# Schreinemakers Analysis - Problem #2: Analysis of an Invariant Point with Application of the Clausius-Clapeyron Equation (An-Gr-CaTs-Ky-Qz)

Dexter Perkins
,
University of North Dakota
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#### Summary

This is a standard Schreinemakers problem: identifying the sequence of stable and metastable reactions around an invariant point. The added wrinkle is that they use the Clausius-Clapeyron Equation to calculate slopes and thus get reactions oriented correctly.

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## Context

#### Audience

I use this in my Petrology class as either an in-class exercise or as homework. It is NOT simple for some students and, so, may be best done in a group.

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

They need to know the basic Schreinemakers process and logic. And, they must know what the Clausius-Clapeyron Equation is and how to calculate reaction slopes.

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

My petrology class is a studio class and so group activities and in-class work are key. This is one of many exercises the students do during the semester.

## Goals

#### Content/concepts goals for this activity

The goal is to get them to (1) be able to do a Schreinemakers analysis, and (2) understand the significance of invariant points and stable/metastable equilibria, (3) be able to use the Clausius-Clapeyron Equation and explain its value.

Mthematical accuracy is important too.

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

Thinking, logic, reasoning, and deduction are involved. -- this problem sometimes stumps students who are looking for a cookbook approach.

## Description of the activity/assignment

This is a standard Schreinemakers problem: identifying the sequence of stable and metastable reactions around an invariant point. The added wrinkle is that they use the Clausius-Clapeyron Equation to calculate slopes and thus get reactions oriented correctly.

## Determining whether students have met the goals

There is only one possible correct solution so evaluating results is straightforward.