In the lead-acid battery during charging, the cathode reaction is

Options

A. formation of `PbO_(2)`
B. formation of `PbSO_(4)`
C. reduction of `Pb^(2+)` to `Pb`
D. decomposition of Pb at the anode

Explanation

To determine the cathode reaction during the charging of a lead-acid battery, we can follow these steps:

### Step 1: Understand the Basics of the Lead-Acid Battery
A lead-acid battery consists of lead (Pb) and lead dioxide (PbO2) as the electrodes and sulfuric acid (H2SO4) as the electrolyte. During charging, the reactions at the electrodes involve the conversion of lead sulfate (PbSO4) back to lead and lead dioxide.

**Hint:** Remember that during charging, the cathode undergoes a reduction reaction.

### Step 2: Identify the Cathode Reaction
In electrochemistry, the cathode is where reduction occurs. In the case of a lead-acid battery, the relevant species at the cathode during charging is lead ions (Pb²⁺).

**Hint:** Focus on the ions present in the electrolyte and the products formed during the charging process.

### Step 3: Write the Cathode Reaction
The cathode reaction involves the reduction of lead ions (Pb²⁺) to solid lead (Pb). The half-reaction can be written as follows:

\[ \text{Pb}^{2+} + 2e^- \rightarrow \text{Pb (s)} \]

This equation shows that lead ions gain two electrons to form solid lead.

**Hint:** Ensure that you balance the charge and mass in the half-reaction.

### Step 4: Conclusion
Thus, the cathode reaction during the charging of a lead-acid battery is the reduction of lead ions to solid lead.

**Final Answer:** The cathode reaction is:
\[ \text{Pb}^{2+} + 2e^- \rightarrow \text{Pb (s)} \]

**Hint:** Check the options provided in the question to find the correct representation of this reaction.