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Chapter 20: Problem 42

A voltaic cell consists of a strip of cadmium metal in a solution of \(\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}\) in one beaker, and in the other beaker a platinum electrode is immersed in a \(\mathrm{NaCl}\) solution, with \(\mathrm{Cl}_{2}\) gas bubbled around the electrode. A salt bridge connects the two beakers. (a) Which electrode serves as the anode and which as the cathode? (b) Does the Cd electrode gain or lose mass as the cell reaction proceeds? (c) Write the equation for the overall cell reaction. (d) What is the emf generated by the cell under standard conditions?

Short Answer

Expert verified
(a) Anode: Cadmium electrode; Cathode: Platinum electrode. (b) The Cd electrode loses mass as the cell reaction proceeds. (c) The overall cell reaction: \(Cd + Cl_2 \rightarrow Cd^{2+} + 2Cl^-\). (d) The emf generated by the cell under standard conditions is 1.763 V.

Step by step solution

01

Identify the half-reactions

Considering the given information, we can identify two half-reactions: (i) Cd in the cadmium electrode reacts with nitrate ions: \[Cd \rightarrow Cd^{2+} + 2e^-\] (ii) Cl2 gas reacts with chloride ions at the platinum electrode: \[Cl_2 + 2e^- \rightarrow 2Cl^-\]
02

Determine the direction of electron flow

To determine the direction of electron flow, we need to find the standard electrode potentials (E°) for each half-reaction. Consulting a table of standard reduction potentials, we get: (i) \(Cd^{2+} + 2e^- \rightarrow Cd\), \(E°_{Cd} = -0.403 V\) (ii) \(Cl_2 + 2e^- \rightarrow 2Cl^-\), \(E°_{Cl} = +1.36 V\) Since Cl2 has a higher reduction potential, the electrons will flow towards the chlorine half-cell, and thus the direction of the electron flow is from the cadmium electrode to the platinum electrode.
03

Write the net cell equation

Combine the two balanced half-reactions and cancel out the electrons to write the net cell equation: \[Cd + Cl_2 \rightarrow Cd^{2+} + 2Cl^-\]
04

Determine the anode and cathode

As the electrons flow from the cadmium electrode, it is the anode (oxidation takes place). The platinum electrode, where the reduction of Cl2 takes place, is the cathode. (a) Anode: Cadmium electrode; Cathode: Platinum electrode
05

Determine if the Cd electrode gains or loses mass

As the cell reaction proceeds, Cd metal is oxidized to Cd2+ ions, thereby losing mass. (b) The Cd electrode loses mass as the cell reaction proceeds.
06

Calculate the overall cell potential

Calculate the emf generated by the cell under standard conditions using the formula: \(E°_{cell} = E°_{cathode} - E°_{anode}\) \(E°_{cell} = 1.36 V - (-0.403 V) = 1.763 V\) (d) The emf generated by the cell under standard conditions is 1.763 V.

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Most popular questions from this chapter

(a) What happens to the emf of a battery as it is used? Why does this happen? (b) The AA-size and D-size alkaline batteries are both \(1.5-\mathrm{V}\) batteries that are based on the same electrode reactions. What is the major difference between the two batteries? What performance feature is most affected by this difference?

Gold exists in two common positive oxidation states, +1 and +3. The standard reduction potentials for these oxidation states are $$ \begin{aligned} \mathrm{Au}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Au}(s) & E_{\mathrm{red}}^{o}=+1.69 \mathrm{~V} \\ \mathrm{Au}^{3+}(a q)+3 \mathrm{e}^{-} \longrightarrow \mathrm{Au}(s) & E_{\mathrm{red}}^{\circ}=+1.50 \mathrm{~V} \end{aligned} $$ (a) Can you use these data to explain why gold does not tarnish in the air? (b) Suggest several substances that should be strong enough oxidizing agents to oxidize gold metal. (c) Miners obtain gold by soaking gold-containing ores in an aqueous solution of sodium cyanide. A very soluble complex ion of gold forms in the aqueous solution because of the redox reaction $$ \begin{aligned} 4 \mathrm{Au}(s)+8 \mathrm{NaCN}(a q)+& 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g) \longrightarrow \\ & 4 \mathrm{Na}\left[\mathrm{Au}(\mathrm{CN})_{2}\right](a q)+4 \mathrm{NaOH}(a q) \end{aligned} $$ What is being oxidized and what is being reduced in this reaction? (d) Gold miners then react the basic aqueous product solution from part (c) with Zn dust to get gold metal. Write a balanced redox reaction for this process. What is being oxidized, and what is being reduced?

(a) What is electrolysis? (b) Are electrolysis reactions thermodynamically spontaneous? Explain. (c) What process occurs at the anode in the electrolysis of molten NaCl? (d) Why is sodium metal not obtained when an aqueous solution of \(\mathrm{NaCl}\) undergoes electrolysis?

(a) Magnesium metal is used as a sacrificial anode to protect underground pipes from corrosion. Why is the magnesium referred to as a "sacrificial anode"? (b) Looking in Appendix \(\mathrm{E}\); suggest what metal the underground pipes could be made from in order for magnesium to be successful as a sacrificial anode.

Indicate whether each of the following statements is true or false: (a) If something is oxidized, it is formally losing electrons. (b) For the reaction \(\mathrm{Fe}^{3+}(a q)+\mathrm{Co}^{2+}(a q) \longrightarrow \mathrm{Fe}^{2+}(a q)+\) \(\mathrm{Co}^{3+}(a q), \mathrm{Fe}^{3+}(a q)\) is the reducing agent and \(\mathrm{Co}^{2+}(a q)\) is the oxidizing agent. (c) If there are no changes in the oxidation state of the reactants or products of a particular reaction, that reaction is not a redox reaction.
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