If the pH of a 1.00-in. rainfall over 1800 miles2 is 3.70, 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.

There are 2.32 x 10^6 kg sulfuric acid in the rainfall.

Solution:

We can find the volume of the solution by the product of 1.00 in and 1800 miles2:

1800 miles2 * 2.59e+6 sq m / 1 sq mi = 4.662 x 10^9 sq m

1.00 in * 1 m / 39.3701 in = 0.0254 m

Volume = 4.662 x 10^9 m^2 * 0.0254 m

= 1.184 x 10^8 m^3 * 1000 L / 1 m3

= 1.184 x 10^11 Liters

We get the molarity of H2SO4 from the concentration of [H+] given by pH = 3.70:

[H+] = 10^-pH = 10^-3.7 = 0.000200 M

[H2SO4] = 0.000100 M

By multiplying the molarity of sulfuric acid by the volume of the solution, we can get the number of moles of sulfuric acid:

1.184 x 10^11 L * 0.000100 mol/L H2SO4 = 2.36 x 10^7 moles H2SO4

We can now calculate for the mass of sulfuric acid in the rainfall:

mass of H2SO4 = 2.36 x 10^7 moles * 98.079 g/mol

= 2.32 x 10^9 g * 1 kg / 1000 g

= 2.32 x 10^6 kg H2SO4