Natural rain water is slightly acidic (pH = 5.6) since there is carbon dioxide in the atmosphere that dissolves to make carbonic acid.
What would be the pH of rainwater if carbon dioxide in the atmosphere was doubled to 800 ppm?
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3$\begingroup$ If we double the concentration of the carbonic acid (which probably isn't quite correct, so I'm just putting as a comment - feel free to ask at the chemistry board for more accuracy on PH), but a doubling of the H+ would yield a pH of roughly 5.3, as .3 is very close to the log of 2, which corresponds to doubling (or halving) the concentration. Cutting the CO2 in half would yield about 5.9. Rain can get quite a bit more acidic than 5.3 though if there are sulfates in the air, (acid rain/burning unscrubbed coal), NO (produced by lightning) or a recent volcanic eruption. $\endgroup$ – userLTK Apr 30 '16 at 15:49
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4$\begingroup$ Generally, I agree with @userLTK but I am not sure whether the "natural rain water" pH of approx. 5.6 does not already include the impact of dissolved atmospheric acids (sulfate, nitrate). Therefore, I would see 5.3 as an lower bound (assuming that anthropogenic emissions of NOx are not increased). I will have a look in some books on Monday at work if there is no answer till then. $\endgroup$ – daniel.neumann Apr 30 '16 at 22:02
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$\begingroup$ butane.chem.uiuc.edu/pshapley/GenChem1/L23/web-L23.pdf $\endgroup$ – DavePhD May 3 '16 at 17:22
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$\begingroup$ @daniel.neumann Good point. I didn't account for the fact that it might be more than just the CO2 bringing the PH to 5.6. $\endgroup$ – userLTK May 12 '16 at 9:03
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"Cutting the $CO_2$ in half would yield about 5.9."
(A valid approach because we expect reversibility in chemistry and physics.)
[pH of 5.9 for 200 ppm $CO_2$]
Atmospheric $CO_2$ of 200 would be about that of the last glacial maximum. So most of the difference between pure water at pH 7 and 5.9 would seem to be other gases dissolved in air.
Side note: A drop to much below 200 ppm $CO_2$ would extinguish all life on Earth except those that live at geothermal vents at the bottom of the ocean, because they do not use $CO_2$.
If a linear relationship is assumed, then if there were 800 ppm of $CO_2$, rain water would have a pH of 5.0. Though, if we assume the log relationship for concentrations that userLTK mentions in the comments, it would be a pH of 5.3.
Bouttes, N., D. Paillard, D. M. Roche, V. Brovkin, and L. Bopp (2011), Last Glacial Maximum CO2 and δ13C successfully reconciled, Geophys. Res. Lett., 38, L02705, doi:10.1029/2010GL044499.
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4$\begingroup$ This doesn't answer the question. This answer discusses the effect of half the current CO2 level, whereas the question asks about the effect of doubling the currently CO2 level to 800 ppm. $\endgroup$ – Fred Sep 2 '17 at 14:55
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$\begingroup$ I'm glad you want to participate, but this should have been a comment . You can get enough rep to comment on any post pretty easily and going through the help center can show you how. $\endgroup$ – Spencer Sep 2 '17 at 15:37
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3$\begingroup$ @Spencer, given that it's sourced and appears to describe what he found, it seems more fitting as an answer... except as Fred said, it's the inverse question the poster asked about $\endgroup$ – JeopardyTempest Sep 2 '17 at 20:28
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$\begingroup$ Added estimates so that the post actually answers the question. $\endgroup$ – farrenthorpe Sep 17 '17 at 3:22
