Problem 1

How is the n value of the d sublevel of a transition element related to the period number of the element?

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Problem 2

Write the general electron configuration of a transition element (a) in Period 5; (b) in Period 6.

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Problem 3

What is the general rule concerning the order in which electrons are removed from a transition metal atom to form an ion? Give an example from Group 5B(5). Name two types of measurements used to study electron configurations of ions.

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Problem 4

What is the maximum number of unpaired d electrons that an atom or ion can possess? Give an example of an atom and an ion that have this number.

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Problem 5

How does the variation in atomic size across a transition series contrast with the change across the main-group elements of the same period? Why?

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Problem 6

(a) What is the lanthanide contraction? (b) How does it affect atomic size down a group of transition elements? (c) How does it influence the densities of the Period 6 transition elements?

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Problem 7

(a) What is the range in electronegativity across the first (3d) transition series? (b) What is the range across Period 4 of the main-group elements? (c) Explain the difference.

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Problem 8

(a) Explain the major difference between the number of oxidation states of most transition elements and that of most main-group elements. (b) Why is the $+2$ oxidation state so common among transition elements? (c) What is valence-state electronegativity? Is the electronegativity of Cr different in $\mathrm{CrO}, \mathrm{Cr}_{2} \mathrm{O}_{3},$ and $\mathrm{CrO}_{3} ?$ Explain.

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Problem 9

(a) What behavior distinguishes paramagnetic and diamagnetic substances? (b) Why are paramagnetic ions common among transition elements but not main-group elements? (c) Why are colored solutions of metal ions common among transition elements but not main-group elements?

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Problem 10

Using the periodic table to locate each element, write the electron configuration of (a) V; (b) Y; (c) Hg.

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Problem 11

Using the periodic table to locate each element, write the electron configuration of (a) Ru; (b) Cu; (c) Ni.

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Problem 12

Using the periodic table to locate each element, write the electron configuration of (a) Os; (b) Co; (c) Ag.

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Problem 13

Using the periodic table to locate each element, write the electron configuration of (a) Zn; (b) Mn; (c) Re.

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Problem 14

Give the electron configuration and the number of unpaired electrons for (a) $\mathrm{Sc}^{3+} ;(\mathrm{b}) \mathrm{Cu}^{2+} ;(\mathrm{c}) \mathrm{Fe}^{3+} ;(\mathrm{d}) \mathrm{Nb}^{3+} .$

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Problem 15

Give the electron configuration and the number of unpaired electrons for (a) $\mathrm{Cr}^{3+} ;(\mathrm{b}) \mathrm{Ti}^{4+} ;(\mathrm{c}) \mathrm{Co}^{3+} ;(\mathrm{d}) \mathrm{Ta}^{2+} .$

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Problem 20

In which compound does Cr exhibit greater metallic behavior, $\mathrm{CrF}_{2}$ or $\mathrm{CrF}_{6}$ ? Explain.

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Problem 21

$\mathrm{VF}_{5}$ is a liquid that boils at $48^{\circ} \mathrm{C},$ whereas $\mathrm{VF}_{3}$ is a solid that melts above $800^{\circ} \mathrm{C} .$ Explain this difference in properties.

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Problem 23

Is $\mathrm{MnO}_{4}^{-}$ or ReO $_{4}^{-}$ a stronger oxidizing agent? Explain.

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Problem 24

Which oxide, $\mathrm{CrO}_{3}$ or $\mathrm{CrO}$ is more acidic in water? Why?

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Problem 25

Which oxide, $\mathrm{Mn}_{2} \mathrm{O}_{3}$ or $\mathrm{Mn}_{2} \mathrm{O}_{7},$ is more basic in water? Why?

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Problem 26

The green patina of Cu-alloy roofs results from corrosion in the presence of $\mathrm{O}_{2}, \mathrm{H}_{2} \mathrm{O}, \mathrm{CO}_{2},$ and sulfur compounds. The other members of Group $1 \mathrm{B}(11), \mathrm{Ag}$ and Au, do not form a patina. Corrosion of $\mathrm{Cu}$ and $\mathrm{Ag}$ in the presence of sulfur compounds leads to a black tarnish, but Au does not tarnish. This pattern is different from that in Group $1 \mathrm{A}(1),$ where ease of oxidation increases down

the group. Explain these different group patterns.

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Problem 27

What atomic property of the lanthanides leads to their remarkably similar chemical properties?

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Problem 28

(a) What is the maximum number of unpaired electrons in a lanthanide ion? (b) How does this number relate to occupancy of the 4$f$ subshell?

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Problem 30

Give the electron configuration of $(a)$ La; $(b) \mathrm{Ce}^{3+} ;(c)$ Es; (d) $U^{4+} .$

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Problem 31

Give the electron configuration of (a) $\mathrm{Pm} ;(\mathrm{b}) \mathrm{Lu}^{3+} ;(\mathrm{c}) \mathrm{Th} ;$ (d) $\mathrm{Fm}^{3+} .$

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Problem 32

Only a few lanthanides show an oxidation state other than $+3 .$ Two of these, europium (Eu) and terbium (Tb), are found near the middle of the series, and their unusual oxidation states can be associated with a half-filled $f$ subshell. (a) Write the electron configurations of $\mathrm{Eu}^{2+}, \mathrm{Eu}^{3+},$ and $\mathrm{Eu}^{4+} .$ Why is $\mathrm{Eu}^{2+}$ a common ion, whereas $\mathrm{Eu}^{4+}$ is unknown? (b) Write the electron configurations of $\mathrm{Tb}^{2+}, \mathrm{Tb}^{3+}$ and $\mathrm{Tb}^{4+} .$ Would you expect Tb to show a $+2$ or a $+4$ oxidation state? Explain.

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Problem 33

Cerium (Ce) and ytterbium (Yb) exhibit some oxidation states in addition to $+3 .$ (a) Write the electron configurations of $\mathrm{Ce}^{2+}, \mathrm{Ce}^{3+},$ and $\mathrm{Ce}^{4+} ;(\mathrm{b})$ Write the electron configurations of $\mathrm{Yb}^{2+}, \mathrm{Yb}^{3+},$ and $\mathrm{Yb}^{4+},(\mathrm{c})$ In addition to the $3+$ ions, the ions $\mathrm{Ce}^{4+}$ and $\mathrm{Yb}^{2+}$ are stable. Suggest a reason for this stability.

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Problem 34

Which lanthanide has the maximum number of unpaired electrons in both its atom and $3+$ ion? Give the number of unpaired electrons in the atom and ion.

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Problem 35

Describe the makeup of a complex ion, including the nature of the ligands and their interaction with the central metal ion. Explain how a complex ion can be positive or negative and how it occurs as part of a neutral coordination compound.

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Problem 37

What is the coordination number of a metal ion in a complex ion? How does it differ from oxidation number?

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Problem 39

What geometries are associated with the coordination numbers 2, 4, and 6?

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Problem 40

What are the coordination numbers of cobalt(III), platinum(II), and platinum(IV) in complexes?

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Problem 43

In what order are the metal ion and ligands given in the name of a complex ion?

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Problem 44

Is a linkage isomer a type of constitutional isomer or stereoisomer? Explain.

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Problem 45

Give systematic names for the following formulas:

(a) $\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{2}$

(b) $\left[\mathrm{Cr}(\mathrm{en})_{3}\right]\left(\mathrm{ClO}_{4}\right)_{3}$

(c) $\mathrm{K}_{4}\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]$

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Problem 46

Give systematic names for the following formulas:

(a) $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{NO}_{2}\right)_{2}\right] \mathrm{Cl}$

(b) $\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]$

(c) $\mathrm{K}_{2}\left[\mathrm{CuCl}_{4}\right]$

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Problem 47

What are the charge and coordination number of the central metal ion(s) in each compound of Problem 23.45?

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Problem 48

What are the charge and coordination number of the central metal ion(s) in each compound of Problem 23.46?

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Problem 49

Give systematic names for the following formulas:

(a) $\mathrm{K}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]$

(b) $\mathrm{Na}_{2}\left[\mathrm{CdC}_{4}\right]$

(c) $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Br}\right] \mathrm{Br}_{2}$

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Problem 50

Give systematic names for the following formulas:

(a) $\mathrm{K}\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right) \mathrm{Cl}_{5}\right]$

(b) $\left[\mathrm{Cu}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\right]\left[\mathrm{Co}(\mathrm{en}) \mathrm{Cl}_{4}\right]$

(c) $\left[\mathrm{Pt}(\mathrm{en})_{2} \mathrm{Br}_{2}\right]\left(\mathrm{ClO}_{4}\right)_{2}$

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Problem 51

What are the charge and coordination number of the central metal ion(s) in each compound of Problem 23.49?

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Problem 52

What are the charge and coordination number of the central metal ion(s) in each compound of Problem 23.50?

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Problem 53

Give formulas corresponding to the following names:

(a) Tetraamminezinc sulfate

(b) Pentaamminechlorochromium(III) chloride

(c) Sodium bis(thiosulfato)argentate(I)

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Problem 54

Give formulas corresponding to the following names:

(a) Dibromobis(ethylenediamine)cobalt(III) sulfate

(b) Hexaamminechromium(III) tetrachlorocuprate(II)

(c) Potassium hexacyanoferrate(II)

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Problem 55

What is the coordination number of the metal ion and the number of individual ions per formula unit in each of the compounds in Problem 23.53?

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Problem 56

What is the coordination number of the metal ion and the number of individual ions per formula unit in each of the compounds in Problem 23.54?

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Problem 57

Give formulas corresponding to the following names:

(a) Hexaaquachromium(III) sulfate

(b) Barium tetrabromoferrate(III)

(c) Bis(ethylenediamine)platinum(II) carbonat

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Problem 58

Give formulas corresponding to the following names:

(a) Potassium tris(oxalato)chromate(III)

(b) Tris(ethylenediamine)cobalt(III) pentacyanoiodomanganate(II)

(c) Diamminediaquabromochloroaluminum nitrate

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Problem 59

Give the coordination number of the metal ion and the number of ions per formula unit in each compound in Problem 23.57.

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Problem 60

Give the coordination number of the metal ion and the number of ions per formula unit in each compound in Problem 23.58.

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Problem 61

Which of these ligands can participate in linkage isomerism:

(a) $\mathrm{NO}_{2}^{-} ;(\mathrm{b}) \mathrm{SO}_{2} ;(\mathrm{c}) \mathrm{NO}_{3}^{-} ?$ Explain with Lewis structures.

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Problem 62

Which of these ligands can participate in linkage isomerism: (a) $\mathrm{SCN}^{-} ;$ (b) $\mathrm{S}_{2} \mathrm{O}_{3}^{2-}$ (thiosulfate); (c) HS $^{-} ?$ Explain with Lewis structures.

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Problem 63

For any of the following that can exist as isomers, state the type of isomerism and draw the structures:

(a) $\left[\mathrm{Pt}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{2} \mathrm{Br}_{2}\right]$

(b) $\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{FCl}\right]$

(c) $\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right)\left(\mathrm{NH}_{3}\right) \mathrm{FCl}\right]$

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Problem 64

For any of the following that can exist as isomers, state the type of isomerism and draw the structures:

(a) $\left[\mathrm{Zn}(\mathrm{en}) \mathrm{F}_{2}\right]$

(b) $\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)\left(\mathrm{NH}_{3}\right) \mathrm{FCl}\right]$

(c) $\left[\mathrm{Pd}(\mathrm{CN})_{2}(\mathrm{OH})_{2}\right]^{2-}$

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Problem 65

For any of the following that can exist as isomers, state the type of isomerism and draw the structures:

(a) $\left[\mathrm{PtCl}_{2} \mathrm{Br}_{2}\right]^{2-}$

(b) $\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{NO}_{2}\right)\right]^{2+}$

(c) $\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{I}_{2}\right]^{2+}$

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Problem 66

For any of the following that can exist as isomers, state the type of isomerism and draw the structures:

(a) $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Br}_{2}$

(b) $\left[\mathrm{Pt}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{3} \mathrm{Cl}\right] \mathrm{Br}$

(c) $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NH}_{3}\right)_{2}\right]^{2+}$

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Problem 67

Chromium(III), like cobalt(III), has a coordination number of 6 in many of its complex ions. Before Alfred Werner, in the 1890s, established the idea of a complex ion, coordination compounds had traditional formulas. Compounds are known that have the traditional formula $\mathrm{CrCl}_{3} \cdot n \mathrm{NH}_{3},$ where $n=3$ to $6 .$ Which of the compounds has an electrical conductivity in aqueous solution similar to that of an equimolar NaCl solution?

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Problem 68

When $\mathrm{MCl}_{4}\left(\mathrm{NH}_{3}\right)_{2}$ is dissolved in water and treated with $\mathrm{AgNO}_{3}, 2 \mathrm{mol}$ of AgCl precipitates immediately for each mole of

$\mathrm{MCl}_{4}\left(\mathrm{NH}_{3}\right)_{2}$ . Give the coordination number of $\mathrm{M}$ in the complex.

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Problem 69

Palladium, like its group neighbor platinum, forms fourcoordinate Pd(II) and six-coordinate Pd(IV) complexes. Write formulas for the complexes with these compositions:

(a) $\mathrm{PdK}\left(\mathrm{NH}_{3}\right) \mathrm{Cl}_{3}$

(b) $\operatorname{PdCl}_{2}\left(\mathrm{NH}_{3}\right)_{2}$

(c) $\mathrm{PdK}_{2} \mathrm{Cl}_{6}$

(d) $\mathrm{Pd}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{4}$

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Problem 70

(a) What is a coordinate covalent bond?

(b) Is it involved when $\mathrm{FeCl}_{3}$ dissolves in water? Explain.

(c) Is it involved when HCl gas dissolves in water? Explain.

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Problem 71

According to valence bond theory, what set of orbitals is used by a Period 4 metal ion in forming (a) a square planar complex; (b) a tetrahedral complex?

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Problem 72

A metal ion uses $d^{2} s p^{3}$ orbitals when forming a complex. What is its coordination number and the shape of the complex?

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Problem 73

A complex in solution absorbs green light. What is the color of the solution?

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Problem 74

In terms of the theory of color absorption, explain two ways that a solution can be blue

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Problem 75

(a) What is the crystal field splitting energy $(\Delta) ?$

(b) How does it arise for an octahedral field of ligands?

(c) How is it different for a tetrahedral field of ligands?

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Problem 76

What is the distinction between a weak-field ligand and a strong-field ligand? Give an example of each.

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Problem 77

Is a complex with the same number of unpaired electrons as the free gaseous metal ion termed high spin or low spin?

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Problem 78

How do the relative magnitudes of $E_{\text { pairing }}$ and $\Delta$ affect the paramagnetism of a complex?

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Problem 79

Why are there both high-spin and low-spin octahedral complexes but only high-spin tetrahedral complexes?

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Problem 80

Give the number of $d$ electrons $\left(n \text { of } d^{n}\right)$ for the central metal ion in ( a $\left[\mathrm{TiCl}_{6}\right]^{2-} ;(\mathrm{b}) \mathrm{K}\left[\mathrm{AuCl}_{4}\right] ;(\mathrm{c})\left[\mathrm{RhCl}_{6}\right]^{3-}$

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Problem 81

Give the number of $d$ electrons $\left(n \text { of } d^{n}\right)$ for the central metal ion in ( a) $\left[\operatorname{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]\left(\mathrm{ClO}_{3}\right)_{2} ;$ (b) $\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{2-}$ (c) $\left[\mathrm{Ru}(\mathrm{NO})(\mathrm{en})_{2} \mathrm{Cl}\right] \mathrm{Br}$

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Problem 82

How many $d$ electrons $\left(n \text { of } d^{n}\right)$ are in the central metal ion in (a) $\mathrm{Ca}\left[\operatorname{IrF}_{6}\right] ;(\mathrm{b})\left[\mathrm{HgI}_{4}\right]^{2-} ;(\mathrm{c})[\mathrm{Co}(\mathrm{EDTA})]^{2-} ?$

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Problem 83

How many $d$ electrons $\left(n \text { of } d^{n}\right)$ are in the central metal ion in (a) $\left[\operatorname{Ru}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{SO}_{4} (\mathrm{b}) \mathrm{Na}_{2}\left[\mathrm{Os}(\mathrm{CN})_{6}\right] ;(\mathrm{c})\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{CO}_{3} \mathrm{I}\right] ?$

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Problem 84

Sketch the orientation of the orbitals relative to the ligands in an octahedral complex to explain the splitting and the relative energies of the $d_{x y}$ and the $d_{x^{2}-y^{2}}$ orbitals.

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Problem 85

The two $e_{g}$ orbitals are identical in energy in an octahedral complex but have different energies in a square planar complex, with the $d_{z^{2}}$ orbital being much lower in energy than the $d_{x^{2}-y^{2}}$ Explain with orbital sketches.

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Problem 86

Which of these ions cannot form both high- and low-spin octahedral complexes: (a) $\mathrm{Ti}^{3+} ;(\mathrm{b}) \mathrm{Co}^{2+} ;(\mathrm{c}) \mathrm{Fe}^{2+} ;(\mathrm{d}) \mathrm{Cu}^{2+} ?$

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Problem 87

Which of these ions cannot form both high- and low-spin octahedral complexes: (a) $\mathrm{Mn}^{3+} ;(\mathrm{b}) \mathrm{Nb}^{3+} ;(\mathrm{c}) \mathrm{Ru}^{3+} ;(\mathrm{d}) \mathrm{Ni}^{2+} ?$

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Problem 88

Draw orbital-energy splitting diagrams and use the spectrochemical series to show the orbital occupancy for each of the following (assuming that $\mathrm{H}_{2} \mathrm{O}$ is a weak-field ligand): $\begin{array}{llll}{\text { (a) }\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}} & {\text { (b) }\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right]^{2+}} & {\text { (c) [FeF }_{6} ]^{3-}}\end{array}$

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Problem 89

Draw orbital-energy splitting diagrams and use the spectrochemical series to show the orbital occupancy for each of the following (assuming that $\mathrm{H}_{2} \mathrm{O}$ is a weak-field ligand): $\begin{array}{ll}{\text { (a) }\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{3-}} & {\text { (b) }\left[\mathrm{Rh}(\mathrm{CO})_{6}\right]^{3+}} & {\text { (c) }\left[\mathrm{Co}(\mathrm{OH})_{6}\right]^{4-}}\end{array}$

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Problem 90

Draw orbital-energy splitting diagrams and use the spectrochemical series to show the orbital occupancy for each of the following (assuming that $\mathrm{H}_{2} \mathrm{O}$ is a weak-field ligand): $\begin{array}{llll}{\text { (a) }\left[\mathrm{MoCl}_{6}\right]^{3-}} & {\text { (b) }\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}} & {\text { (c) }\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}}\end{array}$

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Problem 91

Draw orbital-energy splitting diagrams and use the spectrochemical series to show the orbital occupancy for each of the following (assuming that $\mathrm{H}_{2} \mathrm{O}$ is a weak-field ligand):

(a) $\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\left(\mathrm{C}_{2} \mathrm{O}_{4}^{2-} \text { creates a weaker field than } \mathrm{H}_{2} \mathrm{O} \text { does.) }\right.$

(b) $\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{4-}$

(c) $\left[\mathrm{MnCl}_{6}\right]^{4-}$

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Problem 92

Rank the following in order of increasing $\Delta$ and energy of light absorbed: [ $\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+},\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+},\left[\mathrm{Cr}\left(\mathrm{NO}_{2}\right)_{6}\right]^{3-} .$

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Problem 93

Rank the following in order of decreasing $\Delta$ and energy of light absorbed: [Cr(en) $_{3} ]^{3+},\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{3-},\left[\mathrm{CrCl}_{6}\right]^{3-}$

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Problem 94

A complex, $\mathrm{ML}_{6}^{2+},$ is violet. The same metal forms a complex with another ligand, $\mathrm{Q}$ , that creates a weaker field. What color might $\mathrm{MQ}_{6}^{2+}$ be expected to show? Explain.

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Problem 95

$\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ is violet. Another $\mathrm{CrL}_{6}$ complex is green. Can ligand L be CN $^{-} ?$ Can it be $\mathrm{Cl}^{-} ?$ Explain.

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Problem 96

Octahedral $\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}$ is paramagnetic, whereas planar $\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}$ is diamagnetic, even though both metal ions are $d^{8}$ species. Explain.

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Problem 97

The hexaaqua complex $\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ is green, whereas the hexaammonia complex $\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}$ is violet. Explain.

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Problem 98

Three of the complex ions that are formed by $\mathrm{Co}^{3+}$ are $\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+},\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+},$ and $\left[\mathrm{CoF}_{6}\right]^{3-} .$ These ions have the observed colors (listed in arbitrary order) yellow-orange, green, and blue. Match each complex with its color. Explain.

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Problem 99

When neptunium (Np) and plutonium (Pu) were discovered, the periodic table did not include the actinides, so these elements were placed in Groups 7B(7) and 8B(8). When americium (Am) and curium (Cm) were synthesized, they were placed in Groups 8B(9) and 8B(10). However, during chemical isolation procedures, Glenn Seaborg and his colleagues, who had synthesized these elements, could not find their compounds among other compounds of members of the same groups, which led Seaborg to suggest they were part of a new inner transition series

(a) How do the electron configurations of these elements support Seaborg’s suggestion?

(b) The highest fluorides of Np and Pu are hexafluorides, as is the highest fluoride of uranium. How does this chemical evidence support the placement of Np and Pu as inner transition elements rather than transition elements?

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Problem 100

How many different formulas are there for octahedral complexes with a metal M and four ligands A, B, C, and D? Give the number of isomers for each formula and describe the isomers.

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Problem 101

At one time, it was common to write the formula for copper(I) chloride as $\mathrm{Cu}_{2} \mathrm{Cl}_{2},$ instead of $\mathrm{CuCl}$ , analogously to $\mathrm{Hg}_{2} \mathrm{Cl}_{2}$ for mercury(1) chloride. Use electron configurations to explain why $\mathrm{Hg}_{2} \mathrm{Cl}_{2}$ and CuCl are both correct.

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Problem 102

For the compound $\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right] \mathrm{Cl},$ give:

(a) The coordination number of the metal ion

(b) The oxidation number of the central metal ion

(c) The number of individual ions per formula unit

(d) The moles of AgCl that precipitate when 1 mol of compound is dissolved in water and treated with $\mathrm{AgNO}_{3}$

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Problem 103

Hexafluorocobaltate(III) ion is a high-spin complex. Draw the orbital-energy splitting diagram for its d orbitals.

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Problem 104

A salt of each of the ions in Table 23.3 (p. 1023) is dissolved in water. A Pt electrode is immersed in each solution and connected to a 0.38-V battery. All of the electrolytic cells are run for the same amount of time with the same current.

(a) In which cell(s) will a metal plate out? Explain.

(b) Which cell will plate out the least mass of metal? Explain

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Problem 105

Criticize and correct the following statement: strong-field ligands always give rise to low-spin complexes.

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Problem 106

Some octahedral complexes have distorted shapes. In some, two metal-ligand bonds that are $180^{\circ}$ apart are shorter than the other four. In $\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+},$ for example, two $\mathrm{Cu}-\mathrm{N}$ bonds are 207 $\mathrm{pm}$ long, and the other four are 262 $\mathrm{pm}$ long.

(a) Calculate the longest distance between two N atoms in this complex.

(b) Calculate the shortest distance between two N atoms.

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Problem 107

In many species, a transition metal has an unusually high or low oxidation state. Write balanced equations for the following and find the oxidation state of the transition metal in the product:

(a) Iron(III) ion reacts with hypochlorite ion in basic solution to form ferrate ion $\left(\mathrm{FeO}_{4}^{2-}\right), \mathrm{Cl}^{-},$ and water.

(b) Potassium hexacyanomanganate(II) reacts with $\mathrm{K}$ metal to form $\mathrm{K}_{6}\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]$

(c) Heating sodium superoxide $\left(\mathrm{NaO}_{2}\right)$ with $\mathrm{Co}_{3} \mathrm{O}_{4}$ produces $\mathrm{Na}_{4} \mathrm{CoO}_{4}$ and $\mathrm{O}_{2}$ gas.

(d) Vanadium(III) chloride reacts with Na metal under a $\mathrm{CO}$ atmosphere to produce $\mathrm{Na}\left[\mathrm{V}(\mathrm{CO})_{6}\right]$ and $\mathrm{NaCl.}$

(e) Barium peroxide reacts with nickel(II) ions in basic solution to produce $\mathrm{BaNiO}_{3}$

(f) Bubbling CO through a basic solution of cobalt(II) ion produces $\left[\mathrm{Co (\mathrm{CO})_{4}\right]^{-}, \mathrm{CO}_{3}^{2-},$ and water.

(g) Heating cesium tetrafluorocuprate(II) with $\mathrm{F}_{2}$ gas under pressure gives $\mathrm{Cs}_{2} \mathrm{CuF}_{6}$ .

(h) Heating tantalum(V) chloride with Na metal produces NaCl and $\mathrm{Ta}_{6} \mathrm{Cl}_{15},$ in which half of the Ta is in the $+2$ state.

(i) Potassium tetracyanonickelate(II) reacts with hydrazine $\left(\mathrm{N}_{2} \mathrm{H}_{4}\right)$ in basic solution to form $\mathrm{K}_{4}\left[\mathrm{Ni}_{2}(\mathrm{CN})_{6}\right]$ and $\mathrm{N}_{2}$ gas.

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Problem 108

Draw a Lewis structure with lowest formal charges for $\mathrm{MnO}_{4}^{-}$.

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Problem 109

The coordination compound $\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2 (\mathrm{SCN})_{2}\right]$ displays two types of isomerism. Name the types and give names and structures for the six possible isomers.

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Problem 110

An octahedral complex with three different ligands (A, B, and C) can have formulas with three different ratios of the ligands:

$$

\begin{array}{l}{\left[\mathrm{MA}_{4} \mathrm{BC}\right]^{n+}, \quad \text { such as }\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}\right]^{2+}} \\ {\left[\mathrm{MA}_{3} \mathrm{B}_{2} \mathrm{C}\right]^{n+}, \quad \text { such as }\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3} \mathrm{Br}_{2} \mathrm{Cl}\right]} \\ {\left[\mathrm{MA}_{2} \mathrm{B}_{2} \mathrm{C}_{2}\right]^{n+}, \quad \text { such as }\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Br}_{2}\right]^{+}}\end{array}

$$

For each example, give the name, state the type(s) of isomerism present, and draw all isomers.

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Problem 111

In $\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3},$ the $\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}$ ion absorbs visible light in the blue-violet range, and the compound is yellow-orange. In $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Br}_{3},$ the $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$ ion absorbs visible light in the red range, and the compound is blue-gray. Explain these differences in light absorbed and color of the compound.

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Problem 112

The actinides Pa, U, and Np form a series of complex ions, such as the anion in the compound $\mathrm{Na}_{3}\left[\mathrm{UF}_{8}\right],$ in which thecentral metal ion has an unusual geometry and oxidation state. In the crystal structure, the complex ion can be pictured as resulting from interpenetration of simple cubic arrays of uranium and fluoride ions. (a) What is the coordination number of the metal ion in the complex ion? (b) What is the oxidation state of uranium in the compound? (c) Sketch the complex ion.

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Problem 113

Several coordination isomers, with both $\mathrm{Co}$ and $\mathrm{Cr}$ as $3+$ ions, have the molecular formula $\operatorname{CoCrC}_{6} \mathrm{H}_{12} \mathrm{N}_{12}$ (a) Give the name and formula of the isomer in which the Co complex ion has six $\mathrm{NH}_{3}$ groups. (b) Give the name and formula of the isomer in which the Co complex ion has one $\mathrm{CN}$ and five $\mathrm{NH}_{3}$ groups.

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Problem 114

Consider the square planar complex shown at right. Which of the structures A–F are geometric isomers

of it?

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Problem 115

A shortcut to finding optical isomers is to see if the complex has a plane of symmetry-a plane passing through the metal atom such that every atom on one side of the plane is matched by an identical one at the same distance from the plane on the other side. Any planar complex has a plane of symmetry, since

all atoms lie in one plane. Use this approach to determine whether these exist as optical isomers: (a) [Zn(NH $_{3} )_{2} \mathrm{Cl}_{2} ]$ (tetrahedral); (b) $\left[\mathrm{Pt}(\mathrm{en})_{2}\right]^{2+} ;$ (c) trans-[PtBr__ $\mathrm{Cl}_{2} ]^{2-}$ (d) $\operatorname{trans}-\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{F}_{2}\right]^{+}$ (e) $c i s-\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{F}_{2}\right]^{+}$

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Problem 116

Alfred Werner (see Problem 23.67$)$ prepared two compounds by heating a solution of $\mathrm{PtCl}_{2}$ with triethyl phosphine, $\mathrm{P}\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{3},$ which is a ligand for Pt. Both compounds have, by mass, Pt, $38.8 \% ; \mathrm{Cl}, 14.1 \% ; \mathrm{C}, 28.7 \% ; \mathrm{P}, 12.4 \% ;$ and $\mathrm{H}, 6.02 \%$ . Write formulas, structures, and systematic names for the two isomers.

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Problem 117

Two bidentate ligands used extensively in analytical chemistry are bipyridyl (bipy) and ortho-phenanthroline (o-phen): Draw structures and discuss the possibility of isomers for

(a) $\left[\mathrm{Pt}(\text { bipy }) \mathrm{Cl}_{2}\right]$

(b) $\left[\mathrm{Fe}(o \text { -phen })_{3}\right]^{3+}$

(c) $\left[\mathrm{Co}(\text { bipy })_{2} \mathrm{F}_{2}\right]^{+}$

(d) $\left[\mathrm{Co}(o \text { -phen })\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}\right]^{2+}$

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Problem 118

The effect of entropy on reactions appears in the stabilities of certain complexes. (a) In terms of number of product particles, predict which of the following will be favored in terms of $\Delta S_{\mathrm{rxn}}^{\circ}$ :

$$\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]_{4}^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow$$

$$\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right]^{2+}(a q)+4 \mathrm{NH}_{3}(a q)$$

$$\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)_{2}\right]^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow$$

$$\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right]^{2+}(a q)+2 \mathrm{en}(a q)$$

(b) Given that the $\mathrm{Cu}-\mathrm{N}$ bond strength is approximately the same in both complexes, which complex will be more stable with respect to ligand exchange in water? Explain.

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Problem 119

You know the following about a coordination compound:

(1) The partial empirical formula is $\mathrm{KM}\left(\mathrm{CrO}_{4}\right) \mathrm{Cl}_{2}\left(\mathrm{NH}_{3}\right)_{4}$

(2) It has A (red) and B (blue) crystal forms.

(3) When 1.0 mol of A or $\mathrm{B}$ reacts with 1.0 $\mathrm{mol}$ of $\mathrm{AgNO}_{3}$ 0.50 $\mathrm{mol}$ of a red precipitate forms immediately.

(4) After the reaction in $(3), 1.0$ mol of A reacts very slowly with

1.0 mol of silver oxalate $\left(\mathrm{Ag}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)$ to form 2.0 $\mathrm{mol}$ of a white precipitate. (Oxalate can displace other ligands.)

(5) After the reaction in $(3), 1.0$ mol of $\mathrm{B}$ does not react further

with 1.0 $\mathrm{mol}$ of $\mathrm{AgNO}_{3}$

From this information, determine the following:

(a) The coordination number of M

(b) The group(s) bonded to M ionically and covalently

(c) The stereochemistry of the red and blue forms

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Problem 120

The extent of crystal field splitting is often determined from spectra.(a) Given the wavelength (\lambda) of maximum absorption, find the crystal field splitting energy $(\Delta),$ in $\mathrm{kJ} / \mathrm{mol},$ for each of the following complex ions:

(b) Write a spectrochemical series for the ligands in the Cr complexes. $(\mathrm{c})$ Use the Fe data to state how oxidation state affects $\Delta$ (d) Use the Co, Rh, and Ir data to state how period number affects $\Delta .$

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Problem 121

Ionic liquids have many applications in engineering and materials science. The dissolution of the metavanadate ion in chloroaluminate ionic liquids has been studied:

$$

\mathrm{VO}_{3}^{-}+\mathrm{AlCl}_{4}^{-} \longrightarrow \mathrm{VO}_{2} \mathrm{Cl}_{2}^{-}+\mathrm{AlOCl}_{2}^{-}

$$

At high acid concentration, $\mathrm{VOCl}_{3}$ forms:

$$

\mathrm{V}_{2} \mathrm{O}_{5}+\mathrm{HCl} \longrightarrow \mathrm{VOCl}_{3}+\mathrm{H}_{2} \mathrm{O}

$$

Balance each equation, and state which, if either, is a redox process.

(c) What mass of $\mathrm{VO}_{2} \mathrm{Cl}_{2}^{-}$ or $\mathrm{VOCl}_{3}$ can form from 12.5 $\mathrm{g}$ of $\mathrm{V}_{2} \mathrm{O}_{5}$ and the appropriate concentration of acid?

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Problem 122

The orbital occupancies for the d orbitals of several complex ions are diagrammed below.

(a) Which diagram corresponds to the orbital occupancy of the cobalt ion in $\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-2} ?$

(b) If diagram D depicts the orbital occupancy of the cobalt ion in $\left[\mathrm{CoF}_{6}\right]^{n}$ , what is the value of $n ?$

(c) $\left[\mathrm{NiCl}_{4}\right]^{2-}$ is paramagnetic and $\left[\mathrm{Ni (\mathrm{CN})_{4}\right]^{2-}$ is diamagnetic. Which diagrams correspond to the orbital occupancies of the nickel ions in these species?

(d) Diagram $\mathrm{C}$ shows the orbital occupancy of $\mathrm{V}^{2+}$ in the octahedral complex $\mathrm{VL}_{6}$ Can you determine whether L is a strong- or weak-field ligand? Explain.

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