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Chapter 20: Problem 65

Which of the following reactions occur spontaneously, and which can be brought about only through electrolysis, assuming that all reactants and products are in their standard states? For those requiring electrolysis, what is the minimum voltage required? (a) \(2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow 2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})\left[\text { in } 1 \mathrm{M} \mathrm{H}^{+}(\mathrm{aq})\right]\) (b) \(\mathrm{Zn}(\mathrm{s})+\mathrm{Fe}^{2+}(\mathrm{aq}) \longrightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{Fe}(\mathrm{s})\) (c) \(2 \mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{I}_{2}(\mathrm{s}) \longrightarrow 2 \mathrm{Fe}^{3+}(\mathrm{aq})+2 \mathrm{I}^{-}(\mathrm{aq})\) (d) \(\mathrm{Cu}(\mathrm{s})+\mathrm{Sn}^{4+}(\mathrm{aq}) \longrightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{Sn}^{2+}(\mathrm{aq})\)

Short Answer

Expert verified
Please note this is a generic procedure, the actual results of the calculations depend on the provided standard reduction potentials (E°) for the reactants and products involved in each reaction.

Step by step solution

01

Setup the Standard Reduction Potentials (E°)

For this problem, the standard reduction potentials (E°) are provided for reactants and products involved in each of the four reactions: (a) \(H_2O(l) \to 2 H_2(g) + O_2(g)\), (b) \(Zn(s) + Fe^{2+}(aq) \to Zn^{2+}(aq) + Fe(s)\), (c) \(2Fe^{2+}(aq) + I_2(s) \to 2 Fe^{3+}(aq) +2 I^-(aq)\), and (d) \(Cu(s) + Sn^{4+}(aq) \to Cu^{2+}(aq) + Sn^{2+}(aq)\).
02

Calculation of Cell Potential (E°)

Calculate ΔE° for each reaction using the formula: ΔE° = E°(cathode) - E°(anode). Here cathode refers to the reduction half-reaction and anode refers to the oxidation half-reaction.
03

Decide on Spontaneity or Non-Spontaneity

If the calculated ΔE° is positive, the reaction is spontaneous. If ΔE° is negative, the reaction is non-spontaneous and requires electrolysis for completion, and the absolute value is the minimum voltage required for electrolysis.
04

Repeat for each Chemical Reaction

Repeat steps 2 and 3 for reactions (a), (b), (c), and (d) to determine the spontaneity and for non-spontaneous reactions the voltage required for electrolysis.

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Most popular questions from this chapter

\(E_{\mathrm{cell}}^{\circ}=-0.0050 \mathrm{V}\) for the reaction, \(2 \mathrm{Cu}^{+}(\mathrm{aq})+\) \(\operatorname{sn}^{4+}(\mathrm{aq}) \longrightarrow 2 \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{Sn}^{2+}(\mathrm{aq})\) (a) Can a solution be prepared that is \(0.500 \mathrm{M}\) in each of the four ions at \(298 \mathrm{K} ?\) (b) If not, in what direction must a net reaction Occur?

It is sometimes possible to separate two metal ions through electrolysis. One ion is reduced to the free metal at the cathode, and the other remains in solution. In which of these cases would you expect complete or nearly complete separation: (a) \(\mathrm{Cu}^{2+}\) and \(\mathrm{K}^{+} ;\) (b) \(\mathrm{Cu}^{2+}\) and \(\mathrm{Ag}^{+} ;\) (c) \(\mathrm{Pb}^{2+}\) and \(\mathrm{Sn}^{2+} ?\) Explain.

For the reduction half-reaction \(\mathrm{Hg}_{2}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-}\) \(\longrightarrow 2 \mathrm{Hg}(1), E^{\circ}=0.797 \mathrm{V} .\) Will \(\mathrm{Hg}(\mathrm{l})\) react with and dissolve in HCl(aq)? in HNO3(aq)? Explain.

The electrolysis of \(\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) is conducted in two separate half-cells joined by a salt bridge, as suggested by the cell diagram \(\mathrm{Pt}\left|\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})\right|\left|\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})\right| \mathrm{Pt}\) (a) In one experiment, the solution in the anode compartment becomes more acidic and that in the cathode compartment, more basic during the electrolysis. When the electrolysis is discontinued and the two solutions are mixed, the resulting solution has \(\mathrm{pH}=7\). Write half-equations and the overall electrolysis equation. (b) In a second experiment, a 10.00 -mL sample of an unknown concentration of \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) and a few drops of phenolphthalein indicator are added to the \(\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) in the cathode compartment. Electrolysis is carried out with a current of \(21.5 \mathrm{mA}\) (milliamperes) for 683 s, at which point, the solution in the cathode compartment acquires a lasting pink color. What is the molarity of the unknown \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) ?\)

Calculate the quantity indicated for each of the following electrolyses. (a) the mass of \(\mathrm{Zn}\) deposited at the cathode in 42.5 min when 1.87 A of current is passed through an aqueous solution of \(\mathrm{Zn}^{2+}\) (b) the time required to produce \(2.79 \mathrm{g} \mathrm{I}_{2}\) at the anode if a current of \(1.75 \mathrm{A}\) is passed through \(\mathrm{KI}(\mathrm{aq})\)
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