I think it might be a good idea to have a place dedicated to this issue where information is in one place and easier to search. Also, I welcome everyone with knowledge in this field to help us.
Accurate measurement of CO2 concentration in this hobby is not practical. What we sometimes use is pH drop. However, this is inaccurate due to the fact that atmospheric CO2 levels are location dependent. Industrial areas have higher CO2 levels than rural areas. The atmospheric CO2 levels vary greatly on location and time. For example, Pasadena Los Angeles from 376 to 513 ppm, Phoenix AZ 28%–76% increase, Harvard Forest 350 ppm and Boston 510 ppm CO2. Since the pH drop measurement is based on atmospheric CO2 level then
1.00 pH drop can indicate 36 or 57 ppm CO2
1.25 pH drop can indicate 64 or 101 ppm CO2
1.50 pH drop can indicate 113 or 180 ppm CO2
1.75 pH drop can indicate 201 or 319 ppm CO2
pH drop to CO2,
1.0 pH drop is 10x more CO2 than degassed
1.4 pH drop is 25x more CO2 than degassed
CO2 levels between 1.0 and 1.4 pH drop per location,
20 – 50 ppm CO2 rural
30 – 75 ppm CO2 town
40 – 100 ppm CO2 city
Probe calibration error of only 0.1 pH can make 5 – 26 ppm CO2 measuring error and drop of 1.4 pH can have 100% CO2 difference depending on location.
My point is the inaccuracy of the pH drop system, not the absolute value.
We know low atmospheric CO2 is at Harvard Forest 350 ppm, and high is at Pasadena Los Angeles 513 ppm. Let’s assume these atmospheric CO2 concentrations will create degassed water column equilibriums 3.50 and 5.13 ppm CO2. Then we inject CO2 to desired pH drop.
Drop pH CO2 ppm
degassed 7.23 3.50
1.00 6.23 35.33
1.25 5.98 62.83
1.50 5.73 111.73
1.75 5.48 198.68
Drop pH CO2 ppm
degassed 7.07 5.13
1.00 6.07 51.07
1.25 5.82 90.81
1.50 5.57 161.49
1.75 5.32 287.18
Atmospheric CO2 concentration fluctuations are well documented and can cause significant inconsistencies when using pH drop system to measure dissolved CO2 in injected aquariums.
Further details and theory.
First we look at Henry's law and the solubility of gases.
Gases will dissolve in liquids to an extent that is determined by the equilibrium between the undissolved gas and the gas that has dissolved in the liquid. The equilibrium constant for that equilibrium is:
k = px / Cx
k = the equilibrium constant for the solvation process
px = partial pressure of gas x in equilibrium with a solution containing some of the gas
Cx = the concentration of gas x in the liquid solution
The form of the equilibrium constant shows that the concentration of a solute gas in a solution is directly proportional to the partial pressure
of that gas above the solution. Meaning that doubling partial pressure of CO2 will double the concentration of CO2 in the liquid solution.
To get CO2 partial pressure
from CO2 concentration we look at Dalton's law of partial pressure.
The pressure exerted by an individual gas in a mixture is known as its partial pressure. Therefor the contribution of gas to the total pressure is its partial pressure. Since the gas molecules in an ideal gas behave independently of other gases in the mixture, the partial pressure of CO2 is the same pressure as if there were no other gases in the container. Therefore, if we want to know the partial pressure of CO2 gas in the mixture, we can completely ignore the other gases. The pressures are independent of each other.
For the result we can use Calculator of Dalton’s Partial Pressure
Enter moles to 200 and 400, while set Temperature to 273 K and Volume to 4539.45 L. The two results reveal that doubling atmospheric concentration of CO2 will double the partial pressure of CO2, see 100 and 200 kPa pressure results.
When doubling atmospheric concentration of CO2 doubles the partial pressure of CO2 then it also doubles the concentration of CO2 in the aquarium water column. Atmospheric variations of CO2 levels will significantly be affecting the final water column CO2 levels as seen above. These differences increase with higher pH drop due to the logarithmic scale of pH readings.
Continuous Carbon Dioxide Measurements in a Rural Area in the Upper Spanish Plateau
360 – 500 ppm CO2, Figure 6
Variations in Atmospheric CO2 Mixing Ratios across a Boston, MA Urban to Rural Gradient
Differences between the human and vegetation-dominated environments across Boston’s urbanization gradient were reflected in the annual standard deviations of CO2 mixing ratios in Boston (17.8 ppm), East Worcester (21.5 ppm), West Worcester (15.9 ppm) and Harvard Forest (14.0 ppm). Page 309
Harvard Forest 350 ppm and Boston 510 ppm CO2. Figure 3. Page 310
For example, mean peak city-center mixing ratios in Phoenix, AZ were 28%–76% higher than local background values, although this finding was likely influenced by highly stable atmospheric conditions resulting from local wintertime atmospheric inversion. Page 310
When integrated across the day, Vulcan mobile source emission estimates were 42.7% and 58.7% higher during the weekday compared to weekends in Boston and Worcester, respectively, which is consistent with elevated CO2 mixing ratios observed during weekdays at each site. Page 311
In this study we examined the spatial and temporal variations in atmospheric CO2 mixing ratios and carbon fluxes across Boston’s urbanization gradient. There were large differences in estimated biogenic and anthropogenic carbon fluxes across this gradient with total anthropogenic emissions ranging from 37.3 mg·C·ha−1·yr−1 in urban Boston to 1.5 mg·C·ha−1·yr−1 at the rural Harvard Forest. Despite the ~25-fold difference in local emissions, … . Page 321
Changes in mixing ratio and isotopic composition of CO2 in urban air from the Los Angeles basin, California, between 1972 and 2003
January 2002 through December 2003, Pasadena Los Angeles CO2 range 376 – 513 ppm. Table 2, page 5