# Connecting States to Entropy (10 Favorites)

ACTIVITY in Density, Molecular Motion, Kinetic Molecular Theory, Entropy, Intermolecular Forces, Volume. Last updated October 14, 2019.

### Summary

In this activity, students use blocks to model different states of matter and the Kinetic Molecular Theory to understand the concept of entropy. This is a concept mandated by SAT level or AP level high school chemistry class.

### Grade Level

High school

### AP Chemistry Curriculum Framework

This activity supports the following unit, topic, and learning objective:

__Unit 9: Applications of Thermodynamics__Introduction to Entropy__Topic 9.1:__**ENE-4.A:**Identify the sign and relative magnitude of the entropy change associated with chemical or physical processes.

### Objectives

By the end of this lesson, students should be able to

- Relate entropy to states of matter.

### Chemistry Topics

This lesson supports students’ understanding of

- Entropy
- Kinetic molecular theory
- States of matter

### Time

**Teacher Preparation**: 3 minutes

**Lesson**: 10–30 minutes

### Materials

- 27 centimeter cubes or dice per group (referred to as cubes in the activity)

### Safety

- No specific safety precautions need to be observed for this activity.

### Teacher Notes

- This activity works well with pairs of students.
- Students must understand entropy differences and reason with ΔG= ΔH–TΔS for SAT II and AP tests in chemistry. However, even students in “physics first” programs do not have the physics required to grasp the entropy concept well. Instead of just talking about randomness, I designed this activity to make connections to the microstates ideas of upper level physics. With this model, many more conceptual links can be made and the type of questions asked on the tests (for example, whether products or reactants have higher entropy) can be addressed more reliably by applying a more accurate model. The model works well for states of matter uses.
- I taught thermodynamics on the graduate level and was unhappy with instructors just saying "entropy is randomness" and then relying on memorization or mathematical manipulation in later entropy reasoning. I wanted to make a more basic model connecting entropy to other basic mental models, to higher concepts like that of microstates, and yet have it be useful in application problems like those on the SAT and AP tests. After a couple years of development and testing, I have used this model basically as is for over three years, and it has greatly improved my students' higher level reasoning in the area of entropy, while reinforcing other concepts like phases of matter and thermal energy.
- Entropy should be introduced using this model, as the number of ways (or microstates) a student can make a model of a solid (not too many), a liquid (a lot of ways,
*a whole lot*), and a model of a gas (seemingly infinite, though not actually) using their cubes. This is a better mental model for entropy than talking vaguely about randomness. Also, it is easier to see that more arrangements are possible if there are more particles, again reflecting the microstates concept and matching SAT and AP requirements. Other uses abound. The model can be used frequently: when first discussing the states of matter, for example. If entropy is introduced then, it can be spiraled back to repeatedly so that it will not be a vague new concept when thermodynamics is taught.

**The Lesson**

Students are told that the dice represent particles (atoms, molecules, ions, etc.) that have a great attraction for each other, enough attraction to resist separation because of thermal motion. The particles therefore “want” maximum contact with each other (most faces possible touching another cube) because of the attraction. Students are told to arrange their particles into the most likely arrangement.

Students should produce a large cube (Socratic questioning opportunity as they work), three centimeter cubes on a side if using 27, to represent a solid. The cubes model the solid state. **Random questioning to address: constant volume, shape is rigid unless cut apart, density constant, sits on desk because of gravity but maintains shape because of interparticle forces, etc. Most important to entropy: how many distinguishable ways can this model be made? There is only one, since all cubes look alike.**

Then the students are told that for their next model, there is enough thermal vibration that the cubes can move but not completely break apart. Thus, students build models following the rule that every cube has to share at least one face with every other cube.

Students will make many different arrangements. The cubes model the liquid state: **the volume is still constant, but may take many shapes. They may spread out on the table (wetting) or stick to itself (non-wetting), density is constant, takes shape of container but won’t fill it up, etc.**

Next the students are told to follow what they already know about the KMT theory of gases. They may move the cubes independently from each other, average separation >10 cm (if using cm cubes), while moving them in straight lines until they bounce off each other or other things (this can’t be done *too* realistically!).

**Of course, this time students can put each cube anywhere. Now volume and density are not constants, the particles move around faster if temperature is increased, they run into each other and container walls (collision forces resulting in pressure).**

Students can take notes during pauses, specifically using the terms “number of configurations/microstates” and “entropy” with guidance from the instructor.

### For the Student

### Lesson

**PART I**

The cubes represent particles (atoms, molecules, ions, etc.) that have enough attraction to resist separation because of thermal motion. The particles therefore “want” maximum contact with each other. Arrange the particles into the most likely arrangement. Explain how and why you organized your cubes the way you did. Draw a picture of your cubes.

How many configurations can this model be made into? How does that relate to entropy?

What state do your cubes represent?

**PART II**

Now there is enough thermal vibration for the cubes to move around but not completely break apart. Every cube has to share at least one face with every other cube. Explain how and why you organized your cubes the way you did. Draw a picture of your cubes.

How many configurations can this model be made into? How does that relate to entropy?

What state do your cubes represent?

**PART III**

Follow what you know about the kinetic molecular theory. You may move the cubes independently from each other, average separation >10 cm, while moving them in straight lines until they bounce off each other or other things (this can’t be done *too* realistically!). Explain how and why you organized your cubes the way you did. Draw a picture of your cubes.

How many configurations can this model be made into? How does that relate to entropy?

What state do your cubes represent?

### Analysis

- If you had more blocks, what would happen to the number of possible configurations? How does that relate to the entropy of the system? (
*Note: The term microstates is sometimes used instead of configurations.)* - Which has more entropy …

… one mole of gas or two moles of gas? Explain.

… one mole of liquid or one mole of gas? Explain. - a. If water is synthesized and all three components are gases at the same temperature, is there more entropy in the reactants (hydrogen and oxygen) or the product (water molecules)? Write out the balanced chemical equation, including states, and explain.

b. Does your answer change if the water that is synthesized is in the liquid state? Explain.