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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 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
The anode is the cadmium electrode, and the cathode is the platinum electrode. The Cd electrode loses mass as the cell reaction proceeds. The overall cell reaction is \( Cd + Cl_2 \rightarrow Cd^{2+} + 2Cl^-\). The emf generated by the cell under standard conditions is +1.76V.

Step by step solution

01

(Step 1: Determine Half-Reactions)

We need to identify the two half-reactions occurring in the cell. In the first beaker, we have the cadmium half-reaction, which can be written as: \( Cd^{2+} + 2e^- \leftrightarrow Cd \) In the second beaker, we have the chlorine half-reaction: \( Cl_2 + 2e^- \leftrightarrow 2Cl^- \)
02

(Step 2: Determine the Anode and Cathode)

Recall that the anode is the electrode where oxidation occurs, whereas the cathode is the electrode where reduction occurs. We need to determine which of the two half-reactions is the oxidation half-reaction and which one is the reduction half-reaction. As a general rule, half-reactions with a more positive electrode potential (or reduction potential) will proceed as reductions in an electrochemical cell. For this problem, standard electrode potentials must be consulted (often available in a textbook or online references). We see that the electrode potential for the Cd half-reaction is \( -0.40V \) and for the Cl half-reaction is \( +1.36V \). Therefore, the Cl half-reaction will proceed as a reduction, making the platinum electrode the cathode, and the Cd half-reaction will proceed as an oxidation, making the cadmium electrode the anode.
03

(Step 3: Determine whether the Cd electrode gains or loses mass)

Since the Cd half-reaction is an oxidation, the Cd metal will lose electrons and turn into \( Cd^{2+} \) ions. As a result, the Cd electrode will lose mass as the cell reaction proceeds.
04

(Step 4: Write the overall cell reaction)

Now that we have the anode and cathode half-reactions, we can combine them to find the overall cell reaction. At the anode (oxidation), the Cd half-reaction can be written as: \( Cd \rightarrow Cd^{2+} + 2e^- \) (oxidation half-reaction) At the cathode (reduction), the Cl half-reaction can be written as: \( Cl_2 + 2e^- \rightarrow 2Cl^- \) (reduction half-reaction) Adding the two half-reactions together gives the overall cell reaction: \( Cd + Cl_2 \rightarrow Cd^{2+} + 2Cl^- \)
05

(Step 5: Determine the cell potential (emf) under standard conditions)

To calculate the cell potential (emf), subtract the standard electrode potential of the anode from the standard electrode potential of the cathode: \( E_{cell} = E_{cathode} - E_{anode} \) \( E_{cell} = (+1.36V) - (-0.40V) \) \( E_{cell} = +1.76V \) Therefore, the emf generated by the cell under standard conditions is +1.76V.

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Most popular questions from this chapter

During a period of discharge of a lead-acid battery, 402 \(\mathrm{g}\) of Pb from the anode is converted into PbSO \(_{4}(s) .\) (a) What of Pb from the anode is converted into PbSO \(_{4}(s) .\) (a) What mass of \(\mathrm{PbO}_{2}(s)\) is reduced at the cathode during this same period? (b) How many coulombs of electrical charge are transferred from Pb to PbO \(_{2} ?\)

A voltaic cell is constructed that uses the following half-cell reactions: $$ \begin{array}{c}{\mathrm{Cu}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Cu}(s)} \\ {\mathrm{I}_{2}(s)+2 \mathrm{e}^{-} \quad \longrightarrow 2 \mathrm{I}^{-}(a q)}\end{array} $$ The cell is operated at 298 \(\mathrm{K}\) with \(\left[\mathrm{Cu}^{+}\right]=0.25 M\) and \(\left[\mathrm{I}^{-}\right]=0.035 \mathrm{M}\) (a) Determine \(E\) for the cell at these concentrations. (b) Which electrode is the anode of the cell? (c) Is the answer to part (b) the same as it would be if the cell were operated under standard conditions? (d) If \(\left[\mathrm{Cu}^{+}\right]\) were equal to \(0.15 \mathrm{M},\) at what concentration of I \(\mathrm{I}^{-}\) would the cell have zero potential?

For each of the following reactions, write a balanced equation, calculate the standard emf, calculate \(\Delta G^{\circ}\) at \(298 \mathrm{K},\) and calculate the equilibrium constant \(K\) at 298 \(\mathrm{K}\) (a) Aqueous iodide ion is oxidized to \(\mathrm{I}_{2}(s)\) by \(\mathrm{Hg}_{2}^{2+}(a q)\) . (a) Aqueous iodide ion is oxidized to \(\mathrm{I}_{2}(s)\) by \(\mathrm{Hg}_{2}^{2+}(a q) .\) (b) In acidic solution, copper(l) ion is oxidized to copper(II) ion by nitrate ion. (c) In basic solution, \(\mathrm{Cr}(\mathrm{OH})_{3}(s)\) is oxidized to \(\mathrm{CrO}_{4}^{2-}(a q)\) by \(\mathrm{ClO}^{-}(a q) .\)

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

For a spontaneous reaction \(\mathrm{A}(a q) \rightarrow \mathrm{A}^{-}(a q)+\) \(\mathrm{B}^{+}(a q),\) answer the following questions: (a) If you made a voltaic cell out of this reaction, what half-reaction would be occurring at the cathode, and what half-reaction would be occurring at the anode? (b) Which half-reaction from (a) is higher in potential energy? (c) What is the sign of \(E_{\text { cell }}^{\circ} ?[\) Section 20.3\(]\)
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