Question

Over a period of time, the concentration of sulfuric acid in the lead storage battery of an automobile has decreased from 38.0 percent by mass (density = 1.29 g / mL) to 26.0 percent by mass (1.19 g/mL). Assume the volume of the acid remains constant at 711 mL.

(a) Calculate the total charge in coulombs supplied by the battery. × 10 CEnter your answer in scientific notation.

(b) How long (in hours) will it take to recharge the battery back to the original sulfuric acid using a current of 21.4 A? h

Answer 1

(a)The overall reaction is: Pb + PbO2 + H2SO4 → 2 PbSO4 + 2 H2O

Initial mass of H2SO4: 711 mL x 1.29 g / 1 mL x 0.380 = 348.53 g

Final mass of H2SO4: 711 mL x 1.19 g / 1 mL x 0.260 = 219.98 g

Mass of H2SO4 reacted will be 348.53 g − 219.98 g = 128.55 g

Moles of H2SO4 reacted will be 128.55 g x (1 mol/ 98.09g ) = 1.31 mol

hence

Q= 1.31 mol x (2 mol e^- /2 mol of H2SO4) x (96500 C/ 1 mol e^-) = 1.26 x10⁵C

Answer (a) = 1.26 x10⁵C

b) time (t) = Q/I = 1.26 x10⁵ C/21.1A = 5.97 x10³ sec = 1.66 Hour

Answer (b) = 1.66 Hour