Chapter 21

Henry Taube, 1983 Nobel Prize winner in chemistry, has studied the mechanisms of the oxidation-reduction reactions of transition metal complexes. In one experiment he and his students studied the following reaction: $\begin{array}{rl}\mathrm{Cr}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6^{2+}(aq)+& \mathrm{Co}{\left({\mathrm{NH}}_3\right)}_5{\mathrm{Cl}}^{2+}(aq)\\ ⟶& \mathrm{Cr}(\mathrm{III})\text{ complexes }+\mathrm{Co}(\mathrm{II})\text{ complexes }\end{array}$ Chromium(III) and cobalt(III) complexes are substitutionally inert (no exchange of ligands) under conditions of the experiment. Chromium(II) and cobalt(II) complexes can exchange ligands very rapidly. One of the products of the reaction is $\mathrm{Cr}{\left({\mathrm{H}}_2\mathrm{O}\right)}_5{\mathrm{Cl}}^{2+}.$ Is this consistent with the reaction proceeding through formation of ${\left({\mathrm{H}}_2\mathrm{O}\right)}_5\mathrm{Cr}-\mathrm{Cl}-\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_5$ as an intermediate? Explain.

Qualitatively draw the crystal field splitting of the $d$ orbitals in a trigonal planar complex ion. (Let the $z$ axis be perpendicular to the plane of the complex.)

Qualitatively draw the crystal field splitting for a trigonal bipyramidal complex ion. (Let the $z$ axis be perpendicular to the trigonal plane.)

Sketch a $d$ -orbital energy diagram for the following. a. a linear complex with ligands on the $x$ axis b. a linear complex with ligands on the $y$ axis

Sketch and explain the most likely pattem for the crystal field diagram for the complex ion trans-diamminetetracyanonickelate(II), where ${\mathrm{CN}}^{-}$ produces a much stronger crystal field than ${\mathrm{NH}}_3$. Explain completely and label the $d$ orbitals in your diagram. Assume the ${\mathrm{NH}}_3$ ligands lie on the $z$ axis.

a. Calculate the molar solubility of AgBr in pure water. $K_{\text{sp }}$ for AgBr is $5.0\times {10}^{-13}$ b. Calculate the molar solubility of AgBr in $3.0M{\mathrm{NH}}_3$. The overall formation constant for $\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2^{+}$ is $1.7\times {10}^7$, that is, ${\mathrm{Ag}}^{+}(aq)+2{\mathrm{NH}}_3(aq)⟶\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2^{+}(aq)K=1.7\times {10}^7$ c. Compare the calculated solubilities from parts a and b. Explain any differences. d. What mass of $\mathrm{AgBr}$ will dissolve in $250.0\mathrm{mL}$ of $3.0\mathrm{M}{\mathrm{NH}}_3$ ? e. What effect does adding ${\mathrm{HNO}}_3$ have on the solubilities calculated in parts a and $\mathrm{b}$ ?

The ferrate ion, ${\mathrm{FeO}}_4{}^{2-}$, is such a powerful oxidizing agent that in acidic solution, aqueous ammonia is reduced to elemental nitrogen along with the formation of the iron(III) ion. a. What is the oxidation state of iron in ${\mathrm{FeO}}_4{}^{2-}$, and what is the electron configuration of iron in this polyatomic ion? b. If $25.0\mathrm{mL}$ of a $0.243\mathrm{M}{\mathrm{FeO}}_4^{2-}$ solution is allowed to react with $55.0\mathrm{mL}$ of $1.45M$ aqueous ammonia, what volume of nitrogen gas can form at ${25}^{\circ }\mathrm{C}$ and $1.50\mathrm{atm}$ ?

a. In the absorption spectrum of the complex ion [Cr(NCS) ${{}_6]}^{3-}$, there is a band corresponding to the absorption of a photon of light with an energy of $1.75\times {10}^4{\mathrm{cm}}^{-1}$. Given $1{\mathrm{cm}}^{-1}=$ $1.986\times {10}^{-23}\mathrm{J}$, what is the wavelength of this photon? b. The $\mathrm{Cr}-\mathrm{N}-\mathrm{C}$ bond angle in ${[\mathrm{Cr}(\mathrm{NCS}{)}_6]}^{3-}$ is predicted to be ${180}^{\circ }$. What is the hybridization of the $\mathrm{N}$ atom in the ${\mathrm{NCS}}^{-}$ ligand when a Lewis acid-base reaction occurs between ${\mathrm{Cr}}^{3+}$ and ${\mathrm{NCS}}^{-}$ that would give a ${180}^{\circ }\mathrm{Cr}-\mathrm{N}-\mathrm{C}$ bond angle? ${[\mathrm{Cr}(\mathrm{NCS}{)}_6]}^{3-}$ undergoes substitution by ethylenediammine (en) according to the equation ${[\mathrm{Cr}(\mathrm{NCS}{)}_6]}^{3-}+2\mathrm{en}⟶{[\mathrm{Cr}(\mathrm{NCS}{)}_2(\mathrm{en}{)}_2]}^{+}+4{\mathrm{NCS}}^{-}$ Does ${[\mathrm{Cr}(\mathrm{NCS}{)}_2(\mathrm{en}{)}_2]}^{+}$ exhibit geometric isomerism? Does ${[\mathrm{Cr}(\mathrm{NCS}{)}_2(\mathrm{en}{)}_2]}^{+}$ exhibit optical isomerism?

Ammonia and potassium iodide solutions are added to an aqueous solution of $\mathrm{Cr}{\left({\mathrm{NO}}_3\right)}_3.$ A solid is isolated (compound $\mathrm{A}$ ), and the following data are collected: i. When $0.105\mathrm{g}$ of compound $\mathrm{A}$ was strongly heated in excess ${\mathrm{O}}_2,0.0203\mathrm{g}{\mathrm{CrO}}_3$ was formed. ii. In a second experiment it took $32.93\mathrm{mL}$ of $0.100\mathrm{M}\mathrm{HCl}$ to titrate completely the ${\mathrm{NH}}_3$ present in $0.341\mathrm{g}$ compound $\mathrm{A}$. iii. Compound A was found to contain $73.53\mathrm{\%}$ iodine by mass. iv. The freezing point of water was lowered by ${0.64}^{\circ }\mathrm{C}$ when $0.601$ g compound $A$ was dissolved in $10.00\mathrm{g}{\mathrm{H}}_2\mathrm{O}$ $(K_{\mathrm{f}}={1.86}^{\circ }\mathrm{C}\cdot \mathrm{kg}/\mathrm{mol})$ What is the formula of the compound? What is the structure of the complex ion present? (Hints: ${\mathrm{Cr}}^{3+}$ is expected to be sixcoordinate, with ${\mathrm{NH}}_3$ and possibly ${\mathrm{I}}^{-}$ as ligands. The ${\mathrm{I}}^{-}$ ions will be the counterions if needed.)

There are three salts that contain complex ions of chromium and have the molecular formula ${\mathrm{CrCl}}_3\cdot 6{\mathrm{H}}_2\mathrm{O}$. Treating $0.27\mathrm{g}$ of the first salt with a strong dehydrating agent resulted in a mass loss of $0.036\mathrm{g}$. Treating $270\mathrm{mg}$ of the second salt with the same dehydrating agent resulted in a mass loss of $18\mathrm{mg}$. The third salt did not lose any mass when treated with the same dehydrating agent. Addition of excess aqueous silver nitrate to $100.0-\mathrm{mL}$ portions of $0.100M$ solutions of each salt resulted in the formation of different masses of silver chloride; one solution yielded 1430 $\mathrm{mg}\mathrm{AgCl};$ another, $2870\mathrm{mg}\mathrm{AgCl}$; the third, $4300\mathrm{mg}\mathrm{AgCl}$. Two of the salts are green and one is violet. Suggest probable structural formulas for these salts, defending your answer on the basis of the preceding observations. State which salt is most likely to be violet. Would a study of the magnetic properties of the salts be helpful in determining the structural formulas? Explain.