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 moles of sulphuric acid are lost during the discharge?

9.88

The correct answer is option 1. 9.88

\(\text{Mass of the solution before discharge = 3500 mL × 1.294 g }mL^{-1}\text{ = 4529 g}\)

\(\text{Mass of }H_2SO_4\text{ present in the solution = }\frac{39}{100}× 4529\text{ g = 1766.31 g }\)

\(\text{Mass of the solution after discharge = 3500 mL × 1.139 g }mL^{-1}\text{ = 3986.5 g}\)

\(\text{Mass of }H_2SO_4\text{ present in the solution = }\frac{20}{100}× 3986.5\text{ g = 797.3 g }\)

\(\text{Loss in mass of }H_2SO_4 \text{ during discharge = 1766.31 − 797.3 = 969.01 g}\)

\(\text{Moles of }H_2SO_4\text{ lost during discharge = }\frac{969.01}{98}\text{ = 9.88769 ≈ 9.88}\)