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Chapter 20: Problem 4

Given that \(E_{\text {cell }}^{\circ}=3.20 \mathrm{V}\) for the reaction $$2 \mathrm{Na}(\mathrm{in} \mathrm{Hg})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{Na}^{+}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})$$ What is \(E^{\circ}\) for the reduction \(2 \mathrm{Na}^{+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow\) \(2 \mathrm{Na}(\text { in } \mathrm{Hg}) ?\)

Short Answer

Expert verified
The \(E^{\circ}\) for the reduction \(2 \mathrm{Na}^{+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Na}(\text { in } \mathrm{Hg})\) will be \(-3.20 \mathrm{V}\).

Step by step solution

01

Recognize the Given Cell Reaction

The given cell reaction involving transformation of Na in mercury to \(Na^{+}\) in solution is: \[2\mathrm{Na}(\text {in} \mathrm{Hg})+\mathrm{Cl}_{2}(\text {g})\longrightarrow 2 \mathrm{Na}^{+}(\mathrm{aq})+2\mathrm{Cl}^{-}(\mathrm{aq})\] The provided \(E_{\text {cell }}^{\circ}\) for this reaction is \(3.20 \mathrm{V}\).
02

Determine the Correct Reaction

The reaction for which we want to find the standard cell potential (\(E^{\circ}\)) is the reduction of sodium ions to sodium metal: \[2 \mathrm{Na}^{+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Na}(\text { in } \mathrm{Hg})\] It’s the reverse of one half of the given cell reaction.
03

Apply the Concept of Cell Reversal

In electrochemistry, when a cell reaction is reversed, the polarity of the cell's electromotive force (\(E_{\text {cell }}^{\circ}\)) also reverses. This is due to the fact the reverse cell reaction now involves reduction of Na+ ions to Na metal, whereas in the given cell reaction, Na metal is being oxidized to Na+ ions. Hence, \(E^{\circ} = -E_{\text {cell }}^{\circ}\) for the reduction of \(2 \mathrm{Na}^{+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Na}(\text { in } \mathrm{Hg})\).

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Most popular questions from this chapter

For the reaction \(\mathrm{Zn}(\mathrm{s})+\mathrm{H}^{+}(\mathrm{aq})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) \longrightarrow\) \(\mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1)+\mathrm{NO}(\mathrm{g}),\) describe the voltaic cell in which it occurs, label the anode and cathode,use a table of standard electrode potentials to evaluate \(E_{\text {cell }}^{\circ},\) and balance the equation for the cell reaction.

Consider the reaction \(\operatorname{Co}(\mathrm{s})+\mathrm{Ni}^{2+}(\mathrm{aq}) \longrightarrow\) \(\mathrm{Co}^{2+}(\mathrm{aq})+\mathrm{Ni}(\mathrm{s}), \quad\) with \(\quad E_{\mathrm{cell}}^{\circ}=0.02 \mathrm{V} . \quad\) If \(\quad \mathrm{Co}(\mathrm{s}) \quad\) is added to a solution with \(\left[\mathrm{Ni}^{2+}\right]=1 \mathrm{M},\) should the reaction go to completion? Explain.

Briefly describe each of the following ideas, methods, or devices: (a) salt bridge; (b) standard hydrogen electrode (SHE); (c) cathodic protection; (d) fuel cell.

When deciding whether a particular reaction corresponds to a cell with a positive standard cell potential, which of the following thermodynamic properties would you use to get your answer without performing any calculations? Which would you not use? Explain. (a) \(\Delta G^{\circ} ;\) (b) \(\Delta S^{\circ} ;\) (c) \(\Delta H^{\circ} ;\) (d) \(\Delta U^{\circ} ;\) (e) \(K\).

If a lead storage battery is charged at too high a voltage, gases are produced at each electrode. (It is possible to recharge a lead-storage battery only because of the high overpotential for gas formation on the electrodes.) (a) What are these gases? (b) Write a cell reaction to describe their formation.
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