17.19: Problems

1. Balance the following chemical equations assuming that they occur in aqueous solution.

(a) \({Cu}^0+{Ag}^+\to {Cu}^{2+}+{Ag}^0\)

(b) \({Fe}^{2+}+{Cr}_2O^{2-}_7\to {Fe}^{3+}+{Cr}^{3+}\)

(c) \({Cr}^{2+}+{Cr}_2O^{2-}_7\to {Cr}^{3+}\)

(d) \({Cl}_2+{Br}^-\to {Cl}^-+{Br}_2\)

(e) \(ClO_3\to {Cl}^-+ClO^-_4\)

(f) \(I^-+{IO}^-_3\to I_2\)

(g) \(I^-+O_2\to I_2+{OH}^-\) (basic solution)

(h) \(H_2C_2O^{2-}_4+MnO^-_4\to {CO}_2+{Mn}^{2+}\)

(i) \({Fe}^{2+}+MnO^-_4\to {Fe}^{3+}+{Mn}^{2+}\)

(j) \(H_2O_2+MnO^-_4\to {Mn}^{2+}+O_2\)

(k) \(PbO_2+{Pb}^0+H_2SO_4\to {PbSO}_4\)

(l) \({Fe}^{2+}\to {Fe}^0+{Fe}^{3+}\)

(m) \({Cu}^{2+}+{Fe}^0\to {Cu}^0+{Fe}^{3+}\)

(n) \({Al}^0+{OH}^-\to H_2+Al{\left(OH\right)}^-_4\) (basic solution)

(o) \({Au}^0+{CN}^-+O_2\to Au{\left(CN\right)}^-_4\) (basic solution)

(p) \({Cu}^0+{HNO}_3\to {Cu}^{2+}+NO_2\)

(q) \({Al}^0+{Fe}_2O_3\to {Al}_2O_3+{Fe}^0\)

(r) \(I^-+H_2O_2\to I_2+{OH}^-\) (basic solution)

(s) \(HFeO^-_4+{Mn}^{2+}\to {Fe}^{3+}+{MnO}_2\)

(t) \({Fe}^{2+}+S_2O^{2-}_8\to {Fe}^{3+}+SO^{2-}_4\)

(u) \({Cu}^++O_2\to {Cu}^{2+}+{OH}^-\) (basic solution)

2. Calculate the equilibrium constant,\(K_a\), for the reaction \({Cu}^0+2{Ag}^+\to {Cu}^{2+}+2{Ag}^0\). An excess of clean copper wire is placed in a \({10}^{-1}\ \underline{\mathrm{M}}\) silver nitrate solution. Assuming that molarities adequately approximate the activities of the ions, find the equilibrium concentrations of \({Ag}^+\) and \({Cu}^{2+}\).

3. The standard potentials for reduction of \({Fe}^{2+}\) and \({Fe}^{3+}\) to \({Fe}^0\) are

\[{Fe}^{2+}+2e^-\to {Fe}^0 {\mathcal{E}}^o=-0.447\ \mathrm{v} \nonumber \] \[{Fe}^{3+}+3e^-\to {Fe}^0 {\mathcal{E}}^o=-0.037\ \mathrm{v} \nonumber \]

(a) Find the standard potential for the disproportionation of \({Fe}^{2+}\) to \({Fe}^{3+}\) and \({Fe}^0\): \(\ \ \ {Fe}^{2+}\to {{Fe}^0+Fe}^{3+}\).

(b) Find the standard half-cell potential for the reduction of \({Fe}^{3+}\) to \({Fe}^{2+}\): \({Fe}^{3+}+e^-\to {Fe}^{2+}\).

4. The standard potential for reduction of tris-ethylenediamineruthenium (III) to tris-ethylenediamineruthenium (II) is

\[{\left[Ru{\left(en\right)}_3\right]}^{3+}+e^-\to {\left[Ru{\left(en\right)}_3\right]}^{2+} {\mathcal{E}}^o=+0.210\ \mathrm{v} \nonumber \]

Half-cell potential data are given below for several oxidants. Which of them can oxidize \({\left[Ru{\left(en\right)}_3\right]}^{2+}\) to \({\left[Ru{\left(en\right)}_3\right]}^{3+}\) in acidic (\(\left[H^+\right]\approx {\tilde{a}}_{H^+}={10}^{-1}\)) aqueous solution?

(a) \(UO^{2+}_2+e^-\to UO^+_2\) \({\mathcal{E}}^o=+0.062\ \mathrm{v}\)

(b) \({\left[Ru{\left(NH_3\right)}_6\right]}^{3+}+e^-\to {\left[Ru{\left(NH_3\right)}_6\right]}^{2+}\) \[{\mathcal{E}}^o=+0.10\ \mathrm{v} \nonumber \] (c) \({Cu}^{2+}+e^-\to {Cu}^+\) \({\mathcal{E}}^o=+0.153\ \mathrm{v}\)

(d) \(AgCl+e^-\to {Ag}^0+{Cl}^-\) \({\mathcal{E}}^o=+0.222\ \mathrm{v}\)

(e) \({Hg}_2{Cl}_2+2e^-\to 2{Hg}^0+2{Cl}^-\) \[{\mathcal{E}}^o=+0.268\ \mathrm{v} \nonumber \] (f) \(AgCN+e^-\to {Ag}^0+{CN}^-\) \({\mathcal{E}}^o=-0.017\ \mathrm{v}\)

(g) \(SnO_2+4H^++4e^-\to {Sn}^0+2H_2O\) \[{\mathcal{E}}^o=-0.117\ \mathrm{v} \nonumber \]

5. An electrochemical cell is constructed in which one half cell is a standard hydrogen electrode and the other is a hydrogen electrode immersed in a solution of \(pH=7\) \(\left(\left[H^+\right]\approx {\tilde{a}}_{H^+}={10}^{-7}\right)\). What is the potential difference between the terminals of the cell? What chemical change occurs in this cell?

6. The standard half-cell potential for the reduction of oxygen gas at an inert electrode (like platinum metal) is

\[O_2+4H^++4e^-\to 2H_2O {\mathcal{E}}^o=+1.229\ \mathrm{v} \nonumber \]

An electrochemical cell is constructed in which one half cell is a standard hydrogen electrode and the other cell is a piece of platinum metal, immersed in a \(1\ \underline{M}\) solution of \(HClO_4\), which is continuously in contact with bubbles of oxygen gas at a pressure of \(1\) bar.

(a) What is the potential difference between the terminals of the cell? What chemical change occurs in this cell?

(b) The \(1\ \underline{M}\) \(HClO_4\) solution in part (a) is replaced with pure water \(\left(\left[H^+\right]\approx {\tilde{a}}_{H^+}={10}^{-7}\right)\). What is the potential difference between the terminals of this cell?

(c) The \(1\ \underline{M}\) \(HClO_4\) solution in part (a) is replaced with \(1\ \underline{M}\) \(NaOH\) \(\left(\left[H^+\right]\approx {\tilde{a}}_{H^+}={10}^{-14}\right)\). What is the potential difference between the terminals of this cell?

7. A variable electrical potential source is introduced into the external circuit of the cell in part (a) of problem

6. The negative terminal of the potential source is connected to the oxygen electrode and the positive terminal of the potential source is connected to the standard hydrogen electrode. If the applied electrical potential is 1.3 v, what chemical change occurs? What is the minimum electrical potential that must be applied to electrolyze water if the oxygen electrode contains a \(1\ \underline{M}\) \(HClO_4\) solution? A neutral (\(pH=7\)) solution? A \(1\ \underline{M}\) \(NaOH\) solution?

8. Two platinum electrodes are immersed in \(1\ \underline{M}\) \(HClO_4\). What potential difference must be applied between these electrodes in order to electrolyze water? (Assume that \(P_{O_2}=1\ \mathrm{bar}\) and \(P_{H_2}=1\ \mathrm{bar}\) at their respective electrodes, as will be the case as soon as a few bubbles of gas have accumulated at each electrode.) What potential difference is required if the electrodes are immersed in pure water? In \(1\ \underline{M}\) \(NaOH\)?