Problem 78 - Chemistry The Central Science In Si Units

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In some applications nickel-cadmium batteries have been replaced by nickel- zinc batteries.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) Cathode: Reduction of NiO(OH) to Ni(OH)_2. (b) Anode: Oxidation of Zn. (c) Estimated voltage: 1.66 V. (d) Nickel-zinc has higher specific energy density.

Step 1: Understanding the Cathode Reaction

The cathode is where reduction occurs. Observing the given overall reaction, the species being reduced is nickel; this can be represented in its ionic form. Recognize the reduction of nickel oxide hydroxide to nickel hydroxide.The cathode half-reaction is:\[ 2 ext{NiO(OH)}(s) + 2 ext{H}_2 ext{O}(l) + 2 ext{e}^- \rightarrow 2 ext{Ni(OH)}_2(s) + 2 ext{OH}^-(aq) \]

Step 2: Identifying the Anode Reaction

The anode is where oxidation happens. In this reaction, zinc is oxidized. The anode half-reaction can be directly seen from the zinc part of the overall reaction.The anode half-reaction is:\[ ext{Zn}(s) + 2 ext{OH}^-(aq) \rightarrow ext{Zn(OH)}_2(s) + 2 ext{e}^- \]

Step 3: Calculating the Cell Potential

To estimate the voltage of the nickel-zinc battery, use the standard potential difference between the cadmium and zinc reactions. The standard reduction potential for \( ext{Cd}^{2+} \rightarrow ext{Cd} \) is \(- 0.40 ext{ V} \), and for \( ext{Zn}^{2+} \rightarrow ext{Zn} \) is \(- 0.76 ext{ V} \). The potential difference is \( 0.76 - 0.40 = 0.36 ext{ V} \). Since Ni-Cd battery voltage is around \( 1.30 ext{ V} \), nickel-zinc should be about \( 1.30 + 0.36 = 1.66 ext{ V} \).

Step 4: Comparing Specific Energy Density

Specific energy density relates to the energy per mass. Zinc has a higher specific capacity compared to cadmium due to its lower atomic weight, and typically, nickel-zinc has a higher specific energy density than nickel-cadmium because of this. Therefore, the specific energy density of a nickel-zinc battery is expected to be higher.

Key Concepts

Nickel-Zinc Batteries

Nickel-zinc batteries are a relatively new addition to the world of electrochemical energy storage. These batteries are considered an improvement over the older nickel-cadmium batteries for several reasons.

Nickel-zinc batteries use nickel oxide hydroxide as their cathode material and zinc as their anode material. This type of battery is known for being more environmentally friendly because it does not contain toxic cadmium.

One significant advantage of nickel-zinc batteries is their higher cell potential compared to nickel-cadmium cells, which we will explore in the next section. Additionally, nickel-zinc batteries have a higher energy density, providing more power in a lighter package, making them suitable for applications where weight is a critical factor, such as in electric vehicles and portable electronics.

Cell Potential

In electrochemistry, the cell potential, or electromotive force (EMF), is a measure of the voltage generated by a cell when no current is flowing. It's an essential factor in determining the efficiency of a battery.

The cell potential of a nickel-zinc battery can be calculated using the standard reduction potentials of the materials involved. In the case of nickel-zinc batteries, the relevant reactions involve the reduction of nickel and the oxidation of zinc.

To estimate the cell potential, compare the reduction potentials of zinc and cadmium, the anode materials in nickel-zinc and nickel-cadmium batteries, respectively. You find that zinc has a more negative reduction potential (-0.76 V compared to cadmium's -0.40 V), which allows for a higher cell potential of around 1.66 V for nickel-zinc batteries. This higher voltage translates to higher power output for devices using these batteries.

Half-Reactions

Half-reactions are an essential part of understanding how electrochemical cells operate. Every battery consists of two half-reactions: oxidation and reduction, occurring at the anode and cathode, respectively.

For a nickel-zinc cell, the reduction half-reaction at the cathode involves nickel being reduced from nickel oxide hydroxide to nickel hydroxide. This can be written as: \[ 2 \text{NiO(OH)}(s) + 2 \text{H}_2 \text{O}(l) + 2 \text{e}^- \rightarrow 2 \text{Ni(OH)}_2(s) + 2 \text{OH}^-(aq) \] At the anode, zinc undergoes oxidation, changing from solid zinc to zinc hydroxide and releasing electrons: \[ \text{Zn}(s) + 2 \text{OH}^-(aq) \rightarrow \text{Zn(OH)}_2(s) + 2 \text{e}^- \] These half-reactions are crucial as they not only describe the chemical processes but also help in computing the overall cell potential and understanding energy transfer within the battery.

Energy Density

Energy density is a key factor when evaluating the efficiency and practicality of batteries. It refers to the amount of energy stored in a battery concerning its mass, commonly expressed in watt-hours per kilogram (Wh/kg).

Nickel-zinc batteries offer a higher energy density than nickel-cadmium batteries. This is primarily due to the lower atomic weight of zinc compared to cadmium, allowing for more energy to be stored per unit mass.

Higher energy density is particularly advantageous for applications where battery weight is a concern, such as in electric vehicles, portable electronics, and other devices where long-lasting power and lightweight are crucial. This makes nickel-zinc batteries an attractive choice for both consumer electronics and sustainable transportation solutions.