Modeling chemical systems is a valuable way to learn and verify knowledge through measured data. In this Mathcad document, the chemical system is a river, where several known and unknown chemical processes take place. Modeling the pH variation in rivers is an interesting exercise, not only from an environmental point of view but also because it makes use of basic physical, chemical, biological, and numerical principles obtained through undergraduate courses.

No special knowledge of Mathcad is required. Small exercises within the document show students how to solve equilibrium problems with the simultaneous equation solver and differential equations by an iterative matrix setup. Additional help can easily be found in the Mathcad menu.

The pH model is built systematically using theory and logical assumptions to include or exclude different parameters and processes. After that, a short discussion shows how the initialization values were found.

The final model shows how equilibrium problems can be solved in discrete steps for a dynamic system using the simple assumption that equilibrium reactions are much faster than transport phenomena and biological transformation. Furthermore, the model can predict the effect on pH of changing temperature, ionic strength, buffer capacity, and biological transformation rates.

Figure 1. Modeling pH in Natural Waters. The variation of pH in the Simested River in October 1998.