CO2 from KH and pH: the formula, the chart and where it breaks

The chemistry in one line

When CO2 dissolves in water, part of it reacts to form carbonic acid, which gives up a hydrogen ion and becomes bicarbonate. At equilibrium the three are tied together by the first dissociation constant of carbonic acid, K1:

[CO2] = [HCO3⁻] × 10^(pK1 − pH)

If you know how much bicarbonate is in the water and you measure pH, you can solve for CO2. Carbonate hardness (KH) is the bicarbonate measurement: it is a measure of alkalinity, the water’s capacity to neutralize acid, which in most fresh water comes from bicarbonate and carbonate ^[2].

Turning it into aquarium units

Three conversions get from the equation to the familiar formula:

1. KH to bicarbonate. One German degree is 10 mg/L of CaO equivalent, or 17.848 mg/L as CaCO3 ^[3]. As alkalinity that is 0.35665 mmol/L of bicarbonate per dKH.
2. Moles to milligrams. CO2 has a molar mass of 44.009 g/mol ^[4]; 0.35665 × 44.009 = 15.696.
3. The constant. pK1 depends on temperature. Plummer and Busenberg’s 1982 evaluation of the CO2–water system gives a temperature function for it ^[1]: pK1 = 6.382 at 20 °C, 6.352 at 25 °C and 6.337 at 28 °C.

Put together:

CO2 (mg/L) = 15.696 × KH × 10^(pK1 − pH)

At 25 °C that equals 3.53 × KH × 10^(7 − pH). The charts printed on aquarium test kits and in many books use 3 × KH × 10^(7 − pH), so at the same KH and pH they read about 15 % lower. Both are estimates for an ideal, dilute solution. The CO2 calculator shows the two side by side and the effect of temperature.

A worked example

KH 4 dKH, pH 6.8, 25 °C:

• Temperature-corrected: 15.696 × 4 × 10^(6.352 − 6.8) = 22.4 mg/L
• Chart shortcut: 3 × 4 × 10^(7 − 6.8) = 19.0 mg/L

Turned around, the pH needed for a target at KH 4 and 25 °C is 7.15 for 10 mg/L, 6.85 for 20 mg/L and 6.67 for 30 mg/L. Each 0.1 pH unit is a factor of 1.26 in CO2, and each full unit a factor of 10.

Where the estimate breaks

The formula assumes that bicarbonate is the only thing holding the pH where it is. Anything else that acidifies or buffers the water makes the pH lower than CO2 alone would, and the formula reports the difference as CO2:

• Humic and tannic acids from wood, peat and leaf litter.
• Aqua soils that lower pH; Tropica states its Aquarium Soil does exactly that during the first weeks (root tabs and nutrient substrates).
• Phosphate. EI’s author notes that very high phosphate levels can influence alkalinity ^[10], and phosphate buffers are sold to fix pH.
• pH products of any kind.

Measurement adds its own error. A pH reading that is 0.1 too low makes the estimate 26 % too high; a liquid color test read in 0.2 steps cannot do better than about ±25 %. CO2 also changes through the day as injection runs and plants photosynthesize, so one reading describes one moment.

These are the reasons Aquasabi’s wiki calls CO2 tables based on pH and KH “rather theoretical” and recommends a permanent test instead ^[8]. A drop checker sidesteps the tank’s other buffers because its indicator sits in its own reference water and only exchanges gas with the tank ^[9]; the drop checker guide applies the same formula to it.

Targets

How much CO2 to aim for depends on whom you ask, and even one grower publishes different figures on different pages:

Source	Lower group	Middle group	Demanding group
Tropica plant pages	low need	medium 6–14 mg/L	high approx. 15–25 mg/L
Tropica fertilizer guide	3–5 mg/L “better than nothing”	Medium about 10–15 mg/L	Advanced 15–30 mg/L
Tropica CO2 System Nano page	Easy approx. 3 mg/L	Medium approx. 10 mg/L	Advanced approx. 25 mg/L
EI (Tom Barr)			about 30 mg/L suggested

Sources: ^{[5, 6, 7, 10]}. The grower light ratings guide looks at these differences in more detail.

Tropica’s own method is the one this page describes: measure KH, then add CO2 until the pH in its KH/pH table is reached ^[6]. That works well in water with no other buffers, and the caveats above apply in the same way.