FAQs

How to calculate alkalinity from pH

Step 1. Consider 2 equilibriums for carbonate ions in water.

CO2 + H2O = HCO3(-)+ H+;
K1 = 4.45E-7 (notation "E-7" means "10 in power -7").
HCO3(-) = CO3(-2) + H+;
K2 = 4.69E-11.
Note: K1 and K2 are equilibrium constants (see Reference) of the corresponding reactions that will be used in Step 3.

Step 2 Calculate concentration of H+ and OH- ions. 
[H+] = 1E(-pH)
[OH-] =1E-14/[H+]
In the example at pH=10; [H+]=1E-10, and [OH-]=(1E-14)/(1E-10)=1E-4=0.0001.

Step 3. Calculate fractions of carbonate ions that depends on pH:

Fraction (HCO3(-)) = (K1 x [H+]) / (([H+] x [H+]) + (K1 x [H+]) + (K1 x K2))
Fraction (CO3(-2)) = (K1 x K2) / (([H+] x [H+]) + (K1 x [H+]) + (K1 x K2))
Note: K1, K2 are the constants defined in Step 1.
In the example:
fraction (HCO3(-))=(4.45E-7 x 1E-10)/((1E-10 x 1E-10) + 4.45E-7 x 1E-10 +(4.45E-7 x 4.69E-11)) = 4.45E-17/(1E-20 + 4.45E-17 + 2.087E-17)=4.45E-17/6.537E-17=0.681
fraction (CO3(-2))=(4.45E-7 x 4.69E-11)/((1E-10 x 1E-10) + 4.45E-7 x 1E-10 +(4.45E-7 x 4.69E-11)) = 2.087E-17/(1E-20 + 4.45E-17 + 2.087E-17)= 2.087E-17/6.537E-17 = 0.319.

Step 4. Calculate concentration of carbonate ions

[concentration] = [total concentration carbonates] x fraction.
In the example, total concentration of carbonates is 0.1 M.
[HCO3-] = 0.681 x 0.1 M=0.0681 M
[CO3(-2)] = 0.319 x 0.1 M =0.0319 M

Step 5, Calculate Alkalinity

Alkalinity = [HCO3-] + 2 x [CO3(-2)] + [OH-].
Note: The concentration of H+ is low (1E-10) and can be omitted from the equation.
In the example:
Alkalinity = 0.0681 + 2 x 0.0319 + 0.0001=0.132 (eq/L).
CO3(-2) ion can accept 2 hydrogen ions or 2 equivalents. This is why, the CO3(-2) concentration is multiplied by 2 and units of alkalinity are equivalents per liter (eq/L).