# Construction of a Korjinski Diagram

#### Summary

An interactive powerpoint presentation walks students step-by-step through the process of generating a Korjinski diagram for the system K20-Al2O3-SiO2. Students will use the triangular diagram from the previous exercise to determine which minerals have stability boundaries on the diagram. A second tutorial explains how to plot a natural water composition on the diagram. A Word document provides the thermodynamic data and instructions necessary to create their own diagram for the Ca0-MgO-SiO2 system. An answer key is also provided.

## Context

#### Audience

graduate and upper level undergraduate course in low-temperature geochemistry

#### Skills and concepts that students must have mastered

Balancing chemical reactions involving aqueous species but not redox.

Using Gibbs Free Energies to calculate log K and converting Keq expressions into mathematical relationships that can be plotted on an X-Y scatter plot

Calculating ionic strength, activity coefficients, and activity in aqueous solutions.

#### How the activity is situated in the course

This classroom activity is pursued after students have constructed a triangular diagrams, and are familiar with Mineral Stability diagrams.

Part of a sequence of exercises related to constructing and interpreting stability diagrams.

## Goals

#### Content/concepts goals for this activity

Plotting mineral compositions on an oxide ratio diagram, drawing tie-lines between stable coexisting phases, and generating stability-boundary orientations for pairs of stable phases from the perpendiculars to those tie-lines.

Converting "chemistry into math" using Keq to generate lines representing phase boundaries.

Becoming familiar with concentration units of molarity, molality, ppm, and mg/L.

Using Korjinski diagrams to determine which minerals are stable in given water compositions.

#### Higher order thinking skills goals for this activity

Reinforcing the concept that mass balance and mineral stoichiometry determine the proportions of aqueous species used to balance chemical reactions.

Reinforcing the importance of this type of diagram in describing water/rock interaction and the solution chemistries that result.

Also emphasizes how water chemistries can help identify minerals/rocks with which those waters reacted.

#### Other skills goals for this activity

Becoming comfortable using the properties of logarithms to convert Keq into lines on an x-y scatter plot.

## Description and Teaching Materials

Korjinski diagram tutorial SERC.ppt -- powerpoint of the step by step procedure for creating a Korjinski diagram using Gibbs Free Energies of formation.

KORJDIAG lab template and key SERC.docx -- class worksheet for students to accompany tutorial

units_gamma calculation_plotting point.ppt -- tutorial describing calculations necessary to plot points on Korjinski diagram

CaMgSiThermo Korjinski Diagram SERC.docx -- Problem set for students to complete after learning procedure

Korjinski Problem Set Key Ca_Mg_Si SERC.docx -- Answer key to student problem set

Tutorial for constructing Korjinski diagram (PowerPoint 2007 (.pptx) 2.1MB Dec3 21)

Korjinski worksheet for students (Microsoft Word 2007 (.docx) 34kB Dec3 21)

Plotting water chemistries on a Korjinski diagram (PowerPoint 2007 (.pptx) 1MB Dec3 21)

Korjinski Diagram Exercise (Microsoft Word 2007 (.docx) 16kB Dec3 21)

Problem Set Key (Microsoft Word 2007 (.docx) 150kB Dec3 21)

## Teaching Notes and Tips

I suggest going through the tutorials in class with the students allowing them to complete each step before clicking to show the correct answer to them on the screen. I have included a class template (KORJDIAG lab template and key SERC.doc) for students to use as a worksheet as you go through the procedure for diagram construction. I post these tutorials online so they can refer to them when they are doing their exercise for the CaO-MgO-SiO2 system. For more advanced students it can serve as a stand-alone activity permitting them to quickly review the construction and use of such diagrams.

## Assessment

Did they plot compositions correctly on the oxide ratio diagram and draw in proper tie-lines?

Did they construct an acceptable qualitative diagram?

Did they write all the necessary, correct, balanced chemical reactions?

Did they correctly calculate stability boundaries for these reactions?

Did they correctly plot boundaries and identify metastable extensions?

Did they correctly calculate ionic strength and activities/activity coefficients for Ca2+, Mg2+, and H+?

As we progress through the tutorial in class, I regularly check with students to ensure they understand where the answers are coming from and feel comfortable that they could repeat these steps on their own for their problem set.

## References and Resources

This activity is related to a SERC activity called: "Writing chemical reactions", but this activity is much more detailed and goes well beyond just writing reactions to calculating stability boundaries and plotting them on a Korjinski diagram.

I was unable to find instructions for construction of a Korjinski diagram online although numerous links describe use of such diagrams.