Shriver & Atkins’ Inorganic Chemistry

Peter Atkins, Duward Shriver, Tina Overton

Chapter 20 d-Metal complexes: electronic structure and properties - all with Video Answers

Educators

Chapter Questions

03:20

Problem 1

Determine the configuration (in the form $\mathrm{t}_{2 \mathrm{g}}^{\mathrm{x}} \mathrm{e}^{y}$ or $\mathrm{e}^{x} \mathrm{t}_{2}^{y},$ as appropriate $),$ the number of unpaired electrons, and the ligand-field stabilization energy in terms of $\Delta_{\mathrm{O}}$ or $\Delta_{\mathrm{T}}$ and $P$ for each of the following complexes using the spectrochemical series to decide, where relevant, which are likely to be high-spin and which low-spin. (a) $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+},(\mathrm{b})\left[\mathrm{Fe}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+},(\mathrm{c})\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-},(\mathrm{d})\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}$
(e) $\left[\mathrm{W}(\mathrm{CO})_{6}\right],(\mathrm{f})$ tetrahedral $\left[\mathrm{FeCl}_{4}\right]^{2-},(\mathrm{g})$ tetrahedral $\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]$

Marissa Turner

Numerade Educator

01:02

Problem 2

Both $\mathrm{H}^{-}$ and $\mathrm{P}\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3}$ are ligands of similar field strength, high in the spectrochemical series. Recalling that phosphines act as $\pi$ acceptors, is $\pi$ -acceptor character required for strong-field behaviour? What orbital factors account for the strength of each ligand?

Anatole Borisov

Numerade Educator

01:35

Problem 3

Estimate the spin-only contribution to the magnetic moment for each complex in Exercise 20.1

Alkendra Singh

Numerade Educator

01:37

Problem 4

Solutions of the complexes $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+},\left[\mathrm{Co}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+}($ both $\left.\mathrm{O}_{\mathrm{h}}\right),$ and $\left[\mathrm{CoCl}_{4}\right]^{2-}$ are coloured. One is pink, another is yellow, and the third is blue. Considering the spectrochemical series and the relative magnitudes of $\Delta_{\mathrm{r}}$ and $\Delta_{\mathrm{o}},$ assign each colour to one of the complexes.

Lottie Adams

Numerade Educator

01:48

Problem 5

For each of the following pairs of complexes, identify the one that has the larger LFSE:
(a) $\left[\mathrm{Cr}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+}$ or $\left[\mathrm{Mn}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+}$
(b) $\left[\mathrm{Mn}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+}$ or $\left[\mathrm{Fe}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}$
(c) $\left[\mathrm{Fe}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}$ or $\left[\mathrm{Fe (\mathrm{CN})_{6}\right]^{3-}$
(d) $\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}$ or $\left[\mathrm{Ru}(\mathrm{CN})_{6}\right]^{3-}$
(e) tetrahedral $\left[\mathrm{FeCl}_{4}\right]^{2-}$ or tetrahedral $\left[\mathrm{CoCl}_{4}\right]^{2-}$

Adriano Chikande

Numerade Educator

01:09

Problem 6

Interpret the variation, including the overall trend across the $3 \mathrm{d}$ series, of the following values of oxide lattice enthalpies (in $\mathrm{kJ}$ $\mathrm{mol}^{-1}$ ). All the compounds have the rock-salt structure: $\mathrm{CaO}(3460)$ $\mathrm{TiO}(3878), \mathrm{VO}(3913), \mathrm{MnO}(3810), \mathrm{FeO}(3921), \mathrm{CoO}(3988)$ $\mathrm{NiO}(4071)$.

Nicole Smina

Numerade Educator

07:27

Problem 7

A neutral macrocyclic ligand with four donor atoms produces a red diamagnetic low-spin $\mathrm{d}^{8}$ complex of $\mathrm{Ni}(\mathrm{II})$ if the anion is the weakly coordinating perchlorate ion. When perchlorate is replaced by two thiocyanate ions, $\mathrm{SCN}^{-}$, the complex turns violet and is high-spin with two unpaired electrons. Interpret the change in terms of structure.

Dr. Satish Ingale

Numerade Educator

01:21

Problem 8

Bearing in mind the Jahn-Teller theorem, predict the structure $\operatorname{of}\left[\mathrm{Cr}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+}$

Hitendra Singh

Numerade Educator

05:39

Problem 9

The spectrum of $\mathrm{d}^{1} \mathrm{Ti}^{3+}(\mathrm{aq})$ is attributed to a single electronic transition $\mathrm{e}_{\mathrm{g}} \leftarrow \mathrm{t}_{2 \mathrm{g}} .$ The band shown in Fig. 20.3 is not symmetrical and suggests that more than one state is involved. Suggest how to explain this observation using the Jahn-Teller theorem.

Susan Hallstrom

Numerade Educator

02:52

Problem 10

Write the Russell-Saunders term symbols for states with the angular momentum quantum numbers $(L, S):(a)\left(0, \frac{5}{2}\right),(b)\left(3, \frac{3}{2}\right)$ (c) $\left(2, \frac{1}{2}\right),(\mathrm{d})(1,1)$.

Kim Trang Nguyen

Numerade Educator

01:14

Problem 11

Identify the ground term from each set of terms: (a) $^{1} \mathrm{P},^{3} \mathrm{P},^{3} \mathrm{F},^{1} \mathrm{G}$
(b) $^{3} \mathrm{P},^{5} \mathrm{D},^{3} \mathrm{H},^{1} \mathrm{I},^{1} \mathrm{G},(\mathrm{c})^{6} \mathrm{S},^{4} \mathrm{P},^{4} \mathrm{G},^{2} \mathrm{I}$.

Breanna Ollech

Numerade Educator

09:59

Problem 12

Give the Russell-Saunders terms of the configurations: (a) $4 s^{1}$ (b) $3 p^{2}$. Identify the ground term.

Aniket Bajaj

Numerade Educator

03:37

Problem 13

The gas-phase ion $\mathrm{V}^{3+}$ has a $^{3} \mathrm{F}$ ground term. The $^{1} \mathrm{D}$ and $^{3} \mathrm{P}$ terms lie, respectively, 10642 and $12920 \mathrm{cm}^{-1}$ above it. The energies of the terms are given in terms of Racah parameters as $E\left(^{3} \mathrm{F}\right)=A-8 B$ $E\left(^{3} \mathrm{P}\right)=A+7 B, E\left(^{1} \mathrm{D}\right)=A-3 B+2 \mathrm{C}$. Calculate the values of $B$ and $C$ for $V^{3+}$.

Nidhi Singhi

Numerade Educator

02:28

Problem 14

Write the d-orbital configurations and use the Tanabe-Sugano diagrams (Resource section 6) to identify the ground term of (a) low-spin $\left[\operatorname{Rh}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+},(\mathrm{b})\left[\mathrm{Ti}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+},(\mathrm{c})$ high-spin $\left[\mathrm{Fe}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}$

Kevin Chimex

Numerade Educator

07:23

Problem 15

Using the Tanabe-Sugano diagrams in Resource section 6, estimate $\Delta_{\mathrm{o}}$ and $B$ for $(\mathrm{a})\left[\mathrm{Ni}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+}$ (absorptions at 8500,15400 and $26000 \mathrm{cm}^{-1}$ ) and (b) $\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}(\text { absorptions at } 10750$ $17500,$ and $28200 \mathrm{cm}^{-1}$ ).

Cristian Naxi

Numerade Educator

05:57

Problem 16

The spectrum of $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}$ has a very weak band in the red and two moderate intensity bands in the visible to near-UV. How should these transitions be assigned?

Dr. Satish Ingale

Numerade Educator

02:10

Problem 17

Explain why $\left[\mathrm{FeF}_{6}\right]^{3-}$ is colourless whereas $\left[\mathrm{CoF}_{6}\right]^{3-}$ is coloured but exhibits only a single band in the visible region of the spectrum.

Nadia Lara

Numerade Educator

01:13

Problem 18

The Racah parameter $B$ is $460 \mathrm{cm}^{-1}$ in $\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-}$ and $615 \mathrm{cm}^{-1}$ in $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}$. Consider the nature of bonding with the two ligands and explain the difference in nephelauxetic effect.

Aadit Sharma

Numerade Educator

01:29

Problem 19

An approximately 'octahedral' complex of Co(III) with ammine and chloro ligands gives two bands with $\varepsilon_{\text {max }}$ between 60 and $80 \mathrm{dm}^{3}$ $\mathrm{mol}^{-1} \mathrm{cm}^{-1},$ one weak peak with $\varepsilon_{\max }=2 \mathrm{dm}^{3} \mathrm{mol}^{-1} \mathrm{cm}^{-1},$ and a strong
band at higher energy with $\varepsilon_{\max }=2 \times 10^{4} \mathrm{dm}^{3} \mathrm{mol}^{-1} \mathrm{cm}^{-1} .$ What do you suggest for the origins of these transitions?

Raghvendra Singh

Numerade Educator

01:03

Problem 20

Ordinary bottle glass appears nearly colourless when viewed through the wall of the bottle but green when viewed from the end so that the light has a long path through the glass. The colour is associated with the presence of $\mathrm{Fe}^{3+}$ in the silicate matrix. Suggest which transitions are responsible for the colour.

Jacob Adamczyk

Numerade Educator

01:28

Problem 21

Solutions of $\left[\mathrm{Cr}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}$ ions are pale blue-green but the chromate ion, $\mathrm{CrO}_{4}^{2-},$ is an intense yellow. Characterize the origins of the transitions and explain the relative intensities.

Varsha Aggarwal

Numerade Educator

05:22

Problem 22

Classify the symmetry type of the d orbitals in a tetragonal $C_{4 v}$ symmetry complex, such as $\left[\mathrm{CoCl}\left(\mathrm{NH}_{3}\right)_{5}^{2+}\right.$ where the Cl lies on the $z$ -axis.
(a) Which orbitals will be displaced from their position in the octahedral molecular orbital diagram by $\pi$ interactions with the lone pairs of the $\mathrm{Cl}^{-}$ ligand? (b) Which orbital will move because the $\mathrm{Cl}^{-}$ ligand is not as strong a $\sigma$ base as $\mathrm{NH}_{3}$ ? (c) Sketch the qualitative molecular orbital diagram for the $C_{4 v}$ complex.

Vivek Singh

Numerade Educator

10:52

Problem 23

Consider the molecular orbital diagram for a tetrahedral complex (based on Fig. 20.8 ) and the relevant d-orbital configuration and show that the purple colour of $\mathrm{MnO}_{4}^{-}$ ions cannot arise from a ligand-field transition. Given that the wavenumbers of the two transitions in $\mathrm{MnO}_{4}^{-}$ are 18500 and $32200 \mathrm{cm}^{-1},$ explain how to estimate $\Delta_{\mathrm{T}}$ from an assignment of the two charge-transfer transitions, even though $\Delta_{\mathrm{T}}$ cannot be observed directly.

Susan Hallstrom

Numerade Educator

01:07

Problem 24

The lowest energy band in the spectrum of $\left[\mathrm{Fe}\left(\mathrm{OH}_{2}\right)\right]^{3+}$ (in $1 \mathrm{M}$ $\mathrm{HClO}_{4}$ ) occurs at lower energy than the equivalent transition in the spectrum of $\left[\mathrm{Mn}\left(\mathrm{OH}_{2}\right)\right]^{2+}$. Explain why this is.

Lottie Adams

Numerade Educator