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Relationship Between Free Energy and the Equilibrium Constant (11 Favorites)
LESSON PLAN in Solubility, Entropy, Le Châtelier's Principle, Gibb's Free Energy , Equilibrium Constants, Enthalpy. Last updated June 25, 2021.
Summary
In this lesson, students will explore the relationships between solubility and K_{eq} (specifically K_{sp}), as well as K_{eq} and ΔG^{°}. First, a guided inquiry activity will introduce the relationship between standard free energy and equilibrium constant with the equation ΔG^{°} = -RTlnK_{eq}. Then data collection regarding solubility of potassium nitrate at various temperatures will lead to the calculation of K_{sp} and ΔG^{o} for the dissolution reaction at those temperatures. Students will manipulate the equations ΔG^{°} = -RTlnK_{eq} and ΔG^{° = }ΔH^{°} - TΔS^{°} to derive a linear relationship between 1/T and lnK_{eq}, which will then be graphed to determine values for ΔH^{°} and ΔS^{°}.
Grade Level
High School (AP Chemistry)
AP Chemistry Curriculum Framework
This lesson supports the following units, topics and learning objectives:
- Unit 9: Applications of Thermodynamics
- Topic 9.3: Gibbs Free Energy and Thermodynamic Favorability
- ENE-4.C: Explain whether a physical or chemical process is thermodynamically favored based on an evaluation of ∆G^{°}.
- Topic 9.5: Free Energy and Equilibrium
- ENE-5.A: Explain whether a process is thermodynamically favored using the relationships between K, ΔG^{°}, and T.
- Topic 9.3: Gibbs Free Energy and Thermodynamic Favorability
NGSS Alignment
- HS-PS1-6: Refine the design of a chemical system by specifying a change in conditions that would produce increased amounts of products at equilibrium.
- Scientific and Engineering Practices:
- Using Mathematics and Computational Thinking
- Analyzing and Interpreting Data
Objectives
By the end of this lesson, students should be able to
- Graphically relate the equilibrium constant, K_{eq}, to thermodynamic properties, such as ΔG^{°}, ΔH^{°}, and ΔS^{°}.
- Complete calculations using the equation ΔG^{°} = -RTlnK_{eq}.
- Predict qualitative relationships between ΔG^{°} and K_{eq}, such as, the more negative ΔG^{°} is, the more product-favored the reaction.
Chemistry Topics
This lesson supports students’ understanding of
- Equilibrium, specifically solubility product constant
- Le Chatelier’s Principle
- Free energy
- Enthalpy
- Entropy
- Solubility
Time
Teacher Preparation: 20 minutes
Lesson: 3 hours
- Guided Inquiry Activity: 30 minutes
- Pre-lab questions: 20 minutes
- Lab Activity: 110 minutes (can be shortened by pre-heating water baths)
- Lab Write-up, outside of class: ~40 minutes
- Post-lab Quiz: 15 minutes
Materials (per group)
- 2-decimal balance (groups can share)
- 50-mL graduated cylinder
- Thermometer or temperature sensor and necessary probewear
- Tall form 600-mL beaker (or similar size) (2 groups may share)
- Hot plate (two groups may share)
- Approximately 20 grams potassium nitrate, KNO_{3}
- Other graduated cylinders, at least 25 mL (may be shared between groups)
- Access to deionized water
- Online graphing or spreadsheet program
- Projector
- Copies of guided inquiry, pre-lab, lab, and post-lab quiz (1 per student)
Safety
- Always wear safety goggles when handling chemicals in the lab.
- Students should wash their hands thoroughly before leaving the lab.
- When students complete the lab, instruct them how to clean up their materials and dispose of any chemicals.
- Exercise caution when using a heat source. Hot plates should be turned off and unplugged as soon as they are no longer needed.
Teacher Notes
Placement in Curriculum:
- This lesson and lab is designed to be used as an introduction to the equation, ΔG^{°} = -RTlnK_{eq}.
- It is important that topics of solubility, thermodynamics (including, ΔG^{° }= ΔH^{° }- T ΔS^{°}), and equilibrium expressions (including solubility product constant) have been previously covered.
Guided Inquiry Activity:
- Place students in groups of 3-4. I set the following rules for activities like these and it works well:
- Read aloud
- Make sure everyone has reached consensus before moving forward
- Ask the teacher a question only after asking all group members
- As students are talking in groups, notice if there are common misconceptions or places where each group gets “stuck.” Be sure to address these to the entire class at the end of the activity.
- Question #5 requires the teacher to initial for accuracy because students will use the equation to answer subsequent questions.
- An answer key document is provided for teacher reference.
Pre-Lab Sheet and Pre-Lab Discussion:
- It is suggested that the pre-lab sheet/discussion take place in class or as homework assigned the day before the lab will be carried out. Alternatively, the data collection for the lab is simple enough to skip the pre-lab and complete it before data analysis.
Lab Activity:
- Trouble-shooting:
- There is a risk of creating a supersaturated solution, so students must constantly “disturb” the solution by stirring and scraping down the side with the temperature probe.
- If students are unsure of whether they see crystals, have them write down the temperature. If they see more in the next few seconds, they got it! If they don’t see more form, it was likely a piece of dust and they should keep stirring. The crystals look like stringy white dust particles or “sea monkeys.”
- The 50 mL graduated cylinder will limit the amount of water students can add. They can usually get 5 or 6 data points.
- Warn students that vigorous stirring can damage thermometer and/or break through the bottom of the graduated cylinder.
- Tips for saving time:
- Pre-mass 20 grams of KNO_{3} for students.
- Set up and pre-heat water baths for students. The water doesn’t need to boil, but it does need to get to about 85^{o}C.
- When students are heating the solution in order to get the crystals re-dissolved, tell them to only heat a few degrees higher than the last temperature they recorded.
- If 50 ml graduated cylinders are unavailable, test tubes may be used. Permanent marker may be used to mark the volume level at each data collection point. Each volume may later be measured by filling the test tube to a mark with water, then pouring it into a graduated cylinder.
- Dispose of KNO_{3} solution as the local ordinance directs.
- Students complete a lab handout, but they could also write a formal lab report. I could not find reliable published accepted values for K_{eq} or ΔG^{o} for the dissolution of KNO_{3}, so I tell students they don’t have to calculate percent error values.
- An answer key document is provided and also includes expected results for teacher reference.
- A lab data calculator, created as an Excel document is available for teachers to use in order to check student calculations.
Post-lab Quiz
- A short (optional) post-lab quiz is included for students. I find this is helpful to reiterate understanding. An answer key document is provided for teacher reference.
For the Student
Download the documents for this lesson, including the teacher guide, from the "Downloads box" at the top of the page.