Question

Part A If the pH of a 1.00-in. rainfall over 1700 miles is 3.20, how many kilograms of sulfuric acid, H2SO4, are present, assuming that it is the only acid contributing to the pH? For sulfuric acid, Kal is very large and K 2 is 0.012. Express your answer to two significant figures and include the appropriate units.

Answer 1

H2SO4 (aq)   -------------> H+ (aq) +   HSO4- (aq)

C                                        0                   0

0                                        C                    C

HSO4-   ------------> H+ +    SO42-

C                              C             0

C - x                         C + x         x

[H+] = 10^-3.20

[H+] = 6.31 x 10^-4

C + x = 6.31 x 10^-4

C - x = C + x - 2x         (we can also write like this)

          = 6.31 x 10^-4 - 2x

Ka2 = (C + x) x / (C - x)

0.012 = ( 6.31 x 10^-4) x / 6.31 x 10^-4 - 2x

7.572 x 10^-6 - 0.024 x = 6.31 x 10^-4 x

x = 3.074 x 10^-4

C + x = 6.31 x 10^-4

C = 3.24 x 10^-4 M

[H2SO4] = 3.24 x 10^-4 M

volume = area x height = 1700 mi2 x 1.00 in

            = 4.403 x 10^9 x 0.0254

            = 1.118 x 10^8 m^3

            = 1.118 x 10^11 L

moles of H2SO4 = 3.24 x 10^-4 x 1.118 x 10^11

                          = 3.62 x 10^7 mol

mass of H2SO4 = 3.62 x 10^7 x 98

mass of H2SO4 = 3.55 x 10^9 g

mass of H2SO4 = 3.6 x 10^6 kg