This is a new activity for chemistry students who struggle with the correlation between changes in enthalpy, temperature, entropy, and the Gibbs free energy of a system; which relies on an analogy that most students will be familiar with.

A common topic in chemistry discussion groups and forums is about the use of the terms “spontaneous reaction” versus “thermodynamic favorability”. Recently, more and more instructors have steered away from using the word “spontaneous” to describe systems that have negative Gibbs free energy values. When I asked my second year students (Advanced Placement) what they thought of when they heard the term “spontaneous” they mentioned the words “immediate” and “quick.” And when I asked them to use it in regards to reactions, the students mentioned “the reaction always starts right away”, and “without outside intervention.” These ideas are not always true of reactions that have negative Gibbs free energy values. These reactions are not all going to be instantaneous and may never have a measurable product formed due to activation energy requirements or other outside variables. However, when I asked the students what they thought of when I mentioned the terms “thermodynamic favorability” the students responded with “reactions that could happen with changes in heat” and “a reaction’s best case scenario.” The shift from “spontaneous” to “thermodynamically favorable” could alleviate students’ misconceptions about free energy. In addition, students often mistakenly confuse the fact that spontaneous starts with the letter “s” and the symbol for entropy is “S”. Unfortunately, those students often use the word spontaneous to describe entropy. Therefore, for this activity, I have chosen to use the terms “thermodynamically favorable” to describe reactions that were once called “spontaneous”. The activity was designed to help students generate an understanding of Gibbs free energy and its dependency on enthalpy and entropy changes of the system. As an AP Chemistry Reader myself, I have seen hundreds of papers that prove that this is a very difficult challenge for most students.

### Student’s Background Knowledge

In AP chemistry, I start the topic of Gibbs free energy in March. It is part of my second to last unit of the year about thermodynamics (followed by electrochemistry and then exam review). This activity can also be used in first year courses (see *note below). Before using this activity, my students had shown proficiency in calculating and explaining changes in enthalpy (heats of formation, Hess’ Law, calorimetry, bonds broken minus bonds formed calculations) and entropy (entropy of formation calculations and explanations). This activity is designed to help students understand which systems are the most favorable and which systems are unfavorable. The activity also shows how certain systems have competing enthalpy and entropy favorability and how Gibbs free energy can be evaluated in such systems. Gibbs free energy can be a very abstract idea for students. The analogy can help tie the Gibbs free energy concept to a more tangible and real world scenario.

### The Analogy

The analogy is based on the idea that students would like to create plans to have fun with their friends. As heat can be added or removed from a system, thus being endothermic (+) or exothermic (-), money can be saved in a bank account (+) or spent (-). In a favorable scenario, students will have money to spend, much like a reaction can release heat. Highly entropic systems have many degrees of freedom, or a variety of microstates (+), which could be analogous to students having many different options to have fun with their friends. Systems that have a decreasing entropy (-) will have less degrees of freedom much like students who may be grounded and not free to socialize. An increase in temperature will allow particle to move with more kinetic energy, much like the availability for transportation to bring students from home to their plans. The temperature will directly affect the value of entropy. As temperature is increased on a system, the particles move with more kinetic energy and can have more degrees of freedom or microstates, much like if the students have more means of transportation (most cannot drive!), their options for plans increases. There are four general scenarios:

**The most favorable scenario:**Students will have money to spend, transportation, and many options for their plans analogous to exothermic enthalpy changes, high temperatures (which I later show could be unnecessary), and increasing entropy changes.**The first semi unfavorable scenario:**Students have money to spend but no options (grounded). Therefore, the increase of transportation will be nothing but a nuisance or taunting that makes the situation more unfavorable. This is analogous to having an exothermic reaction that is decreasing entropy and more favorable at low temperatures (This needs some facilitation! See the “*Facilitation Strategies*” section below).**The second semi unfavorable scenario:**Students don’t have money to spend but they have available opportunities to plan their day. If transportation is available the opportunities are more attainable. This is analogous to endothermic reactions with increasing entropy that require high temperatures to make the reaction favorable.**The most unfavorable scenario:**Students will not have money to spend (saving it), no transportation, and no options for their plans (grounded) analogous to endothermic enthalpy changes, low temperatures (which I later show could be unnecessary), and decreasing entropy changes.

### Facilitation Strategies

Don’t overcomplicate the analogy. Students may try to bait you with things like “Well, if I am grounded I could just shop online, play video games, etc. and my entropy could still be increasing” or other loopholes. Start the lesson out with the intention of learning this difficult topic of chemistry and to take the questions at face value. Be available for your students. If they have questions they can raise their hand and you can answer with follow up questions and hints. Try not to give away the answers, but instead coach them toward the right direction. I have my students in teams of three to four and use POGIL activities with roles and process skill development very often. My students are trained on how to approach this type of activity (for POGIL training see www.POGIL.org). Key icons will alert students when they are seeing an important concept. The stop sign icon means the students should stop once they have completed that question and call the teacher over to check in. I check one student’s answers (specifically key questions) to ensure the team is on the right path. I may ask follow up questions and clarify parts that need to be discussed. Each team may arrive at a stop sign at different times, so always have another activity or practice problems ready for the students to do when they complete the assignment. My students worked on practice calculations when they were done with this activity.

The** first section** (page 1, ending with the first stop sign), was fairly simple. My students completed that section in about ten minutes with little help needed. If they struggled with question five, I merely pointed out the bold word “release” and they often said “it’s negative!” because we have discussed that with exothermic reactions all year. If a team worked very well, I often asked them to explain to me why they chose the term “negative” to describe Gibbs free energy in question 5 to see what their misconceptions may have been, if any.

The **second section** (page 2) required a little bit of guidance during question 6b. I reasoned with a few of my students by saying “If you had money to spend but were grounded, and all your friends were taunting you with rides and opportunities to hang out, wouldn’t you be even more upset than if they had left you alone?” That usually resonates with them and helps them decide that increase in transportation will actually be unfavorable in that scenario (much like exothermic reactions that are decreasing entropy will be unfavorable as temperature increases). The students seemed to be able to jump right from the analogy to the real thermodynamic values in question 8 with no issues. A few students needed guidance on question 9c only because they realized there were two indeterminate scenarios and were unsure if they should write about both.

The **third section** (starting on page 3) was a breeze. Most of my students are not mathematically inclined, but due to scaffolding the questions, and the experience with the calculation of products minus reactants for both enthalpy and entropy previously, the students worked through calculations very well. Question 14 stumped a few students so I modeled the idea of collision theory requiring proper orientation and energy and they were then able to remember that reactions require sufficient activation energy (we had covered this a few units ago in kinetics). My students were able to finish sections 1-3 in one class period (42minutes). We ended the first period with the question, “Why is it so difficult for Ms. Drury to find endothermic reactions that decrease entropy?” The students needed some thinking time and eventually we resolved that endothermic reactions tend to involve the breaking of bonds or forces which would generally increase the entropy of a system due to more molecules or gaseous particles being formed. I asked them to review the equations to make sure they were confident about the variables to be used: ∆G⁰=∆H⁰-T∆S⁰, products – reactants, and ∆G⁰=-RTlnK. In addition, I asked them to try to research endothermic reactions that increase in entropy.

The **final section** (questions 15-20) was completed on the following day. The students had no trouble relating Gibbs free energy and the equilibrium constant (we have just finished the acids, bases, and salts unit so they are generally well versed in equilibrium). A few teams were stumped about question 20. I referred back to the model of Y + 2F ↔ YF_{2} and asked, “When is the reaction given above favorable? How can I make that reaction unfavorable?” Those questions usually helped them answer the question.

### Assessment

After the activity, I gave the teams a team quiz. I don’t quiz as a team all the time. Team quizzes usually occur after team activities but before large assessments. I find that team quizzes boost team morale (they see it as a challenge and something different than an individual quiz) and the team quizzes set an expectation for working in the team, in that, the students know they are responsible for understanding the content because they have to pull their weight on the quiz. The students also continue learning during team quizzes. The students are forced to have an open dialogue about the content in order to arrive at a team consensus and argumentation between students helps the students defend their answers and gain confidence with the material. The quiz is closed notebook (but open brain!) and they had 15 minutes to complete the quiz. The average score was 95%! Some misconceptions were ironed out for questions 2 and 3. I included a question that we had not seen before where the students had to solve for temperature and they performed really well! The next two classes were devoted to problem solving including practice AP free response calculations and multiple choice questions.

### Conclusions

I have been teaching Advanced Placement chemistry for 11 years and honors chemistry for 14 years. This is the first year I have tried this approach with Gibbs free energy. The students seemed to have a much better understanding of the relationship between enthalpy, temperature, entropy, and Gibbs free energy. The students are making less mistakes with their unit conversions, and are much more proficient at explaining changes in enthalpy, entropy, and free energy. The unit assessment was given two days after the assignment with stellar results. I used the same exam as last year in order to compare the strategies. This year my students performed 15% better than my students last year. I value this improvement and plan to implement this activity next year as well. The analogy might be too childish or out of character for some teachers, but I like to put myself in my students’ shoes and find any way to help them feel comfortable with the material. I hope you can find value in the activity. I would love to read your successes, suggestions, and ideas on the ChemEdX discussion board!

***Note:** I also introduce the concept of Gibbs free energy to my first year honors students without specific calculations. I have not tried this activity with my first year students yet, however, I anticipate only using the first two pages of the activity next year.

## NGSS

Constructing explanations and designing solutions in 9–12 builds on K–8 experiences and progresses to explanations and designs that are supported by multiple and independent student-generated sources of evidence consistent with scientific ideas, principles, and theories.

Constructing explanations and designing solutions in 9–12 builds on K–8 experiences and progresses to explanations and designs that are supported by multiple and independent student-generated sources of evidence consistent with scientific ideas, principles, and theories. Construct and revise an explanation based on valid and reliable evidence obtained from a variety of sources (including students’ own investigations, models, theories, simulations, peer review) and the assumption that theories and laws that describe the natural world operate today as they did in the past and will continue to do so in the future.