Could we reach a pH of 4.9 by blowing through straws?

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.   • You are adding as much as will dissolve, given its concentration in the exhaled air. The straw parameters are irrelevant. 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. 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. 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

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.