Ongoing acidification of the global ocean necessitates a solid understanding of how biogeochemical processes are driving proton cycling and observed pH changes in natural waters. The standard way of calculating the pH evolution of an aquatic system is to specify first how biogeochemical processes affect total alkalinity, followed by the solution of a nonlinear acid-base equilibrium equation system. This approach, however, does not explicitly reveal how individual biogeochemical processes contribute to the overall proton cycling in the system. Here, we provide an extension of the classical acid-base theory that explicitly quantifies the proton production/consumption by a given process, showing that it can be calculated as the proton-cycling sensitivity times the rate of the biogeochemical process at hand. The proton-cycling sensitivity emerges as a central concept in acid-base chemistry of natural waters and can be further decomposed as the ratio of a stoichiometric coefficient for the proton over the buffer factor. The stoichiometric coefficient for the proton expresses how many moles of protons would be produced per mole of reaction if buffering was absent, and is obtained by bringing the reaction equation of the process into a specific form: the fractional reaction equation at ambient pH. The buffer factor quantifies how acid-base systems attenuate the proton production/consumption by biogeochemical processes, and is identified as the negative of the partial derivative of the total alkalinity with respect to the proton concentration. Applying this new concept to an acidification scenario for the future surface ocean, we illustrate its potential to analyze proton cycling in natural waters. Thereby we show that a reduced buffer factor due to anthropogenic carbon input makes the ocean more vulnerable to any process influencing the pH.