Weak Acid Equilibrium

Michael Stapleton, Slippery Rock University

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Students are asked to calculate the pH of a weak acid aqueous solution. The problems involve a series of generic acids with assigned equilibrium constants (Ka) and total concentrations (Ct). Initially, students are required to hand calculate all problems by algebraic manipulation of the mathematical relationships of the system. The solution is a cubic equation. Through a series of assumptions, the solution is simplified. The assumptions are based on the chemistry of the system given the Ka and Ct for the problem. The problems are then graphically solved. Ultimately, the students develop an Excel worksheet to solve the problems and a Bjerrum plot to display the speciation as a function of pH.

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This is presented in a required upper division (Jr. Sr.) Environmental Geochemistry class as part of an Environmental Geosciences Program.

Skills and concepts that students must have mastered

Students will have completed one year of basic chemistry, one semester of calculus, and a series of basic geology classes.

How the activity is situated in the course

It is part of an acid/base equilibrium unit in the fourth week of the semester. It follows the equilibrium thermodynamic unit.


Content/concepts goals for this activity

o Understand the impact of pH and speciation in a system
o Build on previous unit that covered equilibrium thermodynamics
o Prepare for following units on redox and more complex equilibrium relations presented in geochemical models

Higher order thinking skills goals for this activity

o Ability to mathematically simplify a systems of equations based on an understanding of the chemistry of the system.

Other skills goals for this activity

o Manipulate mathematically a series of equations
o Develop a worksheet to represent the mathematical relationship
o Documentation of a solution to a problem

Description and Teaching Materials

Three file presented below;
- Explaination of Method-Text.pdf - presents the method
- Explaination of Method-Tables.pdf - contains three table with assumption presented
- Condition Examples.pdf - Examples for each condition worked out in Excel

Explaination of Method-Text (Acrobat (PDF) 141kB Jun3 13)
Explaination of Method-Tables (Acrobat (PDF) 500kB Jun3 13)
Excel Plots with Conditions (Acrobat (PDF) 458kB Jun3 13)

Teaching Notes and Tips

Students find they are rusty with algebra and properties of logs. If you have them draw graphs of the systems, give them a blank graph with a scale on both axes. It will make grading easier. Do not overestimate their understanding.


There are homework problems and questions on exams. If do not appear to be preparing for class, we start with an unannounced quiz.

References and Resources