At pH 3.70, H2SO4 can be regarded as being fully dissociated. The dissociation reaction is
H₂SO₄(l) --> 2H⁺(aq) + SO₄²⁻(aq)
Since pH = -log₁₀[H⁺]
[H⁺] =
=
[H⁺] = 2 x 10⁻⁴ M
Since there are 2 moles of H⁺ for every mole of H₂SO₄
[H₂SO₄] = 0.5 * [H⁺]
=0.5 * 2 x 10⁻⁴ M
[H₂SO₄] = 1 x 10⁻⁴ M
Convert the amount of rain and the area into SI units
Rain = 1.00 in * 0.0254 m/in
Rain = 0.0254 m
Area = 1600 miles² * 2589988.11 m²/miles² = 4.661 x 10⁹ m²
Calculate the volume of water
Volume = Rain * Area
=0.0254 m * 4.661 x 10⁹
Volume = 1.184 x 10⁸ m³
Calculate the number of kilo moles of H₂SO₄
kilo moles H₂SO₄ = [H₂SO₄] * Volume
=1.0 x 10⁻⁴ M * 1.184 x 10⁸ m³
kilo moles H₂SO₄ = 11,839 k mole
Calculate the mass of H₂SO₄
mass H₂SO₄ = kilo moles H₂SO₄ * MW H₂SO₄
= 11839 k mol * 98.07848 kg/kmol
mass H₂SO₄ = 1.16 x 10⁶ kg H₂SO₄