Chemistry

Problem

The average concentration of

\text{SO}_2

in the atmosphere over a city on a certain day is 10 ppm, when the average temperature is 298 K. Given that the solubility of

\text{SO}_2

in water at 298 K is

1.3653 \text{ mol litre}^{-1}

and the

pK_a

\text{H}_2\text{SO}_3

is 1.92, estimate the pH of rain on that day. (IIT 2000)

Intuitive explanation

When $\text{SO}_2$ dissolves in rainwater, it forms a weak acid ( $\text{H}_2\text{SO}_3$ ) whose ionization depends on both the dissolved gas concentration and its acid strength. The key is to use Henry's Law to find how much $\text{SO}_2$ actually dissolves from the 10 ppm atmosphere, then treat the resulting solution as a weak acid equilibrium using the given $pK_a$ . The pH emerges from balancing the ionization of this weak acid against its solubility constraint.

Intuitive explanation

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