Smith acid rain

Robert Angus Smith analyzed rain water throughout the British Isles in the 19^th century. He found high levels of acidity in rain water in manufacturing cities and towns. The most acidic rain he reported in his 1872 book Air and Rain was found in Glasgow, Scotland. The reported value (representing an average of several individual samples) was 109.16 grains of sulphuric anhydride per gallon of rain water. Sulfuric anhydride is SO₃; dissolved in water, each mole of SO₃ becomes a mole of sulfuric acid, H₂SO₄.

1) Compute the molar concentration of SO₃, according to Smith's analysis. Note that one British grain = 0.0648 grams, and one British gallon = 4.546 liters.

2) Estimate the pH of Glasgow rain, assuming that each mole of SO₃ becomes one mole of H₂SO₄.

3) Elsewhere in his book, Smith noted that much of the acid found in the rainwater of towns was actually sulphurous acid (H₂SO₃) rather than sulphuric acid (H₂SO₄). What would the pH be if the [SO₃] concentration computed above was equivalent to H₂SO₃? The acid dissociation constant for

H₂SO₃ < ---- > H⁺ + HSO₃^-

is K_a = 1.54x10^-2 . (Hint: considering only the first dissociation constant is sufficient for this problem; however, assuming that equilibrium [H₂SO₃] is the same as initial [H₂SO₃] is not permissible.)

Reference

Robert Angus Smith, Air and Rain, the beginnings of a Chemical Climatology (London: Longmans, Green, & Co., 1872)

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