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Chapter 20: Problem 35

Using standard reduction potentials (Appendix E), calculate the standard emf for each of the following reactions: (a) \(\mathrm{Cl}_{2}(g)+2 \mathrm{I}^{-}(a q) \longrightarrow 2 \mathrm{Cl}^{-}(a q)+\mathrm{I}_{2}(s)\) (b) \(\mathrm{Ni}(s)+2 \mathrm{Ce}^{4+}(a q) \longrightarrow \mathrm{Ni}^{2+}(a q)+2 \mathrm{Ce}^{3+}(a q)\) (c) \(\mathrm{Fe}(s)+2 \mathrm{Fe}^{3+}(a q) \longrightarrow 3 \mathrm{Fe}^{2+}(a q)\) (d) \(2 \mathrm{Al}^{3+}(a q)+3 \mathrm{Ca}(s) \longrightarrow 2 \mathrm{Al}(s)+3 \mathrm{Ca}^{2+}(a q)\)

Short Answer

Expert verified
The standard emf for the given reactions are: (a) +1.90 V (b) +1.98 V (c) +1.21 V (d) +4.53 V

Step by step solution

01

Identify the half-reactions

The given reaction can be divided into two half-reactions: Oxidation: 2\(\mathrm{I}^{-}(a q) \longrightarrow \mathrm{I}_{2}(s) + 2e^-\) Reduction: \(\mathrm{Cl}_{2}(g) + 2e^- \longrightarrow 2\mathrm{Cl}^{-}(a q)\)
02

Find the standard reduction potentials

Using Appendix E, we find the standard reduction potentials for each half-reaction: E掳(I鈦� 鈫� I鈧� + 2e鈦�) = -0.54 V E掳(Cl鈧� + 2e鈦� 鈫� 2Cl鈦�) = +1.36 V
03

Calculate the standard emf

Now we use the Nernst equation to find the standard emf of the cell for reaction (a): \(E_{cell} = E_{cathode} - E_{anode} = (+1.36 \ \text{V}) - (-0.54 \ \text{V}) = +1.90 \ \text{V}\) (b) $\mathrm{Ni}(s)+2 \mathrm{Ce}^{4+}(a q) \longrightarrow \mathrm{Ni}^{2+}(a q)+2 \mathrm{Ce}^{3+}(a q)$
04

Identify the half-reactions

The given reaction can be divided into two half-reactions: Oxidation: \(\mathrm{Ni}(s) \longrightarrow \mathrm{Ni}^{2+}(a q) + 2e^-\) Reduction: \(2\mathrm{Ce}^{4+}(a q) + 2e^- \longrightarrow 2\mathrm{Ce}^{3+}(a q)\)
05

Find the standard reduction potentials

Using Appendix E, we find the standard reduction potentials for each half-reaction: E掳(Ni 鈫� Ni虏鈦� + 2e鈦�) = -0.26 V E掳(2Ce鈦粹伜 + 2e鈦� 鈫� 2Ce鲁鈦�) = +1.72 V
06

Calculate the standard emf

Now we use the Nernst equation to find the standard emf of the cell for reaction (b): \(E_{cell} = E_{cathode} - E_{anode} = (+1.72 \ \text{V}) - (-0.26 \ \text{V}) = +1.98 \ \text{V}\) (c) $\mathrm{Fe}(s)+2 \mathrm{Fe}^{3+}(a q) \longrightarrow 3 \mathrm{Fe}^{2+}(a q)$
07

Identify the half-reactions

The given reaction can be divided into two half-reactions: Oxidation: \(\mathrm{Fe}(s) \longrightarrow \mathrm{Fe}^{2+}(a q) + 2e^-\) Reduction: \(2\mathrm{Fe}^{3+}(a q) + 2e^- \longrightarrow 2\mathrm{Fe}^{2+}(a q)\)
08

Find the standard reduction potentials

Using Appendix E, we find the standard reduction potentials for each half-reaction: E掳(Fe 鈫� Fe虏鈦� + 2e鈦�) = -0.44 V E掳(2Fe鲁鈦� + 2e鈦� 鈫� 2Fe虏鈦�) = +0.77 V
09

Calculate the standard emf

Now we use the Nernst equation to find the standard emf of the cell for reaction (c): \(E_{cell} = E_{cathode} - E_{anode} = (+0.77 \ \text{V}) - (-0.44 \ \text{V}) = +1.21 \ \text{V}\) (d) \(2 \mathrm{Al}^{3+}(a q)+3 \mathrm{Ca}(s) \longrightarrow 2\mathrm{Al}(s)+3 \mathrm{Ca}^{2+}(a q)\)
10

Identify the half-reactions

The given reaction can be divided into two half-reactions: Oxidation: \(3 \mathrm{Ca}(s) \longrightarrow 3 \mathrm{Ca}^{2+}(a q) + 6e^-\) Reduction: \(2\mathrm{Al}^{3+}(a q) + 6e^- \longrightarrow 2\mathrm{Al}(s)\)
11

Find the standard reduction potentials

Using Appendix E, we find the standard reduction potentials for each half-reaction: E掳(3Ca 鈫� 3Ca虏鈦� + 6e鈦�) = -2.87 V E掳(2Al鲁鈦� + 6e鈦� 鈫� 2Al) = +1.66 V
12

Calculate the standard emf

Now we use the Nernst equation to find the standard emf of the cell for reaction (d): \(E_{cell} = E_{cathode} - E_{anode} = (+1.66 \ \text{V}) - (-2.87 \ \text{V}) = +4.53 \ \text{V}\)

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Most popular questions from this chapter

This oxidation-reduction reaction in acidic solution is spontaneous: \(5 \mathrm{Fe}^{2+}(a q)+\mathrm{MnO}_{4}^{-}(a q)+8 \mathrm{H}^{+}(a q)-\rightarrow\) \(5 \mathrm{Fe}^{3+}(a q)+\mathrm{Mn}^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l)\) A solution containing \(\mathrm{KMnO}_{4}\) and \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is poured into one beaker, and a solution of \(\mathrm{FeSO}_{4}\) is poured into another. A salt bridge is used to join the beakers. A platinum foil is placed in each solution, and a wire that passes through a voltmeter connects the two solutions. (a) Sketch the cell, indicating the anode and the cathode, the direction of electron movement through the external circuit, and the direction of ion migrations through the solutions. (b) Sketch the process that occurs at the atomic level at the surface of the anode. (c) Calculate the emf of the cell under standard conditions. (d) Calculate the emf of the cell at \(298 \mathrm{~K}\) when the concentrations are the following: \(\mathrm{pH}=0.0, \quad\left[\mathrm{Fe}^{2+}\right]=0.10 \mathrm{M}, \quad\left[\mathrm{MnO}_{4}^{-}\right]=1.50 \mathrm{M}\) \(\left[\mathrm{Fe}^{3+}\right]=2.5 \times 10^{-4} \mathrm{M},\left[\mathrm{Mn}^{2+}\right]=0.001 \mathrm{M}\)

Predict whether the following reactions will be spontaneous in acidic solution under standard conditions: (a) oxidation of Sn to \(\mathrm{Sn}^{2+}\) by \(\mathrm{I}_{2}\) (to form \(\left.\mathrm{I}^{-}\right)\), (b) reduction of \(\mathrm{Ni}^{2+}\) to \(\mathrm{Ni}\) by \(\mathrm{I}^{-}\left(\right.\) to form \(\left.\mathrm{I}_{2}\right),(\mathrm{c})\) reduction of \(\mathrm{Ce}^{4+}\) to \(\mathrm{Ce}^{3+}\) by \(\mathrm{H}_{2} \mathrm{O}_{2}\), (d) reduction of \(\mathrm{Cu}^{2+}\) to \(\mathrm{Cu}\) by \(\mathrm{Sn}^{2+}\) (to form \(\mathrm{Sn}^{4+}\) ).

(a) \(\mathrm{A} \mathrm{Cr}^{3+}(a q)\) solution is electrolyzed, using a current of \(7.60 \mathrm{~A}\). What mass of \(\mathrm{Cr}(s)\) is plated out after \(2.00\) days? (b) What amperage is required to plate out \(0.250 \mathrm{~mol} \mathrm{Cr}\) from a \(\mathrm{Cr}^{3+}\) solution in a period of \(8.00 \mathrm{~h}\) ?

(a) What is the difference between a battery and a fuel cell? (b) Can the "fuel" of a fuel cell be a solid? Explain.

Hydrazine \(\left(\mathrm{N}_{2} \mathrm{H}_{4}\right)\) and dinitrogen tetroxide \(\left(\mathrm{N}_{2} \mathrm{O}_{4}\right)\) form a self-igniting mixture that has been used as a rocket propellant. The reaction products are \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). (a) Write a balanced chemical equation for this reaction. (b) What is being oxidized, and what is being reduced? (c) Which substance serves as the reducing agent, and which as the oxidizing agent?
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