# CO²-Calculation from KH and pH

In our tanks a complex equilibrium between the water parameters CO², KH and pH is present. Within this small article we will discuss the mathematics between these relations.

### Introduction: Acid chemistry in a nutshell

Dissolving an acid in water will ionize it. For strong acids like HCl a complete ionization is happening leading to separation into H+ and Cl. In chemistry this is emphasized with an arrow to the right side:

`HCl ⇒ H+ + Cl-`

In our aquarium we have dissolved CO2:

`H2O + CO2 ⇒ H2CO3`

In contrast to strong acids the dissolved H2CO3 is a weak acid and only partially ionized. Therefore a part is present as H2CO3 and another part ionized as H+ und HCO3. Since both parts are in equilibrium this state is represented with an arrow in both directions:

`H2CO3 ⇔ H+  + HCO3-`

As discussed the system is in equilibrium and thus there is a fixed ratio between these two sides:

`const. = K = ([H+] * [HCO3-]) / [H2CO3]`

With [H+ ], [HCO3 ] and [H2CO3] as the concentrations of the Ions respectively.

### The aquarium as chemical buffer

The ph Value of such a system can be calculated with

`pH = pK + log([HCO3-] / [H2CO3])`

The value pK is dependet on the acid and temperature. For H2CO3 the values are shown in the following table:

Temperature 15° 20° 25° 30°
pK 6.42 6.38 6.35 6.33

Since the variation is only small with the temperatures in a typical aquarium we can just assume a pK von 6.35. If the concentration of [HCO3 ] and [H2CO3] is equal in size the formula can be solved to:

`pH = 6.35 + log([HCO3-] / [H2CO3]) = 6.35 + log(1) = 6.35`

pH-values above 6.35 result from more hydrogencarbonate HCO3 than H2CO3 -vice versa.

### The relationship with carbonate hardness (dKH)

The hydrogencarbonate HCO3 is exactly the salt that defines the german carbonate hardness dKH.

Therefore the pH-value can also be expressed with the carbonate hardness:

`pH = 6.35 + log(15.664 * dKH / CO2)`

In the formula above we can input the carbonate hardness and the amount of COin mg/l to calculate the corresponding pH value.

As example, for a carbonate hardness of 8° and an amount of 10mg/l CO2 a pH-value of 7,4 is present in the tank.

### CO²-addition to change the pH-value

When COis dissolved in the water then the logarithm is getting smaller and thus the pH-Value is smaller. An result directly seen from the formula is that with higher carbonate hardness a higher amount of CO2 is needed to change the pH.

We hope you got a good overview on the chemistry in our tanks. If you have questions dont hesitate to contact us.