Chapter 24

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 complex 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 won't 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. Furthermore, for a given ligand the complexes of the bivalent metal ions of the first transition series tend to increase in stability in the order \(\mathrm{Mn}(\mathrm{II})<\mathrm{Fe}(\mathrm{II})<\mathrm{Co}(\mathrm{II})<\) Ni(II) < Cu(II). Explain how these two observations are consistent with one another and also consistent with a crystal-field picture of coordination compounds.

Many trace metal ions exist in the bloodstream as complexes with amino acids or small peptides. The anion of the amino acid glycine, symbol gly, is capable of acting 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) \(\left[\mathrm{Co}(\mathrm{gly})_{3}\right]\) (octahedral)? Sketch all possible isomers. Use \(\mathrm{N}\) O to represent the ligand.

Suppose that a transition-metal ion was in a lattice in which it was in contact with just two nearby anions, located on opposite sides of the metal. Diagram the splitting of the metal \(d\) orbitals that would result from such a crystal field. Assuming a strong field, how many unpaired electrons would you expect for a metal ion with six \(d\) electrons? (Hint: Consider the linear axis to be the z-axis).

Metallic elements are essential components of many important enzymes operating within our bodies. Carbonic anhydrase, which contains \(\mathrm{Zn}^{2+}\), is responsible for rapidly interconverting dissolved \(\mathrm{CO}_{2}\) and bicarbonate ion, \(\mathrm{HCO}_{3}^{-}\). The zinc in carbonic anhydrase is coordinated by three nitrogen-containing groups and a water molecule. The enzyme's action depends on the fact that the coordinated water molecule is more acidic than the bulk solvent molecules. Explain this fact in terms of Lewis acid-base theory (Section 16.11).

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 \(\mathrm{B}\) is red-violet. When compound \(\mathrm{A}\) is treated with \(\mathrm{AgNO}_{3}(a q)\), no reaction occurs, whereas compound \(\mathrm{B}\) reacts with \(\mathrm{AgNO}_{3}(a q)\) to form a white precipitate. When compound \(\mathrm{A}\) is treated with \(\mathrm{BaCl}_{2}(a q)\), a white precipitate is formed, whereas compound \(\mathrm{B}\) has no reaction with \(\mathrm{BaCl}_{2}(a q)\). (a) Is Co in the same oxidation state in these complexes? (b) Explain the reactivity of compounds \(\mathrm{A}\) and \(\mathrm{B}\) with \(\mathrm{AgNO}_{3}(a q)\) and \(\mathrm{BaCl}_{2}(a q)\). (c) Are compounds \(A\) and \(B\) isomers of one another? If so, which category from Figure \(24.17\) best describes the isomerism observed for these complexes? (d) Would compounds \(\mathrm{A}\) and \(\mathrm{B}\) be expected to be strong electrolytes, weak electrolytes, or nonelectrolytes?

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 \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\). Write the formula of the compound, using brackets to denote the manganese and its coordination sphere.

The \(E^{\circ}\) values for two iron complexes in acidic solution are as follows: $$ \begin{aligned} \left[\mathrm{Fe}(o-p h e n)_{3}\right]^{3+}(a q)+\mathrm{e}^{-} & \rightleftharpoons\left[\mathrm{Fe}(o-p h e n)_{3}\right]^{2+}(a q) & E^{\circ}=1.12 \mathrm{~V} \\ \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}(a q)+\mathrm{e}^{-} & \rightleftharpoons\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}(a q) & E^{\circ}=0.36 \mathrm{~V} \end{aligned} $$ (a) What do the relative \(E^{\circ}\) values tell about the relative stabilities of the \(\mathrm{Fe}(\mathrm{II})\) and \(\mathrm{Fe}(\mathrm{III})\) complexes in each case? (b) Account for the more positive \(E^{\circ}\) value for the (o-phen) complex. Both of the Fe(II) complexes are low spin. (Hint: consider the charges carried by the ligands in the two cases.)

A palladium complex formed from a solution containing bromide ion and pyridine, \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}\) (a good electronpair donor), is found on elemental analysis to contain \(37.6 \%\) bromine, \(28.3 \%\) carbon, \(6.60 \%\) nitrogen, and \(2.37 \%\) hydrogen by mass. The compound is slightly soluble in several organic solvents; its solutions in water or alcohol do not conduct electricity. It is found experimentally to have a zero dipole moment. Write the chemical formula, and indicate its probable structure.

(a) In early studies it was observed that when the complex \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right] \mathrm{Br}\) was placed in water, the electrical conductivity of a \(0.05 M\) solution changed from an initial value of \(191 \mathrm{ohm}^{-1}\) to a final value of \(374 \mathrm{ohm}^{-1}\) over a period of an hour or so. Suggest an explanation for the observed results. (See Exercise \(24.49\) for relevant comparison data.) (b) Write a balanced chemical equation to describe the reaction. (c) A 500-mL solution is made up by dissolving \(3.87 \mathrm{~g}\) of the complex. As soon as the solution is formed, and before any change in conductivity has occurred, a 25.00-mL portion of the solution is titrated with \(0.0100 \mathrm{M} \mathrm{AgNO}_{3}\) solution. What volume of \(\mathrm{AgNO}_{3}\) solution do you expect to be required to precipitate the free \(\mathrm{Br}^{-}(a q) ?\) (d) Based on the response you gave to part (b), what volume of \(\mathrm{AgNO}_{3}\) solution would be required to titrate a fresh \(25.00-\mathrm{mL}\) sample of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right] \mathrm{Br}\) after all conductivity changes have occurred?

The total concentration of \(\mathrm{Ca}^{2+}\) and \(\mathrm{Mg}^{2+}\) in a sample of hard water was determined by titrating a \(0.100-\mathrm{L}\) sample of the water with a solution of EDTA \(^{4-}\). The EDTA \(^{4-}\) chelates the two cations: $$ \begin{array}{r} \mathrm{Mg}^{2+}+[\mathrm{EDTA}]^{4-}--\rightarrow[\mathrm{Mg}(\mathrm{EDTA})]^{2-} \\\ \mathrm{Ca}^{2+}+[\mathrm{EDTA}]^{--}--\rightarrow[\mathrm{Ca}(\mathrm{EDTA})]^{2-} \end{array} $$ It requires \(31.5 \mathrm{~mL}\) of \(0.0104 M[\mathrm{EDTA}]^{4-}\) solution to reach the end point in the titration. A second \(0.100-\mathrm{L}\) 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 \(0.0104 \mathrm{M}[\mathrm{EDTA}]^{4-}\). Calculate the concentrations of \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) in the hard water in \(\mathrm{mg} / \mathrm{L}\).

Carbon monoxide is toxic because it binds more strongly to the iron in hemoglobin ( \((H b)\) than does \(\mathrm{O}_{2}\), as indicated by these approximate standard free-energy changes in blood: $$ \begin{array}{cl} \mathrm{Hb}+\mathrm{O}_{2} \longrightarrow \mathrm{HbO}_{2} & \Delta G^{\circ}=-70 \mathrm{~kJ} \\ \mathrm{Hb}+\mathrm{CO} \longrightarrow \mathrm{HbCO} & \Delta G^{\circ}=-80 \mathrm{~kJ} \end{array} $$ 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 \(\mathrm{Cd}^{2+}(a q)\) : \(\mathrm{Cd}^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) \rightleftharpoons\left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q)\) \(\Delta H^{\circ}=-57.3 \mathrm{~kJ} ; \quad \Delta S^{\circ}=-67.3 \mathrm{~J} / \mathrm{K} ; \quad \Delta G^{\circ}=-37.2 \mathrm{~kJ}\) $$ \mathrm{Cd}^{2+}(a q)+2 \mathrm{en}(a q) \rightleftharpoons\left[\mathrm{Cd}(\mathrm{en})_{2}\right]^{2+}(a q) $$ \(\Delta H^{\circ}=-56.5 \mathrm{~kJ} ; \quad \Delta S^{\circ}=+14.1 \mathrm{~J} / \mathrm{K} ; \quad \Delta G^{\circ}=-60.7 \mathrm{~kJ}\) (a) Calculate \(\Delta G^{\circ}\) and the equilibrium constant \(K\) for the following ligand exchange reaction: \(\left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q)+2 \mathrm{en}(a q) \rightleftharpoons\) $$ \left[\mathrm{Cd}(\mathrm{en})_{2}\right]^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) $$ (b) Based on the value of \(K\) in part (a), what would you conclude about this reaction? What concept is demonstrated? (c) 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. (d) Based on information in this exercise and in the "A Closer Look" box on the chelate effect, predict the sign of \(\Delta H^{\circ}\) for the following hypothetical reaction: \(\left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q)+4 \mathrm{NH}_{3}(a q) \rightleftharpoons\) $$ \left[\mathrm{Cd}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) $$

The value of \(\Delta\) for the \(\left[\mathrm{CrF}_{6}\right]^{3-}\) complex is \(182 \mathrm{~kJ} / \mathrm{mol}\). 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? (You may need to review Sample Exercise 6.3; remember to divide by Avogadro's number.)

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. \(\left[\mathrm{Ru}(\mathrm{EDTA})\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{-}+\mathrm{L} \longrightarrow[\mathrm{Ru}(\mathrm{EDTA}) \mathrm{L}]^{-}+\mathrm{H}_{2} \mathrm{O}\) The rate constants for several ligands are as follows: $$ \begin{array}{ll} \hline \text { Ligand, } \mathrm{L} & k\left(M^{-1} s^{-1}\right) \\ \hline \text { Pyridine } & 6.3 \times 10^{3} \\ \text { SCN }^{-} & 2.7 \times 10^{2} \\ \mathrm{CH}_{3} \mathrm{CN} & 3.0 \times 10 \\ \hline \end{array} $$ (a) One possible mechanism for this substitution reaction is that the water molecule dissociates from the complex in the rate-determining step, and then the ligand \(\mathrm{L}\) fills the void in a rapid second step. A second possible mechanism is that \(L\) approaches the complex, begins to form a new bond to the metal, 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 basicities of the three ligands toward Ru(III)? (c) Assuming that the complexes are all low spin, how many unpaired electrons are in each?