During the discharge of a lead storage battery, the density of sulphuric acid fell from 1.13 to 1.15 g/`ml^(−1)` and sulphuric acid of the density of 1.3 g/`ml^(−1)`is 40% by mass and that of the density of 1.15 g/`ml^(−1)` is 20% by mass. The battery holds 3.5 litre of acid and the volume practically remained constant during the discharge. Calculate the no. of ampere hour for which the battery must have been used. The charging and discharging reactions are:
`Pb+SO_(4)^(-2)rarrPbSO_(4)+2e^(-)`(charging)
`PbO_(2)+4H^(+)+SO_(4)^(2-)+2erarrPnSO_(4)+2H_(2)O` (discharging)

Explanation

To solve the problem step by step, we will calculate the number of ampere-hours for which the lead storage battery has been used based on the change in density of sulfuric acid during discharge.

### Step 1: Calculate the initial mass of H₂SO₄
The initial density of sulfuric acid is 1.13 g/ml, and the battery holds 3.5 liters of acid.

\[ \text{Initial mass of H₂SO₄} = \text{Density} \times \text{Volume} \]
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