A lead storage battery consists of a lead anode and a grid of lead packed with lead dioxide as the cathode. The electrolyte taken is 39% H₂SO₄ by mass having a density of 1.294 g mL^-1. The battery holds 3.5 L of the acid. During the discharge of the battery, the density of H₂SO₄ falls from 1.294 g mL^-1 to 1.139 g mL^-1 which is 20% by H₂SO₄ mass.

How many ampere-hour must have been used by the battery?

265.05

The correct answer is option 2. 265.05.

Weight of \(H_2SO_4\) at initial \(= 3.5 × 1000 × 0.39 × 1.294 = 1766.31g\)

Weight of \(H_2SO_4\) after decay \(3. 5 × 1000 × 1.139 × 0.20 = 797.31g\)

Amount deposited \(= 969 g\)

\(n\)-factor \(= 1\)

\(W = ZQ\)

\(Q = 969.0 F × \frac{1}{98}\)

\(Q = 9.88 F × \frac{1}{3600}\)

\(Q = 9.88 × 96500 × \frac{1}{3600}\)

\(Q = 265.05\, \ Amp-hr\)