Q.Write the cell reaction of a lead storage battery when it is discharged. How does the density of the electrolyte change when the battery is discharged?

Concept: Lead Acid Battery Recharging — During discharge, both electrodes convert to lead sulfate, consuming sulfuric acid and producing water.

Reasoning:

1. At the anode (Pb): $\text{Pb} + \text{SO}_4^{2-} \rightarrow \text{PbSO}_4 + 2e^-$
2. At the cathode (PbO$_2$): $\text{PbO}_2 + 4\text{H}^+ + \text{SO}_4^{2-} + 2e^- \rightarrow \text{PbSO}_4 + 2\text{H}_2\text{O}$ …

Why this happens — the chemistry of a working battery

A lead storage battery works by converting chemical energy into electrical energy through spontaneous redox reactions. The key to understanding the density change lies in what happens to the sulfuric acid ($H_2SO_4$) during discharge.

The electrolyte is not just a passive conductor — it is an active participant. Sulfuric acid provides the sulfate ions ($SO_4^{2-}$) that form lead sulfate on both electrodes, and it also supplies the $H^+$ ions needed to balance charges. As the battery discharges, $H_2SO_4$ is consumed, so the electrolyte becomes more dilute — its density falls.

Step-by-step reasoning

1. Identify the electrodes and their reactions during discharge

   The negative electrode is spongy lead (Pb). The positive electrode is lead dioxide ($PbO_2$), packed into a grid. Both are immersed in dilute $H_2SO_4$.

   At the negative electrode (anode during discharge — oxidation occurs here):

At the positive electrode (cathode during discharge — reduction occurs here):

2. Combine to get the overall cell reaction

   Adding the two half-reactions (electrons cancel):

Notice: two molecules of sulfuric acid are consumed for every two electrons transferred. Water is produced instead.

3. Track what happens to the electrolyte

   • Before discharge: The electrolyte is concentrated $H_2SO_4$ (density ~1.25–1.30 g/mL in a fully charged battery).
   • During discharge: $H_2SO_4$ is used up, and $H_2O$ is generated. The total volume of electrolyte changes only slightly, but the concentration of $H_2SO_4$ drops significantly.
   • Result: The density of the electrolyte decreases as the battery discharges. …

Method: Combining Half-Reactions to Get the Discharge Reaction, Then Tracking Electrolyte Density

This method builds the overall discharge reaction of a lead storage battery from its two electrode half-reactions, then uses that reaction to reason about how the electrolyte's density changes.

Step 1: Identify the electrodes and the electrolyte

A lead storage battery has:

• A spongy lead negative plate ($\text{Pb}$)
• A lead dioxide positive plate ($\text{PbO}_2$)
• Both dipped in dilute sulfuric acid ($\text{H}_2\text{SO}_4$) electrolyte

Step 2: Write the half-reaction at the negative electrode (anode during discharge)

During discharge, the cell acts as a galvanic cell, so oxidation occurs at the negative plate:

Step 3: Write the half-reaction at the positive electrode (cathode during discharge)

Reduction occurs at the $\text{PbO}_2$ plate:

Step 4: Add the half-reactions to get the overall discharge reaction

Electrons cancel (2$e^-$ on each side):

Step 5: Track what happens to the electrolyte

• Two moles of $\text{H}_2\text{SO}_4$ are consumed for every mole of Pb and PbO$_2$ that reacts.
• Two moles of $\text{H}_2\text{O}$ are produced.
• The solid $\text{PbSO}_4$ formed stays bonded to the plates — it does not dissolve into or thicken the electrolyte. …

Here are the common mistakes students make on this exact question, along with the concept-first reasoning to avoid each.

Mistake 1: Writing the wrong direction for the reaction

The mistake:

Students write the charging reaction instead of the discharging reaction.

For example:

This is the cathode half-reaction during charging, not discharging.

Why it happens:

The question explicitly says “when it is discharged.” Students often memorise the overall reaction without linking it to the direction of electron flow.

How to avoid:

• Remember the mnemonic:
  • Discharge → battery is giving energy → spontaneous reaction.
  • Charge → battery is taking energy → non-spontaneous (electrolysis).
• For discharge, the anode is Pb (oxidation) and the cathode is PbO$_2$ (reduction).
• Write the overall cell reaction for discharge as:

Key check: If you see PbSO$_4$ on the left side, you’ve written the charging reaction. On discharge, PbSO$_4$ is a product.

Mistake 2: Forgetting to include H$_2$SO$_4$ and H$_2$O in the reaction

The mistake:

Writing only the lead and lead dioxide half-reactions without showing the consumption of sulfuric acid and production of water.

Why it happens:

Students focus on the solid electrodes and forget the electrolyte plays a chemical role.

How to avoid:

• Understand that H$_2$SO$_4$ is consumed during discharge (it provides SO$_4^{2-}$ ions to form PbSO$_4$).
• Water is produced as a byproduct.
• Always write the full balanced equation with all species:

Mistake 3: Confusing the density change direction

The mistake:

Saying “density of electrolyte increases” during discharge.

Why it happens:

Students think “battery is working, so something must be getting stronger.” They forget that H$_2$SO$_4$ is a dense liquid, and water is less dense.

How to avoid:

• Density of H$_2$SO$_4$ ≈ 1.84 g/mL (concentrated).
• Density of water = 1.00 g/mL.
• During discharge, H$_2$SO$_4$ is consumed and H$_2$O is produced.
• So the electrolyte becomes more dilute → density decreases.

Correct answer: The density of the electrolyte decreases during discharge.

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