pH of rainwater in equilibrium with 1ppm SO2 in polluted air

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Homework Statement


Calculate the pH of rainwater in equilibrium with SO2 in a polluted air mass for which
the sulfur dioxide concentration is 1ppm.

SO2(g) +H2O(g) = H2SO3(aq) Kh=1M/atm
H2SO3 = HSO3- + H+ Ka=1.7x10-2M

Homework Equations


The Attempt at a Solution



I'm pretty lost for this one.

I converted SO2 1 ppm to 1E-6 atm. Set up EQ expression but have two unknowns.

1 M/atm = (1E-6 atm)[H2O] / [H2SO3]

I don't know where to go from here. Even if I figure can calculate H2SO3 I'll still have two unknowns in second reaction. I don't think water can be 1 M as it is not a liquid. Please can someone give me a suggestion where to start.
 
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First stage is to apply Henry's law to calculate concentration of acid.

Next stage is to calculate equilibrium of acid dissociation - you are given only Ka1, so you are probably expected to ignore fact that acid is diprotic.

Your unknowns in the second equation are combined by the reaction stoichiometry.

Try calculation of pH of a weak acid or a weak base or google ICE table.

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Borek said:
First stage is to apply Henry's law to calculate concentration of acid.

Oh yeah, guess the acid dissociation stuff slipped my mind. I haven't done much of henry's law but looking online does this go in the right direction?

I found pressure of water at 25 C to be 0.032 atm.

An equation showed me P[SO2] = (1 - 0.032 atm)(1E-6) = 9.7E-7 atm
1E-6 is 1 ppm of SO2

Then using henry's law constant

[SO2(aq)] = (1M/atm)(9.7E-7 atm) = 9.7E-7 M

I am not sure how to calculate acid from this though.

Once I get H2SO3 it is just Ka = [H+]2 / [H2SO3] correct?
 
Maharg said:
I found pressure of water at 25 C to be 0.032 atm.

Not sure if that step is necessary. You are not told it is 1 ppm of dry air.

Once I get H2SO3 it is just Ka = [H+]2 / [H2SO3] correct?

That may work if assumption that [HSO3-]=[H+] holds. You should check it after calculating pH.

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How do I take into account the water in the reaction then? Or how do I convert SO2 concentration to acid? That's what I don't I know how to do?
 
So would H2SO3 be 1E-6 M? Using that and doing the quadratic equation to calculate x I get 1E-6 and I don't think my answer makes sense. As when I check my answer I cannot get the same Ka value reported.