Problem 34 - Chemistry The Science in Context

Question

Sometimes the cell reaction of nickel-cadmium batteries is written with Cd metal as the anode and solid \(\mathrm{NiO}_{2}\) as the cathode. Assuming that the products of the reactions are a solid hydroxide of cadmium(II) at the anode and a solid hydroxide of nickel(II) at the cathode, write balanced equations for the cathode and anode half-reactions and the overall cell reaction.

Step-by-Step Solution

Answer

Question: Write balanced half-reactions for the anode and cathode and the overall cell reaction for a nickel-cadmium battery. Answer: The balanced half-reactions and overall cell reaction are as follows: Anode half-reaction: $$\mathrm{Cd}(s) \rightarrow \mathrm{Cd(OH)}_{2}(s) + 2\mathrm{e}^{-}$$ Cathode half-reaction: $$\mathrm{NiO}_{2}(s)+2\mathrm{H}_{2}\mathrm{O}(l)+2\mathrm{e}^{-} \rightarrow \mathrm{Ni(OH)}_{2}(s)$$ Overall cell reaction: $$\mathrm{Cd}(s)+\mathrm{NiO}_{2}(s) +2\mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{Cd(OH)}_{2}(s) + \mathrm{Ni(OH)}_{2}(s)$$

Step 1: Write the half-reaction for the anode

At the anode, the oxidation of Cd metal to solid hydroxide of cadmium(II) occurs. Thus, the half-reaction can be written as: $$\mathrm{Cd}(s) \rightarrow \mathrm{Cd(OH)}_{2}(s)$$

Step 2: Balance the anode half-reaction

In order to balance the anode half-reaction, we need to add 2 electrons to the right side of the equation to account for the fact that cadmium is losing two electrons when it is oxidized. $$\mathrm{Cd}(s) \rightarrow \mathrm{Cd(OH)}_{2}(s) + 2\mathrm{e}^{-}$$ The anode half-reaction is now balanced.

Step 3: Write the half-reaction for the cathode

At the cathode, the reduction of solid NiO₂ to solid hydroxide of nickel(II) occurs. Thus, the half-reaction can be written as: $$\mathrm{NiO}_{2}(s) \rightarrow \mathrm{Ni(OH)}_{2}(s)$$

Step 4: Balance the cathode half-reaction

In order to balance the cathode half-reaction, we need to add water and electrons. First, add 2 H₂O to the left side to balance the oxygen atoms: $$\mathrm{NiO}_{2}(s)+2\mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{Ni(OH)}_{2}(s)$$ Now, add 2 electrons to the left side to balance the hydrogen atoms and charges: $$\mathrm{NiO}_{2}(s)+2\mathrm{H}_{2}\mathrm{O}(l)+2\mathrm{e}^{-} \rightarrow \mathrm{Ni(OH)}_{2}(s)$$ The cathode half-reaction is now balanced.

Step 5: Combine the half-reactions and write the overall cell reaction

Adding the half-reactions for the anode and the cathode together gives: $$\mathrm{Cd}(s)+\mathrm{NiO}_{2}(s) +2\mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{Cd(OH)}_{2}(s) + \mathrm{Ni(OH)}_{2}(s) + 2\mathrm{e}^{-}$$ Since the electrons were added to balance the half-reactions, they will cancel each other out, leaving the overall cell reaction as: $$\mathrm{Cd}(s)+\mathrm{NiO}_{2}(s) +2\mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{Cd(OH)}_{2}(s) + \mathrm{Ni(OH)}_{2}(s)$$

Key Concepts

Half-Reactions

In electrochemistry, half-reactions are fundamental since they depict either the oxidation or reduction process taking place in a galvanic cell. Each half-reaction represents one portion of the full electrochemical reaction.

The concept of half-reactions allows chemists to see how electrons are transferred between substances. In a nickel-cadmium battery, for example, there are two half-reactions: one at the anode and another at the cathode.

• The anode involves an oxidation reaction where electrons are lost.
• The cathode sees a reduction reaction where electrons are gained.

By writing and balancing these half-reactions, you make it easier to analyze and understand the overall cell reaction.

Nickel-Cadmium Battery

Nickel-cadmium batteries are well-known for their durable performance and ability to deliver a steady output of energy. These rechargeable batteries are widely used in various applications, from power tools to emergency lighting systems.

They operate by using nickel oxide and cadmium as electrodes, which engage in chemical reactions to produce electrical energy. Upon discharge, the nickel oxide is reduced, and the cadmium is oxidized, thus powering the device. When charging, these reactions are reversed, allowing the battery to be used many times. Unfortunately, they can suffer from a 'memory effect', which can diminish their effective capacity if not properly managed.

Cell Reaction

The cell reaction refers to the complete electrical chemical process occurring within a galvanic cell. It is the sum of the anode and cathode half-reactions, representing the overall transformation of reactants into products.

In the case of the nickel-cadmium battery, the cell reaction can be succinctly represented after balancing the respective half-reactions. Here's what happens:

• Cadmium at the anode loses electrons, forming cadmium hydroxide.
• Nickel oxide at the cathode gains electrons to become nickel hydroxide.

When these half-reactions are put together, electrons cancel out. This resulting balanced equation shows how electricity is generated and stored in the cell during battery operation.

Oxidation-Reduction

Oxidation-reduction (redox) reactions are central to electrochemistry. These reactions involve the transfer of electrons between chemical species, changing their oxidation states.

Oxidation refers to the loss of electrons, which increases the species' oxidation state. Reduction is the gain of electrons, thereby decreasing the oxidation state. In a nickel-cadmium battery:

• Cadmium oxidizes by losing electrons at the anode.
• Nickel oxide reduces by gaining electrons at the cathode.

Understanding redox reactions helps explain why and how batteries can generate electrical power. The flow of electrons from oxidation to reduction points in the cell forms an electric current, enabling the battery to power an external circuit.