Abstract
Calculating the pH values of carbonic acid solutions is an important task in studies of chemical equilibria in freshwater systems, with applications to environmental chemistry, geology, and hydrology. These pH values are also highly relevant in the context of climate change, since increasing atmospheric CO(2) affects the concentration of dissolved carbon dioxide and carbonic acid, collectively denoted as [H(2)CO(3)*] = [H(2)CO(3(aq))] + [CO(2(aq))]. Solving equilibrium systems to obtain analytical functions is particularly useful when such functions are required, for example, in data fitting. We show here that, although exact or near-exact solutions typically result in third- to fourth-order equations that must be solved numerically, reasonable approximations can be derived that lead to analytical second-order equations. In this framework, the chosen approximations need to meet the boundary conditions of the systems, particularly for c(T) → 0 and for high c(T) values (where c(T) = [H(2)CO(3)*] + [HCO(3)(-)] + [CO(3)(2-)]). Finally, we provide exact solutions for a closed system containing both H(2)CO(3)* and alkalinity, which enables the description of virtually any aquatic environment without assuming equilibrium with atmospheric CO(2). Implications for pH calculations in natural waters are also briefly discussed.