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?
Answer & explanation
Correct answer: option 2
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 \(= 1\)
\(W = ZQ\)
\(Q = 969.0 F × \frac{1}{98}\)
\(Q = 9.88 F × \frac{1}{3600}\)
\(Q = 9.88 × 96500 × \frac{1}{3600}\)
\(Q = 265.05\, \ Amp-hr\)