high-spin.