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Sage Math Cell code to solve the equations developed in Figure 4.This code allows for the direct calculation of the p H (the last solution in set 2).Solutions to Example 1 calculated from equations in Figure 1 and Sage Math Cell code in Figure 2.
This method is an extremely versatile alternative to ICE tables as it allows one to solve for multiple unknowns simultaneously while avoiding simplifying approximations.
For example, the systematic method accounts for the autoionization of water in problems involving weak acid and weak base equilibria; in contrast, most general chemistry textbooks arbitrarily avoid using dilute solutions of acids and bases and instead choose relatively concentrated solutions of acids and bases with comparatively large values in order to ignore the contributions of the autoionization of water.
After assigning variables to each species, the student defined the input (initial) and output (equilibrium) concentrations, along with the known expression and mole balance equations for hydrogen and iodine.
Below is the corresponding Sage Math Cell code for the above problem (Figure 2): Figure 2.
Even given this initial steep learning curve, however, we find this to be an excellent first introduction to coding, which students will likely encounter at some other point in their academic or work careers.
Within 2-3 class periods, students are ready to move on to more complex equilibrium systems (, p H buffers and acid-base titrations), where they are required to account for each reaction occurring in aqueous solution.Because Sage Math can also complete dilution and p H calculations, students do not have to rely on multiple computing devices.Additionally, once students have written code for the first step of a multi-part problem, they can easily modify the code to incorporate any new parameters.Students initially face a steep learning curve, but after about a week are able to solve fairly complex equilibrium problems in just minutes.We find this to be an excellent first introduction to coding, which students will likely encounter elsewhere in their academic or work careers.Natalie Ulrich, College of Arts and Sciences, Maryville University, St. Thomas Spudich, College of Arts and Sciences, Maryville University, St. Eileen Kowalski, Department of Chemistry and Life Science, United States Military Academy, West Point, NY. Kalainoff, Department of Chemistry and Life Science, United States Military Academy, West Point, NY.We discuss our use of Sage Math Cell, a web-based, open-source math-solver, in conjunction with the systematic method, to solve problems involving multi-variable equilibrium reactions while avoiding the use of simplifying approximations.Table 1 lists p H values of weak acid solutions calculated using both the systematic method and ICE tables.Acetic acid is a commonly used example in textbooks because it has a relatively high value.Even at very dilute concentrations, the respective calculated p H values are equivalent up to three decimal places.The calculated p H values start to vary significantly, however, for an acid such as hypoiodous acid ( Table 1.