Problem 1
Balance the following half-equations by finding the number, \(z,\) of electrons: (a) \(\mathrm{Cr}^{2+}+z \mathrm{e}^{-}=\mathrm{Cr}\) (b) \(\left[\mathrm{Cr}_{2} \mathrm{O}_{7}\right]^{2-}+14 \mathrm{H}^{+}+\mathrm{ze}^{-} \rightleftharpoons 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_{2} \mathrm{O}\) (c) \(\left[\mathrm{S}_{4} \mathrm{O}_{6}\right]^{2-}+\mathrm{ze}^{-}=2\left[\mathrm{S}_{2} \mathrm{O}_{3}\right]^{2-}\) (d) \(\mathrm{O}_{2}+4 \mathrm{H}^{+}+\mathrm{ze}^{-}=2 \mathrm{H}_{2} \mathrm{O}\) (e) \(\left[\mathrm{BrO}_{3}\right]^{-}+3 \mathrm{H}_{2} \mathrm{O}+\mathrm{ze}^{-} \rightleftharpoons \mathrm{Br}^{-}+6[\mathrm{OH}]^{-}\) \((f) P b O_{2}+4 H^{+}+\left[S O_{4}\right]^{2-}+z e^{-}=P b S O_{4}+2 H_{2} O\)
Problem 2
For the reaction:\\[ 2 \mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{Zn}(\mathrm{s}) \rightarrow 2 \mathrm{Ag}(\mathrm{s})+\mathrm{Zn}^{2+}(\mathrm{aq}) \\] \(E_{\text {cell }}^{\circ}=1.56 \mathrm{V} .\) Calculate \(\Delta G^{\circ}\) per mole of \(\mathrm{Ag}^{+}\)
Problem 3
What information can you obtain from the following cell diagram? $$\begin{aligned} \mathrm{Pt}\left[\mathrm{H}_{2}(\mathrm{g}, 1 \mathrm{bar})\right] | 2 \mathrm{H}^{+}\left(\mathrm{aq}, 1.0 \mathrm{mol} \mathrm{dm}^{-3}\right) & \\\ & \vdots \mathrm{Ce}^{4+}(\mathrm{aq}), \mathrm{Ce}^{3+}(\mathrm{aq}) | \mathrm{Pt} \end{aligned}$$
Problem 16
Suggest what products are discharged at the anode and cathode during the electrolysis of (a) molten \(\mathrm{KBr} ;(\mathrm{b})\) fused \(\mathrm{CaCl}_{2} ;(\mathrm{c})\) dilute aqueous \(\mathrm{NaCl}\) (d) concentrated aqueous NaCl (brine); (e) aqueous \(\mathrm{CuSO}_{4}\) using Cu electrodes; (f) dilute \(\mathrm{H}_{2} \mathrm{SO}_{4}\) using Pt electrodes.
Problem 18
The manufacture of \(\mathrm{Al}\) by electrolysis of fused \(\mathrm{Al}_{2} \mathrm{O}_{3}\) and \(\mathrm{K}_{3}\left[\mathrm{AlF}_{6}\right]\) demands especially large amounts of electricity, and aluminium refineries are often associated with hydroelectric schemes. Rationalize why this is so.
Problem 22
Discuss the following statements and data. (a) In dilute aqueous solution, \(\left[\mathrm{ClO}_{4}\right]^{-}\) is very difficult to reduce despite the values of \(E^{\circ}\) for the following half- cells at pH 0 : $$\begin{aligned} \left[\mathrm{ClO}_{4}\right]^{-}(\mathrm{aq})+2 \mathrm{H}^{+}(\mathrm{aq})+2 \mathrm{e}^{-} &=\\\ \left[\mathrm{ClO}_{3}\right]^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) & E^{0}=+1.19 \mathrm{V} \\ \left[\mathrm{ClO}_{4}\right]^{-}(\mathrm{aq})+8 \mathrm{H}^{+}(\mathrm{aq})+8 \mathrm{e}^{-} \rightleftharpoons &=\\\\\mathrm{Cl}^{-}(\mathrm{aq})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) & E^{\circ}=+1.24 \mathrm{V}\end{aligned}$$ (b) Lead-acid batteries involve the half-cells: $$\begin{aligned} \mathrm{PbSO}_{4}(\mathrm{s})+2 \mathrm{e}^{-} &=\\\ \mathrm{Pb}(\mathrm{s})+\left[\mathrm{SO}_{4}\right]^{2-}(\mathrm{aq}) & E^{0}=-0.36 \mathrm{V} \\ \mathrm{PbO}_{2}(\mathrm{s})+4 \mathrm{H}^{+}(\mathrm{aq})+\left[\mathrm{SO}_{4}\right]^{2-}(\mathrm{aq})+2 \mathrm{e}^{-} &=\\\ \mathrm{PbSO}_{4}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(1) & E^{0}=+1.69 \mathrm{V} \end{aligned}$$ Batteries can be recharged by reversing the cell reaction.
