Question

In some applications nickel-cadmium batteries have been replaced by nickel- zinc batteries.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

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

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.

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): \( \mathrm{Zn}(s) + 2 \mathrm{OH}^-(aq) \rightarrow \mathrm{Zn(OH)}_2(s) + 2 \mathrm{e}^-\)

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: \(E_{Ni/Zn} = 1.30 - 0.36 = 0.94 \, \mathrm{V}\)

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.

Key concepts

Nickel-Zinc Battery

Nickel-zinc batteries are a type of rechargeable battery that have gained popularity as alternatives to nickel-cadmium batteries. This transition is mainly due to their advantageous properties such as higher energy density and lower environmental impact.

In a nickel-zinc battery, the main components are nickel oxyhydroxide (NiO(OH)) used as the cathode and zinc (Zn) used as the anode. During the discharge process, the cathode undergoes reduction to form nickel hydroxide (Ni(OH)₂), whereas the anode undergoes oxidation to form zinc hydroxide (Zn(OH)₂).

• Reduction: Occurs at the cathode, gaining electrons.
• Oxidation: Occurs at the anode, losing electrons.

The overall reaction taking place inside a nickel-zinc battery is:\[2 \mathrm{H}_{2} \mathrm{O}(l) + 2 \mathrm{NiO(OH)}(s) + \mathrm{Zn}(s) \rightarrow 2 \mathrm{Ni(OH)}_{2}(s) + \mathrm{Zn(OH)}_{2}(s)\]This balanced chemical equation provides insight into the electrochemical reactions that power the battery.

Nickel-zinc batteries are known for their high energy-to-weight ratio and are thus commonly used in applications where weight is a significant factor.

Redox Reactions

Redox reactions, or reduction-oxidation reactions, are central to the functioning of electrochemical cells like nickel-zinc batteries.

In simple terms, a redox reaction involves the transfer of electrons between two substances. One substance undergoes oxidation (loss of electrons), while the other undergoes reduction (gain of electrons).

In the context of a nickel-zinc battery, the cathode half-reaction involves the reduction of nickel oxyhydroxide:\[2 \mathrm{NiO(OH)}(s) + 2 \mathrm{H}_2\mathrm{O}(l) \rightarrow 2 \mathrm{Ni(OH)}_2(s) + 2 \mathrm{OH}^-(aq)\]
And the anode half-reaction involves the oxidation of zinc:\[\mathrm{Zn}(s) + 2 \mathrm{OH}^-(aq) \rightarrow \mathrm{Zn(OH)}_2(s) + 2 \mathrm{e}^-\]
These reactions together constitute the full chemical equation of the cell, demonstrating the importance of electron transfer in generating electrical energy.

Understanding redox reactions is crucial for analyzing and designing efficient electrochemical cells.

Energy Density

Energy density refers to the amount of energy that can be stored in a given system or space. In batteries, energy density is a key performance indicator, usually expressed in terms of energy per unit mass or volume.

A battery with high energy density can store more energy in a smaller, lighter space, which is advantageous for portable devices and electric vehicles.

• Specific energy density: Energy stored per unit mass.
• Volumetric energy density: Energy stored per unit volume.

Nickel-zinc batteries offer a higher specific energy density compared to nickel-cadmium batteries. This is partly because zinc, the active anode material, has a lower molar mass of 65.38 g/mol compared to cadmium, which has a molar mass of 112.411 g/mol. Hence, for equivalent amounts of energy stored, nickel-zinc batteries tend to be lighter.

This higher energy density makes nickel-zinc batteries more favorable for applications where reducing weight and space is critical.