Chapter 23

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), (c) \([\text { Ru(bipy) }]^{3+}\) (a low-spin complex), (d) \(\left[\mathrm{NiCl}_{4}\right]^{2-}\) (tetrahedral), (e) \(\left[\mathrm{PtBr}_{6}\right]^{2-},(f)\left[\mathrm{Ti}(\mathrm{en})_{3}\right]^{2+}\). S in the spectrochemical series?

The complex \(\left[\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) contains five unpaired electrons. Sketch the energy-level diagram for the \(d\) arbitals, 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 NC

Explain why the transition metals in periods 5 anges have \(C\) nearly identical radii in each group.

Based on the molar conductance values listed here for the series of platinum(IV) complexes, write the formula for each complex so as to show which ligands are in the coordination sphere of the metal. By way of example, the molar conductances of \(0.050 \mathrm{M} \mathrm{NaCl}\) and \(\mathrm{BaCl}_{2}\) are \(107 \mathrm{ohm}^{-1}\) and \(197 \mathrm{ohm}^{-1}\), respectively. \begin{tabular}{lc} \hline Complex & Molar Conductance \(\left(o \text { ohm }^{-1}\right)^{*}\) of \(0.050\) M Solution \\ \hline \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{4}\) & 523 \\ \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{4}\) & 228 \\ \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{4}\) & 97 \\ \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{4}\) & 0 \\ \(\left.\mathrm{KPt}_{4}\right) \mathrm{NH}_{5}\) & 108 \\ \hline \end{tabular} "The ohm is a unit of resistance; conductance is the inverse of resistance.

(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 \(\mathrm{AgNO}_{3}(a q)\) forms \(2 \mathrm{~mol}\) of solid \(\mathrm{AgCl}\) 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 \(\mathrm{RuCl}_{3}+5 \mathrm{H}_{2} \mathrm{O}\) has stood for about a year, addition of \(\mathrm{AgNO}_{3}(a q)\) precipitates \(3 \mathrm{~mol}\) of \(\mathrm{AgCl}\) per mole of complex. What has happened in the ensuing time?

The molecule dimethylphosphinoethane \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{PCH}_{2} \mathrm{CH}_{2}\right.\) \(\mathrm{P}\left(\mathrm{CH}_{3}\right)_{2}\), which is abbreviated dmpel is used as a ligand for some complexes that serve as catalysts. A complex that contains this ligand is \(\mathrm{Mo}(\mathrm{CO})_{4}\) (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 \(\mathrm{Na}_{2}\left[\mathrm{Mo}(\mathrm{CN})_{2}(\mathrm{CO})_{2}\right.\) (dmpe)]? (c) Sketch the structure of the \(\left[\mathrm{Mo}(\mathrm{CN})_{2}(\mathrm{CO})_{2}(\text { dmpe })\right]^{2-}\) ion, including all the possible isomers.

Although the cis configuration is known for [ \(\mathrm{Pt}^{\left.(e n) \mathrm{Cl}_{2}\right] \text {, no }}\) trans form is known. (a) Explain why the trans compound is not possible. (b) Would \(\mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\) be more likely than en \(\left(\mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)\) to form the trans compound? Explain.

Which transition metal atom is present in each of the following biologically important molecules: (a) hemoglobin, (b) chlorophylls, (c) siderophores.

Carbon monoxide, \(\mathrm{CO}\), is an important ligand in coordination chemistry. When \(\mathrm{CO}\) is reacted with nickel metal the product is \(\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]\), which is a toxic, pale yellow liquid. (a) What is the oxidation number for nickel in this compound? (b) Given that \(\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]\) is diamagnetic molecule with a tetrahedral geometry, what is the electron configuration of nickel in this compound? (c) Write the name for \(\left[\mathrm{Nu}(\mathrm{CO})_{4}\right]\) using the nomenclature rules for coordination compounds.

Which of the following objects is chiral: (a) a left shoe, (b) a slice of bread, (c) a wood screw, (d) a molecular model of \(\mathrm{Zn}(\mathrm{en}) \mathrm{Cl}_{2}\), (e) a typical golf club?

The complexes \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) and \(\left[\mathrm{VF}_{6}\right]^{3-}\) are both known. (a) Draw the \(d\)-orbital energy-level diagram for V(III) octahedral complexes. (b) What gives rise to the colors of these complexes? (c) Which of the two complexes would you expect to absorb light of higher energy?

One of the more famous species in coordination chemistry is the Creutz-Taube complex: It is named for the two scientists who discovered it and initially studied its properties. The central ligand is pyrazine, a planar six-membered ring with nitrogens at opposite sides. (a) How can you account for the fact that the complex, which has only neutral ligands, has an odd overall charge? (b) The metal is in a low-spin configuration in both cases. Assuming octahedral coordination, draw the d-orbital energy-level diagram for each metal. (c) In many experiments the two metal ions appear to be in exactly equivalent states. Can you think of a reason that this might appear to be so, recognizing that electrons move very rapidly compared to nuclei?

Solutions of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+},\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (both octahedral), and \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) (tetrahedral) are colored. One is pink, one is blue, and one is yellow. Based on the spectrochemical series and remembering that the energy splitting in tetrahedral complexes is normally much less than that in ectahedral ones, assign a color to each complex.

Oxyhemoglobin, with an \(\mathrm{O}_{2}\) bound to iron, is a low-spin \(\mathrm{Fe}\) (II) complex; deoxyhemoglobin, without the \(\mathrm{O}_{2}\) molecule, is a high-spin complex. (a) Assuming that the coordination environment about the metal is octahedral, how many unpaired electrons are centered on the metal ion in each case? (b) What ligand is coordinated to the iron in place of \(\mathrm{O}_{2}\) in deoxyhemoglobin? (c) Explain in a general way why the two forms of hemoglobin have different colors (hemoglobin is red, whereas deoxyhemoglobin has a bluish cast). (d) A 15 -minute exposure to air containing \(400 \mathrm{ppm}\) of CO causes about \(10 \%\) of the hemoglobin in the blood to be converted into the carbon monoxide complex, called carboxyhemoglobin. What does this suggest about the relative equilibrium constants for binding of carbon monoxide and \(\mathrm{O}_{2}\) to hemoglobin? (e) \(\mathrm{CO}\) is a strong-field ligand. What color might you expect carboxyhemoglobin to be?

Consider the tetrahedral anions \(\mathrm{VO}_{4}^{3-}\) (orthovanadate ion), \(\mathrm{CrO}_{4}^{2-}\) (chromate ion), and \(\mathrm{MnO}_{4}^{-}\)(permanganate ion). (a) These anions are isoelectronic. What does this statement mean? (b) Would you expect these anions to exhibit \(d-d\) transitions? Explain. (c) As mentioned in "A Closer Look" on charge- transfer color, the violet color of \(\mathrm{MnO}_{4}^{-}\)is due to a ligand- to-metal charge transfer (LMCT) transition. What is meant by this term? (d) The LMCT transition in \(\mathrm{MnO}_{4}^{-}\)occurs at a wavelength of \(565 \mathrm{~nm}\). The \(\mathrm{CrO}_{4}^{2}\) ion is yellow. Is the wavelength of the LMCT transition for chromate larger or smaller than that for \(\mathrm{MnO}_{4}^{-}\)? Explain. (e) The \(\mathrm{VO}_{4}^{3-}\) ion is colorless. Do you expect the light absorbed by the LMCT to fall in the UV or the IR region of the electromagnetic spectrum? Explain your reasoning.

The red color of ruby is due to the presence of \(\mathrm{Cr}(\mathrm{III})\) ions at octahedral sites in the dose-packed exide lattice of \(\mathrm{Al}_{2} \mathrm{O}_{2}\). Draw the crystal-field splitting diagram for \(\mathrm{Cr}\) (III) in this environment. Suppose that the ruby crystal is subjected to high pressure. What do you predict for the variation in the wavelength of absorption of the ruby as a function of pressure? Explain.

In 2001, chemists at SUNY-Stony Brook succeeded in synthesizing the complex trans-[Fe(CN) \(\left.{ }_{4}(\mathrm{CO})_{2}\right]^{2-}\), which could be a model of complexes that may have played a role in the origin of life. (a) Sketch the structure of the complex. (b) The comnplex is isolated as a sodium salt. Write the complete name of this salt. (c) What is the oxidation state of Fe in this complex? How many \(d\) electrons are associated with the Fe in this complex? (d) Would you expect this complex to be high spin or low spin? Explain.

When Alfred Werner was developing the field of coordination chemistry, it was argued by some that the optical activity he observed in the chiral complexes he had prepared was because of the presence of carbon atoms in the molecule. To disprove this argument, Werner synthesized a chiral complex of cobalt that had no carbon atoms in it, and he was able to resolve it into its enantiomers. Design a cobalt(III) complex that would be chiral if it could be synthesized and that contains no carbon atoms. (It may not be possible to synthesize the complex you design, but we will not worry about that for now.)

Generally speaking, for a given metal and ligand, the stability of a coordination compound is greater for the metal in the \(+3\) rather than in the \(+2\) oxidation state (for metals that form stable \(+3\) ions in the first place). Suggest an explanation, keeping in mind the Lewis acid-base nature of the metalligand bond.

Many trace metal ions exist in the blood complexed with amino acids or small peptides. The anion of the amine acid glycine (gly). NCC(=O)[O-] can act as a bidentate ligand, coordinating to the metal through nitrogen and oxygen atoms. How many isomers are possible for (a) \(\left[\mathrm{Zn}(\mathrm{gly})_{2}\right]\) (tetrahedral), (b) [ \(\left.\mathrm{Pt}(\mathrm{gly})_{2}\right]\) (square planar), (c) [Co(gly) 3\(]\) (octahedral)? Sketch all possible isomers. Use the symbol to represent the ligand.

The coordination complex \(\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\) forms colorless, diamagnetic crystals that melt at \(90{ }^{\circ} \mathrm{C}\). (a) What is the oxidation number of chromium in this compound? (b) Given that \(\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\) is diamagnetic, what is the electron configuration of chromium in this compound? (c) Given that \(\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\) is colorless, would you expect CO to be a weak-field or strongfield ligand? (d) Write the name for \(\left[\mathrm{Cr}(\mathrm{CO})_{4}\right]\) using the nomenclature rules for coordination compounds.

Metallic elements are essential components of many important enzymes operating within our bodies. Carbonic anhydrase, which contains \(Z \mathrm{n}^{2+}\) in its active site, is responsible for rapidly interconverting dissolved \(\mathrm{CO}_{2}\) and bicarbonate ion, \(\mathrm{HCO}_{3}^{-}\). The zinc in carbonic anhydrase is tetrahedrally coordinated by three neutral nitrogen- containing groups and a water molecule. The coordinated water molecule has a pK of 7.5, which is crucial for the enxyme's activity. (a) Draw the active site geometry for the Zn(II) center in carbonic anhydrasc, just writing " \(\mathrm{N}^{\text {" }}\) for the three neutral nitrogen ligands from the protein. (b) Compare the \(p K_{a}\) of carbonic anhydrase's active site with that of pure water, which species is more acidic?

(c) When the coordinated water to the \(\mathrm{Zn}(\mathrm{II})\) center in carbonic anhydrase is deprotonated, what ligands are bound to the Zn(II) center? Assume the three nitrogen ligands are unaffected. (d) The \(\mathrm{F} K_{a}\) of \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{d}\right]^{2+}\) is 10 . Suggest an explanation for the difference between this \(\mathrm{pK} \mathrm{K}_{\text {and }}\) that of carbonic anhydrase. (e) Would you expect carbonic anhydrase to have a decp color, like hemoglobin and other metalion containing proteins do? Explain. Two different compounds have the formulation \(\mathrm{CoBr}\left(\mathrm{SO}_{4}\right) \cdot 5 \mathrm{NH}_{3}\). Compound \(\mathrm{A}\) is dark violet, and compound B is red-violet. When compound \(A\) is treated with \(\mathrm{AgNO}_{3}(\mathrm{Gq})\), no reaction occurs, whereas compound \(\mathrm{B}\)

A manganese complex formed from a solution containing potassium bromide and oxalate ion is purified and analyzed. It contains \(10.0 \% \mathrm{Mn}, 28.6 \%\) potassium, \(8.8 \%\) carbon, and \(29.2 \%\) bromine by mass. The remainder of the compound is oxygen. An aqueous solution of the complex has about the same electrical conductivity as an equimolar solution of \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{\mathrm{S}}\right]\). Write the formula of the compound, using brackets to denote the manganese and its coordination sphere.

The total concentration of \(\mathrm{Ca}^{2+}\) and \(\mathrm{Mg}^{2+}\) in a sample of hard water was determined by titrating a \(0.100\) - L sample of the water with a solution of EDTA \({ }^{4-}\). The EDTA \({ }^{4-}\) chelates the two cations: $$ \begin{aligned} \mathrm{Mg}^{2+}+[\mathrm{EDTA}]^{4-} & \longrightarrow[\mathrm{Mg}(\mathrm{EDTA})]^{2-} \\ \mathrm{Ca}^{2+}+\left[\mathrm{EDTA}^{4-}\right.& \longrightarrow[\mathrm{Ca}(\mathrm{EDTA})]^{2-} \end{aligned} $$ It requires \(31.5 \mathrm{~mL}\) of \(0.0104 \mathrm{M}[\mathrm{EDTA}]^{4-}\) solution to reach the end point in the titration. A second \(0.100-L\) sample was then treated with sulfate ion to precipitate \(\mathrm{Ca}^{2+}\) as calcium sulfate. The \(\mathrm{Mg}^{2+}\) was then titrated with \(18.7 \mathrm{~mL}\) of \(0.0104 \mathrm{M}\) [EDTA] ]- Calculate the concentrations of \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) in the hard water in mg/I.

Carbon monoxide is toxic because it binds more strongly to the iron in hemoglobin (Hb) than does \(\mathrm{O}_{2}\), as indicated by these approximate standard free-energy changes in blood: $$ \begin{array}{ll} \mathrm{Hb}+\mathrm{O}_{2} \longrightarrow \mathrm{HbO}_{2} & \Delta G^{\mathrm{e}}=-70 \mathrm{~kJ} \\ \mathrm{Hb}+\mathrm{CO} \longrightarrow \mathrm{HbCO} & \Delta G^{\mathrm{a}}=-80 \mathrm{~kJ} \end{array} $$ Using these data, estimate the equilibrium constant at \(298 \mathrm{~K}\) for the equilibrium $$ \mathrm{HbO}_{2}+\mathrm{CO} \rightleftharpoons \mathrm{HbCO}+\mathrm{O}_{2} $$

The molecule methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\) can act as a monodentate ligand. The following are equilibrium reactions and the thermochemical data at \(298 \mathrm{~K}\) for reactions of methylamine and en with \(\mathrm{Cd}^{2+}(a q)\) : $$ \begin{aligned} \mathrm{Cd}^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) \rightleftharpoons & {\left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q) } \\ \Delta H^{\circ}=&\left.-57.3 \mathrm{~kJ} ; \Delta S^{\circ}=-67.3 \mathrm{~J} / \mathrm{K} ; \Delta G^{\circ}=-37.2 \mathrm{k}\right] \\ & \mathrm{Cd}^{2+}(a q)+2 \mathrm{en}(a q) \rightleftharpoons\left[\mathrm{Cd}(\mathrm{en})_{2}\right]^{2+}(a q) \\ \Delta H^{\circ}=&\left.-56.5 \mathrm{k} ; ; \Delta S^{\circ}=+14.1 \mathrm{~J} / \mathrm{K} ; \Delta G^{\circ}=-60.7 \mathrm{k}\right] \end{aligned} $$ (a) Calculate \(\Delta G^{\circ}\) and the equilibrium constant \(K\) for the following ligand exchange reaction: $$ \begin{aligned} {\left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q)+} & 2 \mathrm{en}(a q) \rightleftharpoons \\ & {\left[\mathrm{Cd}(\mathrm{en})_{2}\right]^{2+(a q)}+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) } \end{aligned} $$ Based on the value of \(K\) in part (a). what would you conclude about this reaction? What concept is demonstrated? (b) Determine the magnitudes of the enthalpic \(\left(\Delta H^{\circ}\right)\) and the entropic \(\left(-T \Delta S^{\circ}\right)\) contributions to \(\Delta G^{\circ}\) for the ligand exchange reaction. Explain the relative magnitudes. (c) Based on information in this exercise and in the "A Closer Look" box on the chelate effect, predict the sign of \(\Delta H^{2}\) for the following hypothetical reaction: $$ \begin{aligned} {\left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q)+} & 4 \mathrm{NH}_{3}(a q) \rightleftharpoons \\ & {\left[\mathrm{Cd}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) } \end{aligned} $$

The value of \(\Delta\) for the \(\left[\mathrm{CrF}_{6}\right]^{3-}\) complex is \(182 \mathrm{k} / / \mathrm{mol}\). Calculate the expected wavelength of the absorption corresponding to promotion of an electron from the lower-energy to the higher-energy d-orbital set in this complex. Should the complex absorb in the visible range?

A Cu electrode is immersed in a solution that is \(1.00 \mathrm{M}\) in \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) and \(1.00 \mathrm{M}\) in \(\mathrm{NH}_{3}\). When the cathode is a standard hydrogen electrode, the emf of the cell is found to be \(+0.08 \mathrm{~V}\). What is the formation constant for \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) ?

The complex \(\left[\mathrm{Ru}(\mathrm{EDTA})\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{-}\)undergoes substitution reactions with several ligands, replacing the water molecule with the ligand. In all cases, the ruthenium stays in the \(+3\) oxidation state and the ligands use a nitrogen donor atom to bind to the metal. $$ \left[\operatorname{Ru}(\mathrm{EDTA})\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{-}+\mathrm{L} \longrightarrow[\operatorname{Ru}(\mathrm{EDTA}) \mathrm{L}]^{-}+\mathrm{H}_{2} \mathrm{O} $$ The rate constants for several ligands are as follows: (a) One possible mechanism for this substitution reaction is that the water molecule dissociates from the Ru(III) in the rate-determining step, and then the ligand L binds to Ru(III) in a rapid second step. A second possible mechanism is that L approaches the complex, begins to form a new bond to the Ru(III), and displaces the water molecule, all in a single concerted step. Which of these two mechanisms is more consistent with the data? Explain. (b) What do the results suggest about the relative donor ability of the nitrogens of the three ligands toward Ru(TII))? (c) Assuming that the complexes are all low spin, how many unpaired electrons are in each?