*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.

## Comments Solving Chemical Equilibrium Problems

## An open-source, web-based math solver for solving multi-variable.

In conclusion, the systematic method, in conjunction with SageMath, are powerful tools for solving multi-variable problems involving chemical equilibrium reactions. Although students initially encounter a steep learning curve, with practice they can become proficient at solving even relatively complex equilibrium problems.…

## ED 361 196 AUTHOR BouJaoude, Saouma TITLE Chemical Equilibrium Problems.

On chemical equilibrium problems was either conducted abroad or with high school students. Consequently, it is important to identify the conceptual chemical errors and the systematic mathematical errors that students commit when solving chemical equilibrium problems at the first year college level. In…

## Solving Equilibrium Problems Involving Bases

Equilibrium problems involving bases are relatively easy to solve if the value of K b for the base is known. The first step in many base equilibrium calculations involves determining the value of K b for the reaction from the value of K a for the conjugate acid.…

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## Equilibrium Constant and Reaction Quotient Example Problem

This example problem demonstrates how to use the reaction quotient to predict the direction of a chemical reaction towards equilibrium. Problem Hydrogen and Iodine gas react together to form hydrogen iodide gas. The equation for this reaction is H 2 g + I 2 g ↔ 2HIg The equilibrium constant for this reaction is 7.1 x 10 2 at 25 °C.…

## ChemTeam Equilibrium and Ksp

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## Solving Acid-Base Equilibrium Problems - dummies

Solving Acid-Base Equilibrium Problems. The acid and base equilibrium constant expressions describe the relationship between the amounts of reactants and products in aqueous acid-base systems. The concentration of water or any pure liquid or solvent or solid does appear in the equilibrium constant expression.…

## Developing a Problem Solving Strategy for Chemical Equilibrium Problems

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## THE NUMERICAL SOLUTION OF' THE CHEMICAL EQUILIBRIUM PROBLEM - UDSpace Home

Chemical systems by considering the "chemical equilibrium problem," the problem of determining the distribution of chemical species that minimizes the free energy of a system while conserving the mass of each of the chemical elements. Solutions to the chemical equilibrium problem pub- lished up to this time 4,53 apply to those problems for…