Question

If the pH of a 1.00-in. rainfall over 1300 miles2 is 3.30, how many kilograms of sulfuric acid, H2SO4, are present, assuming that it is the only acid contributing to the pH?

For sulfuric acid, Ka1 is very large and Ka2 is 0.012.

Answer 1

Volume of rainfall = Area X height

Height = 1 in = 0.254 dm

1mile2 = 2.59 X 10^8 dm^2

so 1300 miles^2 = 3367 X 10^8 dm^2

Volume = 0.254 X 3367 X 10^8 = 855.218 X 10^8 dm^3

Also,

H₂SO₄ ionizes as

H2SO4 --> H+   + HSO4-

Ka1 is very high so it completely dissociates , due to first dissociation [H+] = Concentraion of H2SO4

HSO4- --> H⁺ + SO4^-2

We also consider it as high dissciation

so each mole of H2SO4 will give 2 moles of H+ (proton)

pH = 3.30 = -log[H+]

So [H+] = 0.000501 M = 0.000501 moles / L or moles / dm^3

Volume = 855.218 X 10^8 dm^3

so moles of H+ present in this volume = 0.000501 X 855.218 X 10^8 = 4.28 X 10^7 moles

So moles of H2SO4 = 4.28 X 10^7 / 2 = 2.14 X 10^7 moles

Molecular weight of H2SO4 = 98 g / mole

so mass of H2SO4 = Moles X molecular weight = 98 x 2.14 X 10^7 grams = 209.72 X 10^7 grams = 2.09 X 10^6 Kg