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# Sample Proposal: Quantitative Reasoning

## Jackson School of Geosciences

### GEO 476M: Chemical Hydrogeology

Please direct all questions about the flag proposal process to the Center for the Core Curriculum].

Department of Geological Sciences

**Please describe specifically the quantitative skills students will learn and apply in the course.**

This course uses a combination of theory and modeling to learn chemistry, and I use various geochemical models as well as the students own spreadsheet model to speed up reactions to see what could or should happen. The students apply their math skills up to basic calculus to be able to understand the basics of thermodynamics and kinetics as it applies to aquatic systems. The students then use these thermodynamic principles combined with mass balance and charge balance equations to solve acid-base problems that are the backbone of all aquatic chemical reactions. These are initially done with pencil, paper and calculator in problem sets, during weekly recitation, and also in class, and at least 20% of every lecture period is devoted to setting up chemical equations and solving for the master variable (e.g. pH). This is done in real time in class, and I use the classic Socratic Method in this class to initially help the students pin down the problem and the approach, and then require the students to come to the board to work through the problem. An important element in this approach is the simplification of the problem using ‘assumptions’ to eliminate variables – and this is probably the hardest skill in the first havl of the class. Here they need to not only know the math, but they also must understand the relationship between the variables and have a feel for the initial state of the system so that they can confidently eliminate variables to be able to work the problem. As the class progresses the students code these equations into their own personal spreadsheet model that does the same basic task as the typical public-domain geochemical equilibrium models, but in this way the students learn how these models work. By the end of the class the students will be able to solve the same problems as above without simplification through assumptions by working in minimization (Newton-Raphson modified for a spreadsheet) to arrive at solution for mineral solubility and element speciation. Finally, all of the students also use the pre-packaged geochemical models to do forward and inverse modeling of the reaction paths that we initially estimated in class using pencil and paper. The entire course is built around this learning model of quantitatively solving chemical problems.

**On what kinds of real-world problems will students use quantitative skills?**

This course is applied chemistry, and uses fundamental chemical principles to understand and predict how groundwater chemistry evolves. Every assignment and problem set involves potential questions that will be faced by professionals in the field of hydrogeology and environmental sciences. Example problems include predicting the rate of mineral dissolution and porosity development using kinetic rate equations and mass-volume relationships, predicting the reactions that will occur when a water is contaminated, or when microbes degrade organic material, or predicting the mobility of toxic elements such as arsenic in groundwater (we discuss in detail the chemistry of arsenic in Bangladeshi groundwater, for example). The students use a combination of traditional thermodynamic equilibrium modeling to speciate the water and describe the rock-water relationship, and combine that with forward and inverse reaction path modeling using commonly used packaged models.

**Describe typical assignments related to Quantitative Reasoning.**

A typical recitation assignment will be to solve for all of the major carbonate species concentrations in Barton Springs given only the pH and an assumption of equilibrium with limestone. This involves several different equations, and most important, several critical assumptions to simplify the system. The students then check their answers against the geochemical model output for the same system, and evaluate where the potential errors are. The final project for the course is an in-depth evaluation of the geochemical evolution of groundwater in a specific aquifer in Texas. The students work on this project throughout the semester, and each recitation session has aspects that are applied to the project. The student’s individual spreadsheet model is used extensively in the project, as are the packaged geochemical codes PhreeqC and Geochemists Workbench. This project is not about the writing, and I have not applied for a writing flag for this course. The Chem-Hydro project is about the chemistry – the students must show that they understand how to critically and quantitatively evaluate the chemical reactions along a flowpath, present hypotheses based on the available data, and then test those hypotheses using the chemical relationships learned for the course.

**Please explain how at least one-half of the course grade is based on content related to Quantitative Reasoning.**

That’s all this course is. There are no writing assignments, there are no book reports or proposals or reviews. Every assignment is quantitative chemistry, or modeling, or learning the sources of data to use for the chemistry or modeling. Only 5% of the grade (class participation) is not directly tied to quantitative aquatic chemistry.

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