Problem 78 - Chemistry: The Central Science in SI Units, Global Edition

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In some applications nickel-cadmium batteries have been replaced by nickel- zinc batteries.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

Step-by-Step Solution

Answer

(a) The cathode half-reaction is: \(2 NiO(OH)(s) + 2 H_2O(l) + 2 e^- \rightarrow 2 Ni(OH)_2(s) + 2 OH^-(aq)\) (b) The anode half-reaction is: \(Zn(s) \rightarrow Zn^{2+}(aq) + 2 e^-\) (c) The expected voltage for a nickel-zinc battery is approximately 0.943 V. (d) The specific energy density of a nickel-zinc battery may be higher or at least competitive with a nickel-cadmium battery.

Step 1: (1) Identify the overall cell reaction (given)

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

Step 2: (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: \(2 NiO(OH)(s) + 2 H_2O(l) + 2 e^- \rightarrow 2 Ni(OH)_2(s) + 2 OH^-(aq)\)

Step 3: (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: \(Zn(s) \rightarrow Zn^{2+}(aq) + 2 e^-\)

Step 4: (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.

Step 5: (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.

Key Concepts

Nickel-Zinc Battery

A Nickel-Zinc battery is a type of rechargeable battery used in various applications as an alternative to the Nickel-Cadmium battery. These batteries have gained popularity due to their eco-friendly nature and efficient energy storage capabilities.

Nickel-Zinc batteries use a chemical reaction between nickel and zinc components to store and release energy. The battery's design consists of nickel (II) hydroxy oxide (NiO(OH)) as the cathode material and zinc as the anode material.

These batteries are appreciated for their higher voltage output and are less harmful to the environment compared to nickel-cadmium batteries, making them a suitable choice for environmentally conscious consumers.

In practical applications, you might find these batteries in power tools, electric vehicles, and even in some consumer electronics due to their advantages in terms of capacity and sustainability.

Cell Reaction

The cell reaction in a Nickel-Zinc battery involves a series of oxidation and reduction reactions. A good understanding of these electrochemical processes is crucial to comprehending how these batteries operate.

In the Nickel-Zinc cell reaction:

• The cathode half-reaction involves the reduction of nickel(II) to form nickel hydroxide. This can be represented as: \[ 2 \text{NiO(OH)}(s) + 2 \text{H}_2\text{O}(l) + 2e^- \rightarrow 2\text{Ni(OH)}_2(s) + 2 \text{OH}^-(aq) \]
• The anode half-reaction involves the oxidation of zinc to zinc ions: \[ \text{Zn}(s) \rightarrow \text{Zn}^{2+}(aq) + 2e^- \]

By combining these half-reactions, the full cell reaction is established, leading to the flow of electrons that generate electrical energy.

This cell combines the benefits of the cathode's reduction potential and the anode's oxidation potential, resulting in an efficient exchange of electrons and a subsequent release of energy.

Energy Density

Energy density is a vital factor when assessing the functionality and efficiency of a battery, such as the Nickel-Zinc type. This term refers to the amount of energy stored in a given system or region of space per unit volume or mass.

One major reason Nickel-Zinc batteries potentially offer higher energy density compared to Nickel-Cadmium ones is the material properties of zinc. Zinc is lighter than cadmium, which might contribute to a greater energy density by weight.
Additionally, the non-toxic nature of zinc makes Nickel-Zinc batteries an eco-friendly alternative, providing safe disposal and recycling as additional advantages.

While the voltage output of Nickel-Zinc batteries is slightly lower than Nickel-Cadmium, the improved energy density might compensate effectively in applications where weight and environmental considerations are prioritized.

Standard Reduction Potential

The concept of standard reduction potential is pivotal in predicting the cell voltage and energy output of a Nickel-Zinc battery. Standard reduction potential refers to the tendency of a chemical species to be reduced, measured under standard conditions.

In electrochemistry, it is crucial for determining which materials will serve as the anode and cathode. For Nickel-Zinc batteries, the relevant reduction potentials are:

• For Zinc: \[ E^0_{Zn^{2+}/Zn} = -0.76 \, \text{V} \]
• For Cadmium (for comparative purposes): \[ E^0_{Cd^{2+}/Cd} = -0.403 \, \text{V} \]

By knowing these values, one can approximate the expected voltage of the battery, which is crucial for evaluating its performance.

The difference in standard reduction potential between Zinc and Cadmium was calculated to estimate the Nickel-Zinc battery's voltage. This theoretical grounding reinforces the practicality of choosing suitable battery types for specific energy applications.