Question

If the pH of a 2.54-cm rainfall over 3700 km2 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, Ka1 is very large and Ka2 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

area = 3700 km2 = 3.7 x 10^9 m2

height = 2.54 cm = 0.0254 m

volume = area x height

            = 3.7 x 10^9 m2 x 0.0254 m

            = 9.40 x 10^7 m^3

            = 9.40 x 10^10 L

moles of H2SO4 = 3.24 x 10^-4 x 9.40 x 10^10

                          = 3.04 x 10^7 mol

mass of H2SO4 = 3.04 x 10^7 x 98

mass of H2SO4 = 2.98 x 10^9 g

mass of H2SO4 = 3.0 x 10^6 kg