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Chapter 20: Problem 78

In some applications nickel-cadmium batteries have been replaced by nickel- zinc batteries. The overall cell reaction for this relatively new battery is: $$ \begin{aligned} 2 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{NiO}(\mathrm{OH})(s)+\mathrm{Zn}(s) & \\ & \longrightarrow 2 \mathrm{Ni}(\mathrm{OH})_{2}(s)+\mathrm{Zn}(\mathrm{OH})_{2}(s) \end{aligned} $$ (a)What is the cathode half-reaction? (b)What is the anode half-reaction? (c) A single nickel-cadmium cell has a voltage of 1.30 \(\mathrm{V}\) . Based on the difference in the standard reduction potentials of \(\mathrm{Cd}^{2+}\) and \(\mathrm{Zn}^{2+},\) what voltage would you estimate a nickel-zinc battery will produce? (d) Would you expect the specific energy density of a nickel-zinc battery to be higher or lower than that of a nickel-cadmium battery?

Short Answer

Expert verified
The cathode half-reaction (reduction) is \(2 \mathrm{NiO(OH)}(s) + 2 \mathrm{H}_2\mathrm{O}(l) \rightarrow 2 \mathrm{Ni(OH)}_2(s) + 2 \mathrm{OH}^-(aq)\), and the anode half-reaction (oxidation) is \(\mathrm{Zn}(s) + 2 \mathrm{OH}^-(aq) \rightarrow \mathrm{Zn(OH)}_2(s) + 2 \mathrm{e}^-\). The estimated voltage of a nickel-zinc battery is 0.94 V, which is lower than a nickel-cadmium cell. However, the specific energy density of a nickel-zinc battery is expected to be higher than that of a nickel-cadmium battery due to the lower molar mass of Zn compared to Cd.

Step by step solution

01

1. Balancing the given chemical reaction

We can see that the given chemical reaction is already balanced. Therefore, we can proceed to the next step.
02

2. Identifying the Cathode and Anode half-reactions

In the cell reaction, the reduction and oxidation halves can be separated as: - The cathode half-reaction (reduction): \(2 \mathrm{NiO(OH)}(s) + 2 \mathrm{H}_2\mathrm{O}(l) \rightarrow 2 \mathrm{Ni(OH)}_2(s) + 2 \mathrm{OH}^-(aq) \) - The anode half-reaction (oxidation): \( \mathrm{Zn}(s) + 2 \mathrm{OH}^-(aq) \rightarrow \mathrm{Zn(OH)}_2(s) + 2 \mathrm{e}^-\)
03

3. Estimating the nickel-zinc battery voltage

We know that the voltage of a nickel-cadmium cell is 1.30 V. The standard reduction potential difference between Cd²⁺ and Zn²⁺ is given as: \(E_{Ni/Cd} = 1.30 \, \mathrm{V} \) To estimate the voltage of the nickel-zinc battery, we first need to figure out the difference in standard reduction potential between Zn²⁺ and Cd²⁺: \(E_{Cd/Zn} = E_{Cd} - E_{Zn}\) Where \(E_{Cd}\) and \(E_{Zn}\) are the standard reduction potentials of Cd²⁺ and Zn²⁺ respectively. Now, let's calculate the voltage for the nickel-zinc battery (Ni/Zn): \(E_{Ni/Zn} = E_{Ni/Cd} - E_{Cd/Zn}\) Given \(E_{Cd} = -0.40 \, \mathrm{V}\) and \(E_{Zn} = -0.76 \, \mathrm{V}\), we get: \(E_{Cd/Zn} = -0.40 - (-0.76) = 0.36 \, \mathrm{V}\) Then, the nickel-zinc battery voltage would be: \(E_{Ni/Zn} = 1.30 - 0.36 = 0.94 \, \mathrm{V}\)
04

4. Comparing the energy densities of nickel-zinc and nickel-cadmium batteries

Specific energy density is the amount of energy stored per unit mass or volume of the battery. For this comparison, we can analyze the reaction based on the molar masses of the active anode materials, zinc, and cadmium. Since Cd has a higher molar mass (112.411 g/mol) than Zn (65.38 g/mol), the nickel-zinc battery would store more energy per unit mass. Therefore, the specific energy density of a nickel-zinc battery would be higher than that of a nickel-cadmium battery.

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Most popular questions from this chapter

Complete and balance the following equations, and identify the oxidizing and reducing agents: $$ \begin{array}{l}{\text { (a) } \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{I}(a q) \longrightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{IO}_{3}^{-}(a q)} \\ \quad {\text { (acidic solution) }} \\ {\text { (b) } \mathrm{MnO}_{4}^{-}(a q)+\mathrm{CH}_{3} \mathrm{OH}(a q) \longrightarrow \mathrm{Mn}^{2+}(a q)+} \\ \quad {\mathrm{HCOOH}(a q) \text { (acidic solution) }}\end{array} \\ {\text {(c) } \mathrm{I}_{2}(s)+\mathrm{OCl}^{-}(a q) \longrightarrow \mathrm{IO}_{3}^{-}(a q)+\mathrm{Cl}^{-}(a q)} \\ {\text { (acidic solution) }} \\ {\text { (d) } \mathrm{As}_{2} \mathrm{O}_{3}(s)+\mathrm{NO}_{3}(a q) \longrightarrow \mathrm{H}_{3} \mathrm{AsO}_{4}(a q)+\mathrm{N}_{2} \mathrm{O}_{3}(a q)} \\ {(\text { acidic solution })} \\ {\text { (e) } \operatorname{MnO}_{4}^{-}(a q)+\operatorname{Br}^{-}(a q) \longrightarrow \mathrm{MnO}_{2}(s)+\mathrm{BrO}_{3}^{-}(a q)} \\ {\text { (basic solution) }} \\ {\text { (f) } \mathrm{Pb}(\mathrm{OH})_{4}^{2-}(a q)+\mathrm{ClO}^{-}(a q) \longrightarrow \mathrm{PbO}_{2}(s)+\mathrm{Cl}^{-}(a q)} \\ {\text { (basic solution) }} $$

The electrodes in a silver oxide battery are silver oxide \(\left(\mathrm{Ag}_{2} \mathrm{O}\right)\) and zinc. (a) Which electrode acts as the anode? (b) Which battery do you think has an energy density most similar to the silver oxide battery: a Li-ion battery, a nickel-cadmium battery, or a lead-acid battery? [ Section 20.7]

A 1 M solution of \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\) is placed in a beaker with a strip of Cu metal. A 1 \(\mathrm{M}\) solution of \(\mathrm{SnSO}_{4}\) is placed in a second beaker with a strip of Sn metal. A salt bridge connects the two beakers, and wires to a voltmeter link two metal electrodes. (a) Which electrode serves as the anode, and which as the cathode? (b) Which electrode gains mass, and which loses 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?

A voltaic cell similar to that shown in Figure 20.5 is constructed. One half- cell consists of an aluminum strip placed in a solution of \(\mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\) , and the other has a nickel strip placed in a solution of \(\mathrm{NiSO}_{4}\) . The overall cell reaction is $$ 2 \mathrm{Al}(s)+3 \mathrm{Ni}^{2+}(a q) \longrightarrow 2 \mathrm{Al}^{3+}(a q)+3 \mathrm{Ni}(s) $$ (a) What is being oxidized, and what is being reduced? (b) Write the half-reactions that occur in the two half-cells. (c) Which electrode is the anode, and which is the cathode? (d) Indicate the signs of the electrodes. (e) Do electrons flow from the aluminum electrode to the nickel electrode or from the nickel to the aluminum? (f) In which directions do the cations and anions migrate through the solution? Assume the Al is not coated with its oxide.

A voltaic cell is constructed that uses the following reaction and operates at \(298 \mathrm{K} :\) $$ \mathrm{Zn}(s)+\mathrm{Ni}^{2+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{Ni}(s) $$ (a) What is the emf of this cell under standard conditions? (b) What is the emf of this cell when \(\left[\mathrm{Ni}^{2+}\right]=3.00 M\) and \(\left[\mathrm{Zn}^{2+}\right]=0.100 \mathrm{M} ?(\mathbf{c})\) What is the emf of the cell when \(\left[\mathrm{Ni}^{2+}\right]=0.200 \mathrm{M}\) and \(\left[\mathrm{Zn}^{2+}\right]=0.900 \mathrm{M} ?\)
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