Chapter 23

Draw the structure for Pt \((\) en \() \mathrm{Cl}_{2}\) and use it to answer the following questions: (a) What is the coordination number for platinum in this complex? (b) What is the coordination geometry? (c) What is the oxidation state of the platinum? (d) How many unpaired electrons are there? [Sections 23.2 and 23.6]

Four-coordinate metals can have either a tetrahedral or a square-planar geometry; both possibilities are shown here for \(\left[\mathrm{PtCl}_{2}\left(\mathrm{NH}_{3}\right)_{2}\right] .\) (a) \(\mathrm{What}\) is the name of this molecule? (b) Would the tetrahedral molecule have a geometric isomer? (c) Would the tetrahedral molecule be diamagnetic or paramagnetic? (d) Would the square-planar molecule have a geometric isomer? (e) Would the square-planar molecule be diamagnetic or paramagnetic? (f) Would determining the number of geometric isomers help you distinguish between the tetrahedral and square-planar geometries? (g) Would measuring the molecule's response to a magnetic field help you distinguish between the two geometries? [Sections 23.4-23.6 ]

The lanthanide contraction explains which of the following periodic trends? (a) The atomic radii of the transitionmetals first decrease and then increase when moving horizontally across each period. (b) When forming ions the period 4 transition metals lose their 4\(s\) electrons before their 3\(d\) electrons. (c) The radii of the period 5 transition metals \((\mathrm{Y}-\mathrm{Cd})\) are very similar to the radii of the period 6 transition metals \((\mathrm{Lu}-\mathrm{Hg}).\)

Which periodic trend is partially responsible for the observation that the maximum oxidation state of the transition-metal elements peaks near groups 7 \(\mathrm{B}\) and 8 \(\mathrm{B} ?\) (a) The number of valence electrons reaches a maximum at group 8 \(\mathrm{B} .\) (b) The effective nuclear charge increases on moving left across each period. (c) The radii of the transition-metal elements reach a minimum for group \(8 \mathrm{B},\) and as the size of the atoms decreases it becomes easier to remove electrons.

For each of the following compounds, determine the electron configuration of the transition-metal ion. \((\mathbf{a})\) TiO, \((\mathbf{b}) \mathrm{TiO}_{2},(\mathbf{c}) \mathrm{NiO},(\mathbf{d}) \mathrm{ZnO}\) .

Among the period 4 transition metals \((\mathrm{Sc}-\mathrm{Zn}),\) which elements do not form ions where there are partially filled 3d orbitals?

Write out the ground-state electron configurations of (a) \(\mathrm{Ti}^{3+},(\mathbf{b}) \mathrm{Ru}^{2+},(\mathbf{c}) \mathrm{Au}^{3+},(\mathbf{d}) \mathrm{Mn}^{4+} .\)

How many electrons are in the valence \(d\) orbitals in these transition-metal ions? (a) \(\mathrm{Co}^{3+},(\mathbf{b}) \mathrm{Cu}^{+},(\mathbf{c}) \mathrm{Cd}^{2+},(\mathbf{d}) \mathrm{Os}^{3+}.\)

Which type of substance is attracted by a magnetic field, a diamagnetic substance or a paramagnetic substance?

Which type of magnetic material cannot be used to make permanent magnets, a ferromagnetic substance, an anti-ferromagnetic substance, or a ferrimagnetic substance?

The most important oxides of iron are magnetite, \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) and hematite, \(\mathrm{Fe}_{2} \mathrm{O}_{3} .\) (a) What are the oxidation states of iron in these compounds? (b) One of these iron oxides is ferrimagnetic, and the other is antiferromagnetic. Which iron oxide is more likely to be ferrimagnetic? Explain.

(a) Using Werner's definition of valence, which property is the same as oxidation number, primary valence or secondary valence? (b) What term do we normally use for the other type of valence? (c) Why can \(\mathrm{NH}_{3}\) serve as a ligand but BH \(_{3}\) cannot?

Crystals of hydrated chromium(III) chloride are green, have an empirical formula of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O},\) and are highly soluble, (a) Write the complex ion that exists in this compound. (b) If the complex is treated with excess \(\mathrm{AgNO}_{3}(a q)\) how many moles of AgCl will precipitate per mole of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) dissolved in solution? (c) Crystals of anhydrous chromium(III) chloride are violet and insoluble in aqueous solution. The coordination geometry of chromium in these crystals is octahedral, as is almost always the case for \(\mathrm{Cr}^{3+} .\) How can this be the case if the ratio of \(\mathrm{Cr}\) to Clis not 1:6 ?

Indicate the coordination number and the oxidation number of the metal for each of the following complexes: (a) \(\mathrm{Na}_{2}\left[\mathrm{CdCl}_{4}\right]\) (b) \(\mathrm{K}_{2}\left[\mathrm{MoOCl}_{4}\right]\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (d) \(\left[\mathrm{Ni}(\mathrm{CN})_{5}\right]^{3-}\) (e) \(\mathrm{K}_{3}\left[\mathrm{V}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\) (f) \(\left[\mathrm{Zn}(\mathrm{en})_{2}\right] \mathrm{Br}_{2}\)

Indicate the coordination number and the oxidation number of the metal for each of the following complexes: (a) \(\mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\) (b) \(\mathrm{Na}_{2}\left[\mathrm{CdBr}_{4}\right]\) (c) \(\left[\mathrm{Pt}(\mathrm{en})_{3}\right]\left(\mathrm{ClO}_{4}\right)_{4}\) (d) \(\left[\mathrm{Co}(\mathrm{en})_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\right]^{+}\) (e) \(\mathrm{NH}_{4}\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{NCS})_{4}\right]\) (f) \(\left[\mathrm{Cu}(\mathrm{bipy})_{2} \mathrm{I}\right] \mathrm{I}\)

For each of the following molecules or polyatomic ions, draw the Lewis structure and indicate if it can act as a monodentate ligand, a bidentate ligand, or is unlikely to act as a ligand at all: (a) ethylamine, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2}\) , (b) trimethylphosphine, \(\mathrm{P}\left(\mathrm{CH}_{3}\right)_{3},\) (c) carbonate, \(\mathrm{CO}_{3}^{2-},\) \((\mathbf{d})\) ethane \(, \mathrm{C}_{2} \mathrm{H}_{6}.\)

Polydentate ligands can vary in the number of coordination positions they occupy. In each of the following, identify the polydentate ligand present and indicate the probable number of coordination positions it occupies: (a) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}(0-\mathrm{phen})\right] \mathrm{Cl}_{3}\) (b) \(\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right] \mathrm{Br}\) (c) \([\mathrm{Ca}(\mathrm{EDTA})]^{2-}\) (d) \(\left[\mathrm{Zn}(\mathrm{en})_{2}\right]\left(\mathrm{ClO}_{4}\right)_{2}\)

For each of the following pairs, identify the molecule or ion that is more likely to act as a ligand in a metal complex: (a) acetonitrile \(\left(\mathrm{CH}_{3} \mathrm{CN}\right)\) or ammonium \(\left(\mathrm{NH}_{4}^{+}\right)\) (b) hydride \(\left(\mathrm{H}^{-}\right)\) or hydronium \(\left(\mathrm{H}_{3} \mathrm{O}^{+}\right),(\mathbf{c})\) carbon monoxide \((\mathrm{CO})\) or methane \(\left(\mathrm{CH}_{4}\right)\) .

Write the formula for each of the following compounds, being sure to use brackets to indicate the coordination sphere: (a) hexamminechromium(III) nitrate (b) tetraamminecarbonatocobalt(III) sulfate (c) dichlorobis(ethylenediamine)platinum(IV) bromide (d) potassium diaquatetrabromovanadate(III) (e) bis(ethylenediamine) zinc(II) tetraiodomercurate(II)

Write the names of the following compounds, using the standard nomenclature rules for coordination complexes: (a) \(\left[\mathrm{Rh}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (b) \(\mathrm{K}_{2}\left[\mathrm{TiCl}_{6}\right]\) (c) \(\mathrm{MoOCI}_{4}\) (d) \(\left[\operatorname{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\right] \mathrm{Br}_{2}\)

Write names for the following coordination compounds: (a) \(\left[\mathrm{Cd}(\mathrm{en}) \mathrm{Cl}_{2}\right]\) (b) \(\mathrm{K}_{4}\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]\) (c) \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{CO}_{3}\right)\right] \mathrm{Cl}\) (d) \(\left[\operatorname{Ir}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]\left(\mathrm{NO}_{3}\right)_{3}\)

Consider the following three complexes: (Complex 1) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{SCN}\right]^{2+}\) (Complex 2) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]^{2+}\) (Complex 3) \(\mathrm{CoClBr} \cdot 5 \mathrm{NH}_{3}\) Which of the three complexes can have (a) geometric isomers, (b) linkage isomers, (c) optical isomers, (d) coordination-sphere isomers?

A four-coordinate complex \(\mathrm{MA}_{2} \mathrm{B}_{2}\) is prepared and found to have two different isomers. Is it possible to determine from this information whether the complex is square planar or tetrahedral? If so, which is it?

Consider an octahedral complex \(\mathrm{MA}_{3} \mathrm{B}_{3} .\) How many geo- metric isomers are expected for this compound? Will any of the isomers be optically active? If so, which ones?

Determine if each of the following complexes exhibits geometric isomerism. If geometric isomers exist, determine how many there are. (a) tetrahedral \(\left[\operatorname{Cd}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}_{2}\right],(\mathbf{b})\) square-planar \(\left[\operatorname{IrCl}_{2}\left(\mathrm{PH}_{3}\right)_{2}\right]^{-},(\mathbf{c})\) octahedral \(\left[\mathrm{Fe}(o-\mathrm{phen})_{2} \mathrm{Cl}_{2}\right]^{+}.\)

Determine if each of the following complexes exhibits geometric isomerism. If geometric isomers exist, determine how many there are. (a) [ Rh(bipy) \((o-\) phen \()_{2} ]^{3+},\) \((\mathbf{b})\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3}(\mathrm{bipy}) \mathrm{Br}\right]^{2+},(\mathbf{c})\) square-planar \(\left[\mathrm{Pd}(\mathrm{en})(\mathrm{CN})_{2}\right].\)

Determine if each of the following metal complexes is chiral and therefore has an optical isomer: (a) tetrahedral \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}_{2}\right],(\mathbf{b})\) octahedral trans-[Ru(bipy) \()_{2} \mathrm{Cl}_{2} ],(\mathbf{c})\) octahedral cis-[Ru(bipy) \(_{2} \mathrm{Cl}_{2} ] .\)

Determine if each of the following metal complexes is chiral and therefore has an optical isomer: (a) square planar \(\left[\mathrm{Pd}(\mathrm{en})(\mathrm{CN})_{2}\right],(\mathbf{b})\) octahedral \(\left[\mathrm{Ni}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+},(\mathbf{c})\) octahe- dral \(\operatorname{cis}-\left[\mathrm{V}(\mathrm{en})_{2} \mathrm{ClBr}\right]\)

(a) If a complex absorbs light at \(610 \mathrm{nm},\) what color would you expect the complex to be? (b) What is the energy in joules of a photon with a wavelength of 610 \(\mathrm{nm} ?\) (c) What is the energy of this absorption in \(\mathrm{kJ} / \mathrm{mol}\) ?

(a) A complex absorbs photons with an energy of 4.51 \(\times 10^{-19} \mathrm{J}\) . What is the wavelength of these photons? (b) If this is the only place in the visible spectrum where the complex absorbs light, what color would you expect the complex to be?

Identify each of the following coordination complexes as either diamagnetic or paramagnetic: (a) \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\) (b) square planar \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) (c) \(\left[\mathrm{Ru}(\mathrm{bipy})_{3}\right]^{2+}\) (d) \(\left[\mathrm{CoCl}_{4}\right]^{2-}\)

If the lobes of a given \(d\)-orbital point directly at the ligands, will an electron in that orbital have a higher or lower energy than an electron in a \(d\)-orbital whose lobes do not point directly at the ligands?

The lobes of which \(d\) orbitals point directly between the ligands in (a) octahedral geometry, (b) tetrahedral geometry?

(a) Sketch a diagram that shows the definition of the crystal-field splitting energy \((\Delta)\) for an octahedral crystal-field. (b) What is the relationship between the magnitude of \(\Delta\) and the energy of the \(d\)-\(d\) transition for a \(d^{1}\) complex? (c) Calculate \(\Delta\) in \(\mathrm{k} J / \mathrm{mol}\) if a \(d^{1}\) complex has an absorption maximum at 545 \(\mathrm{nm} .\)

As shown in Figure 23.26, the \(d-d\) transition of \(\left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) produces an absorption maximum at a wavelength of about 500 \(\mathrm{nm}\) . (a) What is the magnitude of \(\Delta\) for \(\left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) in \(\mathrm{kJ} / \mathrm{mol} ?\) (b) How would the magnitude of \(\Delta\)change if the \(\mathrm{H}_{2} \mathrm{O}\) ligands in \(\left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) were replaced with \(\mathrm{NH}_{3}\) ligands?

Give the number of (valence) \(d\) electrons associated with the central metal ion in each of the following complexes: (a) \(\mathrm{K}_{3}\left[\mathrm{TiCl}_{6}\right],(\mathbf{b}) \mathrm{Na}_{3}\left[\mathrm{Co}\left(\mathrm{NO}_{2}\right)_{6}\right],(\mathbf{c})\left[\mathrm{Ru}(\mathrm{en})_{3}\right] \mathrm{Br}_{3},\) \((\mathbf{d})[\mathrm{Mo}(\mathrm{EDTA})] \mathrm{ClO}_{4},(\mathbf{e}) \mathrm{K}_{3}\left[\mathrm{ReCl}_{6}\right].\)

Give the number of (valence) \(d\) electrons associated with the central metal ion in each of the following complexes: (a) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right (\mathbf{b})\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]\left(\mathrm{NO}_{3}\right)_{2},(\mathbf{c}) \mathrm{Na}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]\) (d) \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right] \mathrm{ClO}_{4},(\mathbf{e})[\operatorname{Sr}(\mathrm{EDTA})]^{2-}\)

A classmate says, "A weak-field ligand usually means the complex is high spin." Is your classmate correct? Explain.

For a given metal ion and set of ligands, is the crystal-field splitting energy larger for a tetrahedral or an octahedral geometry?

For each of the following metals, write the electronic configuration of the atom and its \(2+\) ion: (a) \(\mathrm{Mn},(\mathbf{b}) \mathrm{Ru},(\mathbf{c}) \mathrm{Rh}\). Draw the crystal-field energy-level diagram for the \(d\) orbitals of an octahedral complex, and show the placement of the \(d\) electrons for each \(2+\) ion, assuming a strong-field complex. How many unpaired electrons are there in each case?

For each of the following metals, write the electronic configuration of the atom and its \(3+\) ion: (a) Fe, (b) Mo, (c) Co. Draw the crystal-field energy- level diagram for the \(d\) orbitals of an octahedral complex, and show the placement of the \(d\) electrons for each \(3+\) ion, assuming a weak-field complex. How many unpaired electrons are there in each case?

Draw the crystal-field energy-level diagrams and show the placement of \(d\) electrons for each of the following: (a) \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (four unpaired electrons), \((\mathbf{b})\left[\operatorname{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (a high-spin complex), (c) \(\left[\mathrm{Ru}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{2+}\) (a low-spin complex) \((\mathbf{d})\left[\operatorname{Ir} \mathrm{Cl}_{6}\right]^{2-}\) (a low-spin complex) \((\mathbf{e})\left[\mathrm{Cr}(\mathrm{en})_{3}\right]^{3+}\) \((\mathbf{f})\left[\mathrm{NiF}_{6}\right]^{4-}.\)

Draw the crystal-field energy-level diagrams and show the placement of electrons for the following complexes: (a) \(\left[\mathrm{VCl}_{6}\right]^{3-},\) (b) \(\left[\mathrm{FeF}_{6}\right]^{3-}\) | (a high-spin complex) \((\mathbf{c})\left[\mathrm{Ru}(\mathrm{bipy})_{3}\right]^{3+}\) (a low-spin complex), \((\mathbf{d})\left[\mathrm{NiCl}_{4}\right]^{2-}\) (tetrahedral), ( e) \(\left[\mathrm{PtBr}_{6}\right]^{2-},(\mathbf{f})\left[\mathrm{Ti}(\mathrm{en})_{3}\right]^{2+}\).

The complex \(\left[\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) contains five unpaired electrons. Sketch the energy-level diagram for the \(d\) orbitals, and indicate the placement of electrons for this complex ion. Is the ion a high-spin or a low-spin complex?

The ion \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) has one unpaired electron, whereas \(\left[\mathrm{Fe}(\mathrm{NCS})_{6}\right]^{3-}\) has five unpaired electrons. From these results, what can you conclude about whether each complex is high spin or low spin? What can you say about the placement of \(\mathrm{NCS}^{-}\) in the spectrochemical series?

Explain why the transition metals in periods 5 and 6 have nearly identical radii in each group.

(a) A compound with formula \(\mathrm{RuCl}_{3}\) \(\cdot 5 \mathrm{H}_{2} \mathrm{O}\) is dissolved in water, forming a solution that is approximately the same color as the solid. Immediately after forming the solution, the addition of excess AgNO \(_{3}(a q)\) forms 2 mol of solid AgCl per mole of complex. Write the formula for the compound, showing which ligands are likely to be present in the coordination sphere. (b) After a solution of \(\mathrm{RuCl}_{3}\) \(\cdot 5 \mathrm{H}_{2} \mathrm{O}\) has stood for about a year, addition of \(\mathrm{AgNO}_{3}(a q)\) precipitates 3 mol of AgCl per mole of complex. What has happened in the ensuing time?

Sketch the structure of the complex in each of the following compounds and give the full compound name: (a) \(\operatorname{cis}-\left[\operatorname{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]\left(\mathrm{NO}_{3}\right)_{2}\) (b) \(\mathrm{Na}_{2}\left[\mathrm{Ru}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}_{5}\right]\) (c) \(\operatorname{trans} \mathrm{NH}_{4}\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]\) (d) \(\operatorname{cis}-\left[\operatorname{Ru}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]\)

The molecule dimethylphosphinoethane \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{P} \mathrm{CH}_{2} \mathrm{CH}_{2}\right.\) \(\mathrm{P}\left(\mathrm{CH}_{3}\right)_{2},\) which is abbreviated dmpe] is used as a ligand for some complexes that serve as catalysts. A complex that contains this ligand is Mo \((\mathrm{CO})_{4}(\mathrm{dmpe})\) . (a) Draw the Lewis structure for dmpe, and compare it with ethylenediamine as a coordinating ligand. (b) What is the oxidation state of Mo in \(\mathrm{Na}_{2}\left[\mathrm{Mo}(\mathrm{CN})_{2}(\mathrm{CO})_{2}(\mathrm{dmpe})\right] ?(\mathbf{c})\) Sketch the structure of the \(\left[\mathrm{Mo}(\mathrm{CN})_{2}(\mathrm{CO})_{2}(\mathrm{dmpe})\right]^{2-}\) ion, including all the possible isomers.

The square-planar complex \(\left[\mathrm{Pt}(\mathrm{en}) \mathrm{Cl}_{2}\right]\) only forms in one of two possible geometric isomers. Which isomer is not observed: cis or trans?