In some applications nickel-cadmium batteries have been replaced by nickel- zinc batteries.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?

Step by step solution

01

(1) Identify the overall cell reaction (given)

The overall cell reaction for the nickel-zinc battery is given by: \(2 H_2O(l) + 2 NiO(OH)(s) + Zn(s) \rightarrow 2 Ni(OH)_2(s) + Zn(OH)_2(s)\)

02

(2) Determine the cathode half-reaction

The cathode half-reaction is the reduction reaction. In this case, nickel(II) is reduced to nickel(0). The cathode half-reaction can be written as: \(2 NiO(OH)(s) + 2 H_2O(l) + 2 e^- \rightarrow 2 Ni(OH)_2(s) + 2 OH^-(aq)\)

03

(3) Determine the anode half-reaction

The anode half-reaction is the oxidation reaction. In this case, zinc(0) is oxidized to zinc(II). The anode half-reaction can be written as: \(Zn(s) \rightarrow Zn^{2+}(aq) + 2 e^-\)

04

(4) Calculate the expected cell voltage for a nickel-zinc battery

To estimate the voltage for a nickel-zinc battery, we will first find the difference in the standard reduction potentials of Cd²⁺ and Zn²⁺ ions. The standard reduction potentials are: \\ \(E^0_{Cd^{2+}/Cd} = -0.403 V\) \\ \(E^0_{Zn^{2+}/Zn} = -0.76 V\) \\ We'll calculate the difference between them: \\ \(E^0_{Zn-Cd} = E^0_{Zn^{2+}/Zn} - E^0_{Cd^{2+}/Cd} = (-0.76 V) - (-0.403 V) = -0.357 V\) \\ Now, we'll add this difference to the voltage of a nickel-cadmium cell: \\ \(E_\text{nickel-zinc cell} = E_\text{nickel-cadmium cell} + E^0_{Zn-Cd} = 1.30 V + (-0.357 V) = 0.943 V\) \\ So the expected voltage for a nickel-zinc battery is approximately 0.943 V.

05

(5) Compare the specific energy densities of nickel-zinc and nickel-cadmium batteries

The specific energy density of a battery depends on many factors, including its electrochemical reactions and materials. Although we cannot make a precise comparison without more detailed information, it is possible to draw some inferences from the information provided. The nickel-zinc cell has a lower voltage, and zinc is lighter than cadmium, which may result in a higher specific energy density by weight. Furthermore, the replacement of toxic cadmium with more environmentally friendly zinc may lead to other benefits in terms of energy density, disposal, and recycling. Overall, it would be reasonable to expect that the specific energy density of a nickel-zinc battery may be higher or at least competitive with a nickel-cadmium battery.

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