Chapter 21

Use the following half-reactions to write three spontaneous reactions, calculate \(E_{\text {cell }}^{\circ}\) for each reaction, and rank the strengths of the oxidizing and reducing agents: (1) \(\mathrm{Au}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Au}(s)\) \(E^{\circ}=1.69 \mathrm{~V}\) (2) \(\mathrm{N}_{2} \mathrm{O}(g)+2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \quad E^{\circ}=1.77 \mathrm{~V}\) (3) \(\mathrm{Cr}^{3+}(a q)+3 \mathrm{e}^{-} \longrightarrow \mathrm{Cr}(s) \quad E^{\circ}=-0.74 \mathrm{~V}\)

Use the following half-reactions to write three spontaneous reactions, calculate \(E_{\text {cell }}^{\circ}\) for each reaction, and rank the strengths of the oxidizing and reducing agents: (1) \(2 \mathrm{HClO}(a q)+2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(I)\) \(E^{\circ}=1.63 \mathrm{~V}\) (2) \(\mathrm{Pt}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pt}(s) \quad E^{\circ}=1.20 \mathrm{~V}\) (3) \(\mathrm{PbSO}_{4}(s)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pb}(s)+\mathrm{SO}_{4}^{2-}(a q) \quad E^{\circ}=-0.31 \mathrm{~V}\)

When metal \(\mathrm{A}\) is placed in a solution of a salt of metal \(\mathrm{B}\), the surface of metal A changes color. When metal \(\mathrm{B}\) is placed in acid solution, gas bubbles form on the surface of the metal. When metal \(\mathrm{A}\) is placed in a solution of a salt of metal \(\mathrm{C},\) no change is observed in the solution or on the surface of metal A. (a) Will metal C cause formation of \(\mathrm{H}_{2}\) when placed in acid solution? (b) Rank metals \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C}\) in order of decreasing reducing strength.

(a) How do the relative magnitudes of \(Q\) and \(K\) relate to the signs of \(\Delta G\) and \(E_{\text {cell }} ?\) Explain. (b) Can a cell do work when \(Q / K>1\) or \(Q / K<1 ?\) Explain. 21.53 A voltaic cell consists of \(\mathrm{A} / \mathrm{A}^{+}\) and \(\mathrm{B} / \mathrm{B}^{+}\) half-cells, where A and \(B\) are metals and the A electrode is negative. The initial \(\left[\mathrm{A}^{+}\right] /\left[\mathrm{B}^{+}\right]\) is such that \(E_{\text {cell }}>E_{\text {cell }}^{\circ}\) (a) How do \(\left[\mathrm{A}^{+}\right]\) and \(\left[\mathrm{B}^{+}\right]\) change as the cell operates? (b) How does \(E_{\text {cell }}\) change as the cell operates? (c) What is \(\left[\mathrm{A}^{+}\right] /\left[\mathrm{B}^{+}\right]\) when \(E_{\text {cell }}=E_{\text {cell }}^{\circ} ?\) Explain. (d) Is it possible for \(E_{\text {cell }}\) to be less than \(E_{\text {cell }}^{\circ} ?\) Explain.

A voltaic cell consists of \(\mathrm{A} / \mathrm{A}^{+}\) and \(\mathrm{B} / \mathrm{B}^{+}\) half-cells, where A and \(B\) are metals and the A electrode is negative. The initial \(\left[\mathrm{A}^{+}\right] /\left[\mathrm{B}^{+}\right]\) is such that \(E_{\text {cell }}>E_{\text {cell }}^{\circ}\) (a) How do \(\left[\mathrm{A}^{+}\right]\) and \(\left[\mathrm{B}^{+}\right]\) change as the cell operates? (b) How does \(E_{\text {cell }}\) change as the cell operates? (c) What is \(\left[\mathrm{A}^{+}\right] /\left[\mathrm{B}^{+}\right]\) when \(E_{\text {cell }}=E_{\text {cell }}^{\circ} ?\) Explain. (d) Is it possible for \(E_{\text {cell to be less than } E_{\text {cell }}^{\circ} \text { ? Explain. }}\)

What are \(E_{\text {cell }}^{\circ}\) and \(\Delta G^{\circ}\) of a redox reaction at \(25^{\circ} \mathrm{C}\) for which \(n=1\) and \(K=5.0 \times 10^{4} ?\)

What are \(E_{\text {cell }}^{\circ}\) and \(\Delta G^{\circ}\) of a redox reaction at \(25^{\circ} \mathrm{C}\) for which \(n=1\) and \(K=5.0 \times 10^{-6} ?\)

What are \(E_{\text {cell }}^{\circ}\) and \(\Delta G^{\circ}\) of a redox reaction at \(25^{\circ} \mathrm{C}\) for which \(n=2\) and \(K=65 ?\)

What are \(E_{\text {cell }}^{\circ}\) and \(\Delta G^{\circ}\) of a redox reaction at \(25^{\circ} \mathrm{C}\) for which \(n=2\) and \(K=0.065 ?\)

A voltaic cell consists of an \(\mathrm{Mn} / \mathrm{Mn}^{2+}\) half-cell and a \(\mathrm{Pb} / \mathrm{Pb}^{2+}\) half-cell. Calculate \(\left[\mathrm{Pb}^{2+}\right]\) when \(\left[\mathrm{Mn}^{2+}\right]\) is \(1.4 M\) and \(E_{\text {cell }}\) is \(0.44 \mathrm{~V}\).