Equation for seawater pH vs ambient air CO2 levels?

rkpetersen · Feb 11, 2018

Is there an equation, table, chart, etc that correlates CO2 level in ambient air in ppm with the expected equilibrium pH of seawater kept in that air? I've done a brief search but haven't found this information.

I'm curious, because like many, I have a relatively low tank pH, despite ample circulation, skimming, and very low dissolved organic levels. I got a CO2 monitor, and my indoor CO2 is indeed elevated, at around 600 ppm. Not at all extreme for indoor air, but still, 50% higher than nominal outdoor CO2 levels. Is this sufficient to cause a pH depression of 0.2-0.3 units?

I can't easily run an outside line, and I'm not enthusiastic about starting up CO2 scrubbing again, given the need to change media very frequently and the inability to regenerate said media easily. But I may reconsider one or both strategies anyway.

Randy Holmes-Farley · Feb 11, 2018

I show the equation in this article (equation 2, copied below), and perhaps more usefully, figures 1 and 2 shows it graphed out for a few scenarios

Chemistry And The Aquarium: The Relationship Between Alkalinity And pH ? Advanced Aquarist | Aquarist Magazine and Blog
http://www.advancedaquarist.com/2002/5/chemistry

Carbonate alkalinity (Ac) is mathematically defined as:

1. Ac = [HCO3-] + 2[CO3--]

Where [X] means the concentration of species X. Carbonate (CO3--) is counted twice because it contributes two units of alkalinity for each unit of concentration. The relationship between the amount of bicarbonate and carbonate to pH is well defined if the system is at equilibrium with the atmosphere. Substituting these known relationships into equation 1, we get:

2. Ac = (K1KHPCO2 / [H+]) + 2(K1K2KHPCO2 / [H+]2)

where pCO2 is the concentration CO2 in the air. Current carbon dioxide concentrations are around 350 ppm and have been rising with time, from less than 300 ppm in preindustrial times. KH is the Henry's law constant for CO2(which describes the solubility of CO2 in water from the air to form carbonic acid, H2CO3), K1 is the first dissociation constant for H2CO3 (describing the dissociation of H2CO3 to HCO3-), and K2 is the second dissociation constant for H2CO3 (describing the dissociation of HCO3- to CO3--).

It is not easy to look at equation 2 and see any particular relationship between alkalinity and pH, but it is easy to see graphically. Using equations 2 and 3 (the definition of pH), we can plot the relationship graphically (Figure 1).

Randy Holmes-Farley · Feb 11, 2018

rkpetersen said:
Is there an equation, table, chart, etc that correlates CO2 level in ambient air in ppm with the expected equilibrium pH of seawater kept in that air? I've done a brief search but haven't found this information.

I'm curious, because like many, I have a relatively low tank pH, despite ample circulation, skimming, and very low dissolved organic levels. I got a CO2 monitor, and my indoor CO2 is indeed elevated, at around 600 ppm. Not at all extreme for indoor air, but still, 50% higher than nominal outdoor CO2 levels. Is this sufficient to cause a pH depression of 0.2-0.3 units?

I can't easily run an outside line, and I'm not enthusiastic about starting up CO2 scrubbing again, given the need to change media very frequently and the inability to regenerate said media easily. But I may reconsider one or both strategies anyway.

You can see the effect in Figure 2 of 350 ppm going to 700 ppm, so 600 ppm is just a bit closer to the 350 graph from the 700. It is substantial. More than 0.2 pH units, less than 0.3.

Randy Holmes-Farley · Feb 11, 2018

As a rule of thumb, a doubling of CO2 is a drop of 0.3 pH units.

rkpetersen · Feb 11, 2018

Thanks Randy. That certainly sounds like the primary/only source of my low pH.

Perhaps I should rename my aquarium 'Future Earth Ocean Reef'.;Meh

rkpetersen · Feb 11, 2018

Found this graph adapted from an older Science article, although it's probably still more or less valid. Surprisingly easy to unintentionally acidify an aquarium, or an ocean.