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: Thermodynamics and Electrochemistry
  • Topic 9.3: Gibbs Free Energy and Thermodynamic Favorability
    • 9.3.A: Explain whether a physical or chemical process is thermodynamically favored based on an evaluation of ∆G^°.
  • Topic 9.5: Free Energy and Equilibrium
    • 9.5.A: Explain whether a process is thermodynamically favored using the relationships between K, ΔG^°, and T.

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, KNO₃
• 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 KNO₃ 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^oC.
  • 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 KNO₃ 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 KNO₃, 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.