Alkalinity is a water characteristic that quantifies the capacity of water to accept hydrogen ions (H+). Alkalinity of natural water is mainly due to the presence of two forms of the carbonate ions that act as a buffer system. Alkalinity is a sum of ion concentrations (represented as brackets): Alkalinity = [HCO3-] + 2x[CO3(-2)] + [OH-] - [H+]. Since HCO3- and CO3(-2) carbonate ions exist in equilibrium, their fractions depend on pH of the solution. pH is the way to express the concentration of H+ such as pH=-log10[H+]. As an example, calculate alkalinity at pH 9 if the total molar concentration of carbonate ions in water is 0.1 M.

Calculate concentrations of H+ and OH- ions from pH of the solution: Note: that the notation ‘E-9’ means ‘ten in power -9’. [H+] = 1E(-pH) [OH-] =1E-14/[H+] In our example at pH=9: [H+]=1E-9, and [OH-] = (1E-14)/(1E-9) = 1E-5 = 0.00001

Calculate fractions of carbonate ions that depend 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)). K1 and K2 are the known constants that describe equilibria of carbonate ions (see reference): K1 = 4.45E-7; K2 = 4.69E-11. In our example: fraction (HCO3(-)) = (4.45E-7 x 1E-9)/((1E-9 x 1E-9) + 4.45E-7 x 1E-9 + (4.45E-7 x 4.69E-11)) = 4.45E-16/(1E-18 + 4.45E-16 + 2.087E-17) = 4.45E-16/4.669E-16=0.953 fraction (CO3(-2)) = (4.45E-7 x 4.69E-11)/((1E-9 x 1E-9) + 4.45E-7 x 1E-9 +(4.45E-7 x 4.69E-11)) = 2.087E-17/(1E-18 + 4.45E-16 + 2.087E-17) = 2.087E-17/4.669E-16 = 0.045

Calculate concentration of carbonate ions: [concentration] = [total concentration of carbonates] x fraction. In our example, total concentration of carbonates is 0.1 M. [HCO3-] = 0.953 x 0.1 M=0.0953 M [CO3(-2)] = 0.045 x 0.1 M =0.0045 M

Calculate Alkalinity. Alkalinity = [HCO3-] + 2 x [CO3(-2)] + [OH-]. Note: the concentration of H+ is very low (1E-9) and can be omitted from the equation. In our example: Alkalinity = 0.0953 + 2 x 0.0045 + 0.00001 = 0.1043 (eq/L) CO3(-2) ion can accept two hydrogen ions or two equivalents. This is why the CO3(-2) concentration is multiplied by 2 and units of alkalinity are equivalents per Liter (eq/L).