Calc pH of Rainwater w/ SO2: 1ppm in Polluted Air Mass

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Discussion Overview

The discussion revolves around calculating the pH of rainwater in equilibrium with sulfur dioxide (SO2) in a polluted air mass, specifically at a concentration of 1 ppm. The conversation includes aspects of chemistry such as Henry's law, acid dissociation, and the stoichiometry of the reactions involved.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about how to set up the equilibrium expression and mentions having two unknowns in their calculations.
  • Another participant suggests applying Henry's law to calculate the concentration of the acid and notes that only the first dissociation constant (Ka1) is provided, implying that the diprotic nature of the acid can be ignored for this problem.
  • A participant calculates the concentration of dissolved SO2 using Henry's law and questions how to proceed to find the concentration of H2SO3.
  • There is a discussion about whether the pressure of water at 25°C is necessary for the calculations, with one participant suggesting it may not be relevant if the air is not specified as dry.
  • One participant proposes that the total concentration of acid can be assumed to be that of dissolved SO2.
  • Another participant questions the calculation of H2SO3 concentration and expresses doubt about the results obtained from the quadratic equation used to find the concentration of H+. They note a discrepancy with the reported Ka value.
  • A later reply suggests that a pH of 6 appears reasonable based on the calculations presented.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and approaches to the problem, with no consensus reached on the correct method or final answer. Disagreements arise regarding the relevance of certain calculations and assumptions made about the system.

Contextual Notes

Participants mention the need to consider the stoichiometry of the reactions and the assumptions made about the concentrations of species involved, particularly regarding the relationship between H2SO3, HSO3-, and H+.

Maharg
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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?
 
Assume total concentration of acid is that of dissolved SO2.

Otherwise - calculating pH is a rather wide subject:

lectures on pH calculation.
 
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.
 
pH 6 looks OK to me.

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