This paper presents a model that uses only pH, alkalinity, and temperature to estimate the concentrations of major ions in rivers (Na+, K+, Mg2+, Ca2+, HCO3−, SO42−, Cl−, and NO3−) together with the equilibrium concentrations of minor ions and heavy metals (Fe3+, Mn2+, Cd2+, Cu2+, Al3+, Pb2+, and Zn2+). Mining operations have been increasing, which has led to changes in the pollution loads to receiving water systems, meanwhile most developing countries cannot afford water quality monitoring. A possible solution is to implement less resource-demanding monitoring programs, supported by mathematical models that minimize the required sampling and analysis, while still being able to detect water quality changes, thereby allowing implementation of measures to protect the water resources. The present model was developed using existing theories for: (i) carbonate equilibrium; (ii) total alkalinity; (iii) statistics of major ions; (iv) solubility of minerals; and (v) conductivity of salts in water. The model includes two options to estimate the concentrations of major ions: (1) a generalized method, which employs standard values from a world-wide data base; and (2) a customized method, which requires specific baseline data for the river of interest. The model was tested using data from four monitoring stations in Swedish rivers with satisfactory results.