Chapter 22

Titanium is the seventh most abundant metal in the earth's crust. It is strong, lightweight, and resistant to corrosion; these properties lead to its use in aircraft engines. To obtain metallic titanium, ilmenite (FeTiOs), an ore of titanium, is first treated with sulfuric acid to form FesO, and \(\mathrm{Ti}\left(\mathrm{SO}_{4}\right)_{2}\). After separating these compounds, the latter substance is converted to \(\mathrm{TiO}_{2}\) in basic solution: \(\mathrm{FeTiO}_{3}(\mathrm{s})+3 \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \longrightarrow\) $$ \mathrm{Ti}^{4+}(\mathrm{aq})+4 \mathrm{OH}^{-}(\mathrm{aq}) \longrightarrow \mathrm{TiO}_{2}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{aq})+\mathrm{Ti}\left(\mathrm{SO}_{4}\right)_{2}(\mathrm{aq})+3 \mathrm{H}_{2} \mathrm{O}(\ell) $$ What volume of \(18.0 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) is required to react completely with \(1.00 \mathrm{kg}\) of ilmenite? What mass of \(\mathrm{TiO}_{2} \mathrm{can}\) theoretically be produced by this sequence of reactions?

A \(A\) 0.213-g sample of uranyl(VI) nitrate, UO,(NO,), is dissolved in \(20.0 \mathrm{mL}\) of \(1.0 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) and shaken with Zn. The zinc reduces the uranyl ion, \(\mathrm{UO}_{2}^{2+}\), to a uranium ion, U". To determine the value of \(n,\) this solution is titrated with KMnO_. Permanganate is reduced to Mn \(^{2+}\) and \(\mathrm{U}^{n+}\) is oxidized back to \(\mathrm{UO}_{2}^{2+}\) (a) In the titration, \(12.47 \mathrm{mL}\) of \(0.0173 \mathrm{M} \mathrm{KMnO}_{4}\) was required to reach the equivalence point. Use this information to determine the charge on the ion \(\mathrm{U}^{n+}\) (b) With the identity of \(U^{n+}\) now established, write a balanced net ionic equation for the reduction of \(\mathrm{UO}_{2}^{2+}\) by zinc (assume acidic conditions). (c) Write a balanced net ionic equation for the oxidation of \(\mathrm{U}^{n+}\) to \(\mathrm{UO}_{2}^{2+}\) by \(\mathrm{MnO}_{4}^{-}\) in acid.

A The transition metals form a class of compounds called metal carbonyls, an example of which is the teurahedral complex \(\mathrm{Ni}(\mathrm{CO})_{4}\). Given the following thermodynamic data: $$\begin{array}{lcc} \hline & \Delta H_{f}^{\circ}(\mathrm{kJ} / \mathrm{mol}) & \mathrm{S}^{\circ}(\mathrm{J} / \mathrm{K} \cdot \mathrm{mol}) \\ \hline \mathrm{Ni} & 0 & 29.87 \\ \mathrm{CO}(\mathrm{g}) & -110.525 & +197.674 \\ \mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{g}) & -602.9 & +410.6 \\ \hline \end{array}$$ (a) Calculate the equilibrium constant for the formation of \(\mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{g})\) from nickel metal and CO gas. (b) Is the reaction of \(\mathrm{Ni}(\mathrm{s})\) and \(\mathrm{CO}(\mathrm{g})\) product-or reactant-favored? (c) Is the reaction more or less product-favored at higher temperatures? How could this reaction be used in the purification of nickel metal?

An this question, we explore the differences between metal coordination by monodentate and bidentate ligands. Formation constants, \(K_{f},\) for \(\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}(\mathrm{aq})\) and \(\left[\mathrm{Ni}(\mathrm{en})_{3}\right]^{2+}(\mathrm{aq})\) are as follows: $$\begin{aligned} \mathrm{Ni}^{2+}(\mathrm{aq})+6 \mathrm{NH}_{3}(\mathrm{aq}) & \longrightarrow\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}(\mathrm{aq}) & & K_{f}=10^{8} \\ \mathrm{Ni}^{2+}(\mathrm{aq})+3 \mathrm{en}(\mathrm{aq}) & \longrightarrow\left[\mathrm{Ni}(\mathrm{en})_{3}\right]^{2+}(\mathrm{aq}) & & K_{f}=10^{18} \end{aligned}$$ The difference in \(K_{f}\) between these complexes indicates a higher thermodynamic stability for the chelated complex, caused by the chelate effect. Recall that \(K\) is related to the standard free energy of the reaction by \(\Delta G^{\circ}=-R T \ln K\) and \(\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ} .\) We know from experiment that \(\Delta H^{\circ}\) for the \(\mathrm{NH}_{3}\) reaction is \(-109 \mathrm{kJ} / \mathrm{mol},\) and \(\Delta H^{\circ}\) for the ethylenediamine reaction is \(-117 \mathrm{kJ} / \mathrm{mol}\). Is the difference in \(\Delta H^{\circ}\) sufficient to account for the \(10^{10}\) difference in \(K_{f}\) ? Comment on the role of entropy in the second reaction.