Be sure to answer all parts. Over a period of time, the concentration of sulfuri

Question

Be sure to answer all parts.

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 706 mL.

(a) Calculate the total charge in coulombs supplied by the battery. Enter 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 22.8 A?

Explanation / Answer

(a) Initial density of H2SO4 = 1.29 g/mL * 38/100 = 0.4902 g/mL

Final density of H2SO4 = 1.19 g/mL * 26/100 = 0.3094 g/mL

The denisty of H2SO4 used by battery = 0.4902-0.3094 = 0.1808 g/mL

i.e. The mass of H2SO4 used by battery = 0.1808 g/mL * 706 mL = 127.6448 g

For 49 g of H2SO4 - 96485.33 C of charge required

i.e. For 127.6448 g of H2SO4, the total charge supplied by battery (q) = (127.6448/49) * 96485.33 = 2.51*105 C

(b) q = i*t

i.e. 2.51*105 C = 22.8 A * t

i.e. t = 11024 s = 11024/3600 = 3.062 h

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