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According to Wikipedia's article on Breathing:

The permanent gases in gas we exhale are 4% to 5% by volume more carbon dioxide and 4% to 5% by volume less oxygen than was inhaled.

If I started with a clean beaker of pure water and measured the pH carefully and quickly, I might get a value close to 7.0. If I left it out in the air for a while, far from concentrated sources of pollution, it would equilibrate with the local CO2 concentration which would be 300 to 500 ppm depending on local variables and natural sources (people, plants), and that would lead to a (carefully) measured pH below 6, and probably somewhere around 5.8 or 5.7. Is that about right so far?

Now suppose that I then took turns with lab mates and constantly blew bubbles into the water through long straws that contained some charcoal and other filters to absorb organics from my breath, leaving only the added 4 to 5% CO2 from our respiration.

If the average area of all the bubbles present was about the same or greater than the average area of the water exposed to the air, would I be roughly correct in using a number like 0.02 or 0.03 atmospheres for the CO2 partial pressure in the plot as displayed below, and getting a pH of about 4.9?

Is this what would happen, or are there significant effects that I've neglected?

related: answer to Formation of carbonic acid from breath?

Screenshots from Effect of Dissolved CO2 on the pH of Water, Byck, Harold T., Science 19 Feb 1932, Vol. 75, Issue 1938, pp. 224, DOI: 10.1126/science.75.1938.224.

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uhoh
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    You are adding as much as will dissolve, given its concentration in the exhaled air. The straw parameters are irrelevant. – Ivan Neretin Jun 14 '17 at 12:18
  • Just curious. How long would it take for the CO2 to equilibrate with the water? It's OK if u don't have the answer. – Tan Yong Boon Jun 14 '17 at 13:30
  • @TanYongBoon I don't know, I'd guess it would take more than five minutes and less than a day to get most of the way there, so say split the difference on a log scale and call it 2 hours? That's why I said we! – uhoh Jun 14 '17 at 13:38
  • You would reach the saturation point of $\ce{CO2}$ in water because the simplified scenario is that your are continuously sparging $\ce{CO2}$ into your beaker. What is being ignored is gas diffusion and bubble dynamics at the bubble-water interface. – J. Ari Jun 14 '17 at 17:08
  • @J.Ari can you make a statement about the resulting pH when saturated? The concentration of dissolved CO${}_2$ is only part of the problem. Are you agreeing or disagreeing with the calculations and conclusion of the attached paper? – uhoh Jun 14 '17 at 17:31
  • If you follow the link below, there is another derivation presented that shows the ultimate pH as 5.65. I don't follow why you say the dissolved $\ce{CO2}$ is only part of the problem. In the simplified case, this is an equilibrium problem only so the dissolved content is the only major factor.

    http://ion.chem.usu.edu/~sbialkow/Classes/3650/Carbonate/Carbonic%20Acid.html

     – J. Ari Jun 15 '17 at 11:35
  • @J.Ari the gas is 5% CO2, 95% O2+N2+Ar... It's not like there is a bottle of pure CO2 bubbling through the water. The complicating factor is that the water has one interface with 5% CO2 (0.05 atm partial pressure) and another interface with roughly 0.05% CO2. In any event, the solution would not be saturated with CO2. I'm thinking of simplifying the question and removing the dual-interface issue which is interesting but should probably be isolated and asked separately, unless you'd like to post an answer as-is? – uhoh Jun 15 '17 at 12:14
  • Seeking clarity...in your second comment, you say you are looking at this is like an equilibrium problem. So, given the orders of magnitude difference between the concentrations of $\ce{CO2}$ in the breath vs the air that you quoted, the equilibrium case will be dominated by the breath both from a thermodynamics standpoint and a mass transport standpoint. – J. Ari Jun 15 '17 at 13:37
  • @J.Ari Please post that as an answer! It's the beauty of the stackexchange system that answers can be voted on. I don't think that statement is necessarily true. But if you include it as the basis of an answer, defend it with an equation or a link or a fundamental principle and several chemist up vote it, it will be more convincing to me. Right now it is hard for me to distinguish correct comments from incorrect comments on this subject. Go for it, don't be shy! Thanks! – uhoh Jun 15 '17 at 15:01

1 Answers1

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See here for partial pressure of $\ce{CO2}$ from exhaled breath that I used (28 mmHg = 0.037 atm). I am assuming Henry's law is applicable to calculate:

${7.4*10^{-4} M} = [\ce{CO2}_{(aq)}]$

Used Henry's Law Constant of $2*10^{-3} \frac{M}{atm} $

See here for equilibrium definition and equilibrium constant value ($K=4.45*10^{-7}{M}$) I used: $$K = \frac{[H^+]^2}{[\ce{CO2}_{(aq)}]}$$ I then solved for pH from the above equation after rearranging to solve for $[H^+]$, and got a pH of 5.2; so I don't think we can achieve pH of 4.9 from only breathing air into the beaker.

J. Ari
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  • Thanks for your post! Can you add the numerical value for the equilibrium constant you used here within your answer itself please? Links go dead all the time, and if that link breaks your answer is no longer useful, and people don't have to go opening up new windows and hunting for a number somewhere. Just type the number inside your answer and it will stay there more reliably for future users and be more easily findable for me too! Also it will be interesting to see if your calculation also produces about pH 5.7 for 350 or 400 ppm CO2. – uhoh Jun 20 '17 at 15:30
  • @uhoh Did you have a look at https://en.wikipedia.org/wiki/Carbonic_acid? pKa (first dissociation) = 3.6, overall (including CO2) 6.3; and according the lower part of the page & table the statement that fizzy bottled water (of 2.5 atm pressure) reaches even pH 3.7 ... – Buttonwood Jun 20 '17 at 15:39
  • @Buttonwood update That's pretty surprising, I hadn't looked there but I have now! I think there is a lot I can learn about chemical equilibrium by just focusing on the CO2/H2O system. Thanks! You are right to guess that part of my interest is of the form how low can it go? but the other part is to ask about the complete experiment. Thus the title "Could we reach a pH of 4.9 by blowing through straws?" & discussion of charcoal etc. I'm going to go purée some red cabbage soon for indicator and go grab a bottle of fizzy water and have some fun! :) Mmmm... fizzy purple cabbage water. – uhoh Jun 21 '17 at 05:52
  • Thanks for the updated answer, looks good! For this one let's just assume there's a cover over the glass so that the CO2 concentration in the air above the liquid is the same as the air in the bubbles, so there's no trouble with dual interfaces. I'll read some more about that problem, and ask a separate question if it's not answered here already. Thanks! – uhoh Jun 21 '17 at 05:56