# Chemistry A Molecular Approach

## Educators

ES

### Problem 1

When a transition metal atom forms an ion, which electrons are lost first?

Anna M.

### Problem 2

Explain why transition metals exhibit multiple oxidation states instead of a single oxidation state (like most of the main-group metals).

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 3

Why is the $+2$ oxidation state so common for transition metals?

Anna M.

### Problem 4

Explain why atomic radii of elements in the third row of the transition metals are no larger than those of elements in the second row.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 5

Gold is the most electronegative transition metal. Explain.

Anna M.

### Problem 6

Briefly define each term.
$$\begin{array}{l}{\text { a. coordination number }} \\ {\text { b. ligand }} \\ {\text { c. bidentate and polydentate }} \\ {\text { d. complex ion }} \\ {\text { e. chelating agent }}\end{array}$$

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 7

Using the Lewis acid-base definition, how would you categorize a ligand? How would you categorize a transition metal ion?

Anna M.

### Problem 8

Explain the differences between each pair of isomer types.
$$\begin{array}{l}{\text { a. structural isomer and stereoisomer }} \\ {\text { b. linka ge isomer and coordination isomer }} \\ {\text { c. geometric isomer and optical isomer }}\end{array}$$

### Problem 9

Which complex ion geometry has the potential to exhibit cistrans isomerism: linear, tetrahedral, square planar, octahedral?

### Problem 10

How can you tell whether a complex ion is optically active?

### Problem 11

Explain the differences between weak-field and strong-field metal complexes.

Anna M.

### Problem 12

Explain why compounds of $\mathrm{Sc}^{3+}$ are colorless, but compounds of $\mathrm{Ti}^{3}$ are colored.

### Problem 13

Explain why compounds of $\mathrm{Zn}^{2+}$ are white, but compounds of $\mathrm{Cu}^{2+}$ are often blue or green.

### Problem 14

Explain the differences between high-spin and low-spin metal complexes.

### Problem 15

Why are almost all tetrahedral complexes high-spin?

Anna M.

### Problem 16

Many transition metal compounds are colored. How does crystal field theory account for this?

### Problem 17

Write the ground state electron configuration for each atom and ion pair.
$$\begin{array}{ll}{\text { a. } \mathrm{N}_{1}, \mathrm{Ni}^{2+}} & {\text { b. } \mathrm{Mn}, \mathrm{Mn}^{4+}} \\ {\text { c. } \mathrm{Y}, \mathrm{Y}^{+}} & {\text { d. } \mathrm{Ta}^{2+}}\end{array}$$

Sam L.

### Problem 18

Write the ground state electron configuration for each atom and ion pair.
$$a. Z r, Z r^{2+} \quad b. \mathrm{Co}, \mathrm{Ca}^{2+}\quad c. \mathrm{TC}, \mathrm{Tc}^{3+} \quad d. \mathrm{Os}, \mathrm{Os}^{4+}$$

### Problem 19

Determine the highest possible oxidation state for each element.
$$a. \mathrm{V} \quad b. Re \quad c. Pd$$

Sam L.

### Problem 20

Which first-row transition metal(s) has the following highest possible oxidation state?
$$\begin{array}{llll}{\text { a. }+3} & {\text { b. }+7} & {\text { c. }+4}\end{array}$$

### Problem 21

Determine the oxidation state and coordination number of the metal ion in each complexion.
$$\begin{array}{ll}{\text { a. }\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}} & {\text { b. }\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]^{-}} \\ {\text { c. }\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]^{2-}} & {\text { d. }\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}}\end{array}$$

Sam L.

### Problem 22

Determine the oxidation state and coordination number of the metal ion in each complexion.
$$\begin{array}{ll}{\text { a. }\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Br}\right]^{2+}} & {\text { b. }\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}} \\ {\text { c. }\left[\mathrm{Co}(\mathrm{ox})_{3}\right]^{4-}} & {\text { d. }\left[\mathrm{PdCl}_{4}\right]^{2-}}\end{array}$$

### Problem 23

Name each complex ion or coordination compound.
$$\begin{array}{ll}{\text { a. }\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}} & {\text { b. }\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]^{2-}} \\ {\text { c. }\left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{\mathrm{s}} \mathrm{Br}\right] \mathrm{SO}_{4}} & {\text { d. }\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NH}_{3}\right)(\mathrm{OH})\right] \mathrm{Cl}_{2}}\end{array}$$

Sam L.

### Problem 24

Name each complex ion or coordination compound.
$$\begin{array}{ll}{\text { a. }\left[\mathrm{Cu}(\mathrm{en})_{2}\right]^{2+}} & {\text { b. }\left[\mathrm{Mn}(\mathrm{CO})_{3}\left(\mathrm{NO}_{2}\right)_{3}\right]^{2+}} \\ {\text { c. } \mathrm{Na}\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}(\mathrm{ox})_{2}\right]} & {\text { d. }\left[\mathrm{Co}(\mathrm{en})_{3}\right]\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]}\end{array}$$

### Problem 25

Write the formula for each complex ion or coordination compound.
$$\begin{array}{l}{\text { a. hexaaquanickel(II) chloride }} \\ {\text { b. pentacarbonylchloromanganese(I) }} \\ {\text { c. ammonium diaquatetrabromovanadate(III) }} \\ {\text { d. tris(ethylenenediamine)cobalt(III) trioxalatoferrate(III) }}\end{array}$$

### Problem 26

Write the formula for each complex ion or coordination compound.
$$\begin{array}{l}{\text { a. hexaaquanickel(II) chloride }} \\ {\text { b. pentacarbonylchloromanganese(I) }} \\ {\text { c. ammonium diaquatetrabromovanadate(III) }} \\ {\text { d. tris(ethylenediamine)cobalt(II) trioxalatoferrate(III) }}\end{array}$$

### Problem 27

Write the formula and the name of each complex ion.
a. a complex ion with $\mathrm{Co}^{3+}$ as the central ion and three $\mathrm{NH}_{3}$ molecules and three CN- ions as ligands
b. a complex ion with $\mathrm{Cr}^{3+}$ as the central ion and a coordination number of 6 with ethylenediamine ligands

Anna M.

### Problem 28

Write the formula and the name of each complex ion or coordination compound.
a. a complex ion with four water molecules and two ONO- ions connected to an Fe(III) ion
b. a coordination compound made of two complex ions: one a complex of V(II) with two ethylenediamine molecules and two Cl ions as ligands and the other a complex of Ni(II) having a coordination number of 4 with $C 1^{-}$ ions as ligands

### Problem 29

Draw two linkage isomers of $\left[\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{NO}_{2}\right)\right]^{2+}$

Anna M.

### Problem 30

Draw two linkage isomers of $\left[\mathrm{PtCl}_{3}(\mathrm{SCN})\right]^{2-}$

### Problem 31

Write the formulas and names for the coordination isomers of $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{2} .$

Anna M.

### Problem 32

Write the formulas and names for the coordination isomers of $\left[\mathrm{Co}(\mathrm{en})_{3}\right]\left[\mathrm{Cr}(\mathrm{ox})_{3}\right] .$

### Problem 33

Which complexes exhibit geometric isomerism?
$$\begin{array}{ll}{\text { a. }\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{\mathrm{s}}(\mathrm{OH})\right]^{2+}} & {\text { b. }\left[\mathrm{Cr}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}} \\ {\text { c. }\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{2}\right]^{+}} & {\text { d. }\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right) \mathrm{Cl}_{3}\right]^{+}} \\ {\text { e. }\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}(\mathrm{CN})_{2}\right]}\end{array}$$

Sam L.

### Problem 34

Which complexes exhibit geometric isomerism?
$$\begin{array}{ll}{\text { a. }\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}(\mathrm{ox})_{2}\right]^{-}} & {\text { b. }\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}} \\ {\text { c. }\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{ox})\right]^{+}} & {\text { d. }\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{en})\right]^{2+}} \\ {\text { e. }\left[\mathrm{Ni}(\mathrm{CO})_{2} \mathrm{Cl}_{2}\right]}\end{array}$$

### Problem 35

If $\mathrm{W}, \mathrm{X}, \mathrm{Y},$ and $\mathrm{Z}$ are different monodentate ligands, how many geometric isomers are there for each ion?
$$\begin{array}{l}{\text { a. square planar [NiWXYZ] }^{2+}} \\ {\text { b. tetrahedral }\left[\text { Zn WXYZ }^{2+}\right.}\end{array}$$

Sam L.

### Problem 36

How many geometric isomers are there for each species?
$$\text { a. } \left[\mathrm{Fe}(\mathrm{CO})_{3} \mathrm{Cl}_{3}\right] \quad \text { b. }\left[\mathrm{Mn}(\mathrm{CO})_{2} \mathrm{Cl}_{2} \mathrm{Br}_{2}\right]^{+}$$

### Problem 37

Draw the structures and label the type for all the isomers of each ion.
$$\begin{array}{l}{\text { a. }\left[\mathrm{Cr}(\mathrm{CO})_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]^{3+}} \\ {\text { b. }\left[\mathrm{Pd}(\mathrm{CO})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}^{+}\right.}\end{array}$$

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### Problem 38

Draw the structures and label the type for all the isomers of each species.
$$\text { a. } \left[\mathrm{Fe}(\mathrm{CO})_{4} \mathrm{Cl}_{2}\right]^{+} \quad \text { b. }\left[\mathrm{Pt}(\mathrm{en}) \mathrm{Cl}_{2}\right]$$

### Problem 39

Determine if either isomer of $\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{ox})_{2}\right]^{-}$ is optically active.

Sam L.

### Problem 40

Determine if either isomer of $\left[\mathrm{Fe}(\mathrm{CO})_{3} \mathrm{Cl}_{3}\right]$ is optically active.

### Problem 41

Draw the octahedral crystal field splitting diagram for each metal ion.
$$\begin{array}{ll}{\text { a. } Z n^{2+}} & {\text { b. } F e^{3+}(\text { high- and low-spin })} \\ {\text { c. } V^{3+}} & {\text { d. } C o^{2+}(\text { high-spin })}\end{array}$$

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### Problem 42

Draw the octahedral crystal field splitting diagram for each metal ion.
$$\begin{array}{l}{\text { a. } \mathrm{Cr}^{3+}} \\ {\text { b. } \mathrm{Cu}^{2+}} \\ {\text { c. } \mathrm{Mn}^{3+}} \\ {\text { d. } \mathrm{Fe}^{2+}(\mathrm{low}-\mathrm{spin})}\end{array}$$

### Problem 43

The $\left[\mathrm{CrCl}_{6}\right]^{3-}$ ion has a maximum in its absorption spectrum at 735 $\mathrm{nm}$ . Calculate the crystal field splitting energy (in kl/mol) for this ion.

Anna M.

### Problem 44

The absorption spectrum of the complex ion $\left[\mathrm{Rh}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}$ has maximum absorbance at 295 $\mathrm{nm}$ . Calculate the crystal field splitting energy (in kJ/mol) for this ion.

### Problem 45

Three complex ions of cobalt(III), $\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-},\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}$ and $\left[\mathrm{CoF}_{6}\right]^{3-}$ , absorb light at wavelengths of (in no particular
order) $290 \mathrm{nm}, 440 \mathrm{nm},$ and 770 $\mathrm{nm}$ . Match each complex ion to the appropriate wavelength absorbed. What color would you expect each solution to be?

Sam L.

### Problem 46

Three bottles of aqueous solutions are discovered in an abandoned lab. The solutions are green, yellow, and purple. It is known that three complex ions of chromium(III) were commonly used in that lab: $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+},\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+},$ and
$\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4} \mathrm{Cl}_{2}\right]^{+} .$ Determine the likely identity of each of the colored solutions.

### Problem 47

The $\left[\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}$ ion is paramagnetic with five unpaired electrons. The $\mathrm{NH}_{3}$ ligand is usually a strong field ligand. Is NH_3 acting as a strong field ligand in this case?

Sam L.

### Problem 48

The complex $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ is paramagnetic. Is the $\mathrm{H}_{2} \mathrm{O}$ ligand inducing a strong or weak field?

### Problem 49

How many unpaired electrons would you expect for each complexion?
$$\begin{array}{l}{\text { a. }\left[\mathrm{RhCl}_{6}\right]^{3-}} \\ {\text { b. }\left[\mathrm{Co}(\mathrm{OH})_{6}\right]^{4-}} \\ {\text { c. } \operatorname{cis}-\left[\mathrm{Fe}(\mathrm{en})_{2}\left(\mathrm{NO}_{2}\right)_{2}\right]^{+}}\end{array}$$

Sam L.

### Problem 50

How many unpaired electrons would you expect for each complexion?
$$\begin{array}{l}{\text { a. }\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}} \\ {\text { b. }\left[\mathrm{MnF}_{6}\right]^{4-}} \\ {\text { c. }\left[\mathrm{Ru}(\mathrm{en})_{3}\right]^{2+}}\end{array}$$

### Problem 51

How many unpaired electrons would you expect for the complex ion $\left[\mathrm{CoCl}_{4}\right]^{2-}$ if it is a tetrahedral shape?

Sam L.

### Problem 52

The complex ion $\left[\mathrm{PdCl}_{4}\right]^{2-}$ is known to be diamagnetic. Use this information to determine if it is a tetrahedral or square planar structure.

### Problem 53

What structural feature do hemoglobin, cytochrome $\mathrm{c},$ and chlorophyll have in common?

Anna M.

### Problem 54

Identify the central metal atom in each complex.
$$\begin{array}{l}{\text { a. hemoglobin }} \\ {\text { b. carbonic anhydrase }} \\ {\text { c. chlorophyll }} \\ {\text { d. iron blue }}\end{array}$$

### Problem 55

Hemoglobin exists in two predominant forms in our bodies. One form, known as oxyhemoglobin, has $\mathrm{O}_{2}$ bound to the iron and the other, known as deoxyhemoglobin, has a water molecule bound instead. Oxyhemoglobin is a low-spin complex that gives arterial blood its red color, and deoxyhemoglobin is a high-spin complex that gives venous blood its darker color. Explain these observations in terms of crystal field spitting. Would you categorize $\mathrm{O}_{2}$ as a strong- or weak-field ligand?

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### Problem 56

Carbon monoxide and the cyanide ion are both toxic because they bind more strongly than oxygen to the iron in hemoglobin (Hb).
$$\begin{array}{ll}{\mathrm{Hb}+\mathrm{O}_{2} \Longrightarrow \mathrm{HbO}_{2}} & {K=2 \times 10^{12}} \\ {\mathrm{Hb}+\mathrm{CO} \rightleftharpoons \mathrm{HbCO}} & {K=1 \times 10^{14}}\end{array}$$
Calculate the equilibrium constant value for this reaction:
$$\mathrm{HbO}_{2}+\mathrm{CO} \rightleftharpoons \mathrm{HbCO}+\mathrm{O}_{2}$$
Does the equilibrium favor reactants or products?

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### Problem 57

Recall from Chapter 8 that Cr and Cu are exceptions to the normal orbital filling, resulting in a [Arl 4$s^{1} 3 d^{x}$ configuration. Write the ground state electron configuration for each species.
$$\text { a. } \mathrm{Cr}, \mathrm{Cr}^{+}, \mathrm{Cr}^{2+}, \mathrm{Cr}^{3+} \quad \text { b. } \quad \mathrm{Cu}, \mathrm{Cu}^{+}, \mathrm{Cu}^{2+}$$

Sam L.

### Problem 58

Most of the second row transition metals do not follow the normal orbital filling pattern. Five of them - Nb, Mo, Ru, Rh, and Ag-have a $[\mathrm{Kr}] 5 s^{1} 4 d^{x}$ configuration and $\mathrm{Pd}$ hasa {Kr} 4 d 10 configuration. Write the ground state electron configuration for each species.
$$\begin{array}{l}{\text { a. Mo, } \mathrm{Mo}^{+}, \mathrm{Ag}, \mathrm{Ag}^{+}} \\ {\text { b. } \mathrm{Ru}, \mathrm{Ru}^{3+}} \\ {\text { c. } \mathrm{Rh}, \mathrm{Ru}^{2+}} \\ {\text { d. } \mathrm{Pd}, \mathrm{Pd}^{+}, \mathrm{Pd}^{2+}}\end{array}$$

### Problem 59

Draw the Lewis diagrams for each ligand. Indicate the lone pair(s) that may be donated to the metal. Indicate any you expect to be bidentate or polydentate.
$$\text { a. } \mathrm{NH}_{3} \quad \text { b. } \mathrm{SCN}^{-} \quad \text { c. } \mathrm{H}_{2} \mathrm{O}$$

Anna M.

### Problem 60

Draw the Lewis diagrams for each ligand. Indicate the lone pair(s) that may be donated to the metal. Indicate any you expect to be bidentate or polydentate.
a. CN
b. bipyridyl (bipy), which has the following structure:
$\mathrm{c} \cdot \mathrm{NO}_{2}^{-}$

### Problem 61

List all the different formulas for an octahedral complex made from a metal (M) and three different ligands $(A, B,$ and $C) .$ Describe any isomers for each complex.

Anna M.

### Problem 62

Amino acids, such as glycine (gly), form complexes with the trace metal ions found in the bloodstream. Glycine, whose structure is shown here, acts as a bidentate ligand coordinating with the nitrogen atom and one of the oxygen atoms.
Draw all the possible isomers of:
$$\begin{array}{l}{\text { a. square planar }\left[\mathrm{Ni}(\mathrm{gly})_{2}\right]} \\ {\text { b. tetrahedral }\left[\mathrm{Zn}(\mathrm{gly})_{2}\right]} \\ {\text { c. octahedral }\left[\mathrm{Fe}(\mathrm{gly})_{3}\right]}\end{array}$$

### Problem 63

Oxalic acid solutions remove rust stains. Draw a complex ion that is likely responsible for this effect. Does it have any isomers?

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### Problem 64

$\mathrm{w}, \mathrm{X}, \mathrm{Y},$ and $\mathrm{Z}$ are different monodentate ligands.
a. Is the square planar [NiWXYZ] $^{2+}$ optically active?
b. Is the tetrahedral $[\mathrm{ZnW} \mathrm{XYZ}]^{2+}$ optically active?

### Problem 65

Hexacyanomanganate(III) ion is a low-spin complex. Draw the crystal field splitting diagram with electrons filled in appropriately. Is this complex paramagnetic or diamagnetic?

Sam L.

### Problem 66

Determine the color and approximate wavelength absorbed most strongly by each solution.
$$\begin{array}{l}{\text { a. blue solution }} \\ {\text { b. red solution }} \\ {\text { c. yellow solution }}\end{array}$$

### Problem 67

Draw the structures of all the geometric isomers of $\left[\mathrm{Ru}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]^{+}$ . Draw the mirror images of any that are chiral.

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### Problem 68

A 0.32 mol amount of $\mathrm{NH}_{3}$ is dissolved in 0.47 $\mathrm{L}$ of a 0.38 $\mathrm{M}$ silver nitrate solution. Calculate the equilibrium concentrations of all species in the solution.

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### Problem 69

When a solution of $\mathrm{PtCl}_{2}$ reacts with the ligand trimethylphosphine, $\mathrm{P}\left(\mathrm{CH}_{3}\right)_{3},$ two compounds are produced. The compounds share the same elemental analysis: $46.796 \mathrm{Pt} ; 17.0 \% \mathrm{Cl} ; 14.8 \% \mathrm{P}$ ;
$17.2 \% \mathrm{C} ; 4.34 \%$ H. Determine the formula, draw the structure, and give the systematic name for each compound.

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### Problem 70

Draw a crystal field splitting diagram for a trigonal planar complexion. Assume the plane of the molecule is perpendicular to the z axis.

### Problem 71

Draw a crystal field splitting diagram for a trigonal bipyramidal complex ion. Assume the axial positions are on the $z$ axis.

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### Problem 72

Explain why $\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}$ is paramagnetic, while $\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}$ is diamagnetic.

### Problem 73

Sulfide $\left(5^{2-}\right)$ salts are notoriously insoluble in aqueous solution.
a. Calculate the molar solubility of nickel(II) sulfide in water. $K_{\mathrm{p} \mathrm{p}}(\mathrm{NiS})=3 \times 10^{-16}$
b. Nickel(II) ions form a complex ion in the presence of ammonia with a formation constant $\left(K_{t}\right)$ of $2.0 \times 10^{8} :$ $\mathrm{Ni}^{2+}+6 \mathrm{NH}_{3} \rightleftharpoons\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+} .$ Calculate the molar
solubility of $\mathrm{NiS}$ in 3.0 $\mathrm{MNH}_{3}$
C. Explain any differences between the answers to parts a and b.

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### Problem 74

Calculate the solubility of Zn(OH) $_{2}(s)$ in 2.0 $\mathrm{M}$ NaOH solution.
(Hint: you must take into account the formation of $\mathrm{Zn}(\mathrm{OH})_{4}^{2-}$ , which has a $K_{t}=2 \times 10^{15} )$

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### Problem 75

Halide complexes of metal $M$ of the form $\left[\mathrm{MX}_{6}\right]^{3-}$ are found to be stable in aqueous solution. But it is possible that they undergo rapid ligand exchange with water (or other ligands) that is not detectable because the complexes are less stable. This property is referred to as their lability. Suggest an experiment to measure the lability of these complexes that does not employ radioactive labels.

Sam L.

### Problem 76

The $K_{t}$ for $\left[\mathrm{Cu}(\mathrm{en})_{2}\right]^{2+}$ is much larger than the one for
$\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}$ . This difference is primarily an entropy effect. Explain why and calculate the difference between the $\Delta S^{\circ}$ values at 298 $\mathrm{K}$ for the complete dissociation of the two complex ions. (Hint: the value of $\Delta H$ is about the same for both systems.)

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### Problem 77

When solid $\mathrm{Cd}(\mathrm{OH})_{2}$ is added to a solution of 0.10 $\mathrm{M}$ Nal, some of it dissolves. Calculate the $\mathrm{pH}$ of the solution at equilibrium.

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### Problem 78

Two ligands, A and B, both form complexes with a particular metal ion. When the metal ion complexes with ligand A, the solution is green. When the metal ion complexes with ligand B, the solution is violet. Which of the two ligands results in the largest $\Delta ?$

### Problem 79

Which element has the higher ionization energy, Cu or Au?

Anna M.

### Problem 80

The complexes of $\mathrm{Fe}^{3+}$ have magnetic properties that depend on whether the ligands are strong or weak field. Explain why this observation supports the idea that electrons are lost from the 4 orbital before the 3$d$ orbitals in the transition metals.

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### Problem 81

Choose a row of the transition metals in the periodic table. Have each group member look up and graph (where appropriate) a separate trend for the elements in that row, choosing from electron configuration, atomic size, ionization energy, and electronegativity. Each member should present a graph to the group and describe the general trend and any notable exceptions. If possible, form new groups made up of individuals who researched the same property for different rows of the periodic table.

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### Problem 82

Have each group member write down the names and formulas for two coordination compounds. Taking turns, show each formula to the group and have the rest of the group name the compound, with each member contributing one step in the process. Once all group members have had their formulas named, repeat the process by showing each formula name to the group and having group members determine the correct formula.

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### Problem 83

Working individually, draw a pair of coordination compounds that are isomers. Take turns showing your drawings to the group and having them identify the type of isomerism and the reasons your drawing demonstrates that type of isomerism. If your group misidentifies your type of isomerism, rather than telling them the correct answer right away, point out the part of the structure that prevents it from being the type of isomerism they thought it was.

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### Problem 84

Divide the electron configurations $d^{1}$ through $d^{10}$ among the group members so that every configuration is assigned to at least two group members. Working individually, draw the orbital diagram for the configurations assigned to you, including both high-spin and low-spin diagrams where possible. Present your diagrams to your group. Combine everyone's diagrams into one set for the group.

### Problem 85

Working individually, review one of the applications of coordination complexes. Without referring to the text or mentioning the key words in the heading of the subsection, describe the application you reviewed. As group members each describe the application they reviewed, take turns attempting to identify the key words from the heading of the subsection they are describing.

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### Problem 86

Many aqueous solutions of complex ions display brilliant colors that depend on the identities of the metal ion and ligand(s). Some ligands bind selectively to certain metal ions, producing complex ions with characteristic colors. These distinctive complex ions serve as qualitative indicators of the presence of particular metal ions. For example, $\mathrm{Fe}^{3+}$ is identified by the rapid formation of the intensely colored pentaaquathio-cyanatoiron(III) complex ion, $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{SCN}\right]^{2+}$ when thiocyanate, $\mathrm{SCN}^{-},$ is added to a solution containing hexaaquairon(III), $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+},$ according to the following chemical equation:
$$\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}(a q)+\mathrm{SCN}^{-}(a q) \rightleftharpoons\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{\mathrm{s}} \mathrm{SCN}\right]^{2+}(a q)$$
The absorption spectrum of an aqueous solution of $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{\mathrm{s}} \mathrm{SCN}\right]^{2+}$ is shown in Figure at*.Use the information provided to answer the following questions:
a. Determine the color of the aqueous solution of $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{SCN}\right]^{2+}$ based on the spectrum shown in Figure a.
b. Calculate the crystal field splitting energy, $\Delta,$ of $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{\mathrm{s}} \mathrm{SCN}\right]^{2+},$ in $\mathrm{kJ} / \mathrm{mol} .$
C. The hexaaquairon(III) complex ion, $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+},$ produces a pale violet aqueous solution. Is the crystal field splitting energy, $\Delta,$ of $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$ smaller or larger than the $\Delta$ of $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{\mathrm{s}} \mathrm{SCN}\right]^{2+7}$ ?
d. On the basis of your answers to parts $\mathrm{b}$ and $\mathrm{c}$ , compare the cystal field strengths of water and thiocyanate ligands.
e. The complex ion hexacyanoferrate(III), $\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-},$ is red in aqueous solution. What can you conclude about the relative crystal field splitting energies of $\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}$ and $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{SCN}\right]^{2+2}$