Abstract: This post describes a simple device used to demonstrate and clarify some challenging concepts in thermodynamics at the General Chemistry level. The device is referred to as "the Box". It is a closed rectangular box containing a rectangular partitioning piece and several bouncy balls. The two largest faces are made of clear plastic sheets so students can watch the bouncy balls move between regions of the Box when it is shaken. The partitioning piece separates the Box into a Reactants region and a Products region; the vertical dimension reflects a reaction’s enthalpy change and the horizontal dimension reflects the entropy. Each bouncy ball represents the collection of atoms from the balanced equation arranged as either reactants or products, depending on which region it is in. A forward reaction “occurs” when a bouncy ball moves from the Reactant to the Product region, and a reverse reaction "occurs" when a bouncy ball moves from the Product to the Reactant region. The tendency of a system to react in either direction is influenced by the dimensions of the partition and the extent to which the Box is shaken. More vigorous shaking represents a higher temperature reservoir, and higher bouncing reflects a higher system temperature.
The demonstration can be used to provide visual clarification of difficult concepts in General Chemistry such as why a reaction system that gives off energy gets warmer, and why equilibrium constants change with temperature the way they do with different ∆H's and ∆S's.
Introduction: Many General Chemistry 1 students struggle with the concept of putting energy into a reaction (endothermic reactions) yet the temperature goes down, or getting energy out of a reaction (exothermic reactions) yet the temperature goes up. Or even if they understand that the energy given-off or taken-in involves the surroundings, they may ask why the temperature of the reacting system changes also. Similarly, many General Chemistry 2 students do little more than memorize the Gibbs free energy equation presented in their textbooks and lectures,
As an instructor, I had tried verbal, written, and pictorial explanations of these challenging concepts, but I was not suitably effective. An active, visual demonstration seemed more desirable for developing student reasoning1 than less-active arguments. Without such reasoning, students may wind up depending on memorization and may not be positioned to do well in upper-level Physical Chemistry.
Thermodynamics at the General Chemistry level depends on several realizations, not all of which are as intuitive for the student as one might hope. The key points I emphasize, and the key points the Box demonstration supports include:
- The arrangement of nuclei and electrons in the reactants and products of a reaction system have different energies, and that difference shows up in ∆H and ∆U.
- The number of "ways" the collection of nuclei and electrons can exist and still be identified as reactants or products is reflected in the entropy, S, of the reactants or products. These are sometimes referred to as microstates2.
- The nuclei and electrons will arrange themselves primarily in a lower energy arrangement versus a higher energy arrangement, but at higher temperatures the higher energy arrangement will be "occupied" with higher probability.
- The probability with which the nuclei and electrons arrange themselves as products versus reactants will also depend on the number of ways they can exist as products versus reactants. For instance, for processes with a given ∆U, the higher the number of ways the nuclei and electrons can exist as products versus reactants, the higher the probability of finding them as products.
- Chemical equilibrium reflects the relative probability of the collection of nuclei and electrons to exist as products versus reactants at a given temperature.
Each of these concepts can be demonstrated with the Box, and it can consequently be effectively used in addressing student difficulties in understanding the basics of Chemical Thermodynamics.
Materials: The Box is a rectangular box with the two largest faces being transparent. The specific dimensions are not important – it just needs to be big enough to be seen in the classroom, but not so big that the operator(s) can't shake it vigorously. The version we use is about 100cm x 60cm x 10cm. It also includes lengths of PVC pipe attached to the vertical sides to serve as handles. There is an additional rectangular piece inside the Box which is placed in a lower corner, abutting the bottom and one of the sides. It serves to partition the Box into Reactant and Product regions with specific dimensions which are related to the ∆H and ∆S of the reaction being examined. It is not essential to have Boxes with different-sized partitions to demonstrate different thermodynamic situations as once students see one example, they seem to be able to understand how different dimensions would affect the demonstration. The version we use is about 50cm x 40cm x 10cm.
The Box will also contain at least 2 bouncy balls – 1" diameter is common, but larger ones will work. Balls can be added or removed from the Box through the flexible region of contact between the transparent faces and the more-rigid frame, a joint that can be adequately sealed off during the demonstrations with duct tape. A sketch of the Box is provided in Figure 1, and a photograph in Figure 2.
Figure 1. Sketch of the Box. Here the partition piece is in the lower left corner and has a horizontal dimension larger than half the width of the Box. Assuming the reactant region is on the left, this set-up is suitable for examining an exothermic reaction with a negative ∆S.
Figure 2. Photograph of the Box. Notice two bouncy (green) balls inside, bottom right. Strips of duct tape are positioned along the top and bottom. Removing a strip of duct tape allows for addition or removal of the balls.
General Features of the Demonstration: The vertical edge of the partitioning piece inside the Box defines a plane extending from the top of the Box to the bottom. The region to the left of this plane can be identified as the Reactants region, and the region to the right can be identified as the Products region. Each bouncy ball represents a complete set of the atoms in a balanced equation, and when it is in the Reactants region it represents the atoms arranged as reactants and in the Products region it represents the atoms arranged as products. When balls move from the left portion to the right, it represents the reaction proceeding in the forward direction. Furthermore, the tendency for balls to spend time in one region or the other reflects the concentrations of the reactants or products, and the relative tendency of the balls to spend time in the Products vs the Reactants regions reflects the chemical equilibrium, Keq. Examples of the set-up and results are shown in Figure 3 below.
Shaking the Box represents the available thermal energy, and the extent of bouncing by the balls represents the temperature or, alternatively, the range of thermal energies of the occupied microstates. More vigorous shaking leads to higher temperatures. While this association of shaking and temperature is easy to accept, the fact that the Reactant and Product regions are shaken simultaneously also reinforces the important concept that any arrangement of atoms can be hot or cold, independent of whether it is a high energy arrangement, i.e., with weaker bonds, or a low energy arrangement, i.e., with stronger bonds. The shaking and subsequent bouncing can be viewed as having the system in contact with a thermal reservoir and showing that, at equilibrium, products and reactants are at the same temperature.
The vertical axis of the Box represents enthalpy or energy. It is up to the demonstrator to indicate if this is a constant pressure or constant volume system. The height and location of the shelf of the partitioning piece reflects ∆H or ∆U for the reaction. With the shelf on the left-side of the Box, the demonstration reflects an exothermic reaction, and similarly if the shelf is on the right, the demonstration reflects an endothermic reaction.
The horizontal axis represents the number of possible ways the reacting system can exist, and as such, it is related to entropy. The longer the horizontal dimension of a region, the higher the entropy of that region. For instance, if the shelf of the partitioning piece is on the left and its horizontal dimension is longer than half the width of the Box, then the entropy of the reactants will be higher than the entropy of the products, and ∆S will be negative, as in the top row of Figure 3.
There are two important details about how entropy is treated in the demonstration. They don't impact the main lessons of the demonstration, but they should be acknowledged:
1) While the horizontal dimension is most easily understood as a number of ways the reaction system can exist as products or reactants, the entropy is related to the logarithm of that length. In other words, the length of the reactants or product regions should not be presented as being proportional to their entropies. Fortunately, this demonstration is not quantitative, and the only important realization is that a longer region reflects a higher entropy – just not proportionately.
2) Entropy is a relatively strong function of the concentrations, yet the length of the partitioning shelf does not change as the reaction progresses. Consequently, the demonstration is most useful when showing the direction a reaction will take from given starting conditions. That direction winds up being easiest to recognize when you start with equal numbers of bouncy balls in each region. And since the direction a reaction goes is reflective of the equilibrium constant, and that constant is defined using standard state concentrations, it is convenient to identify equal numbers of bouncy balls in the different regions as the standard states. There is nothing that supports the notion that equal numbers of bouncy balls in the regions is equivalent to 1M or 1 bar or pure phases, but the reaction quotient Q, in such a situation can reasonably be taken to be 1, and that is consistent with standard states. Furthermore, identifying equal numbers of bouncy balls in a region as representing standard states allows the lengths of the regions to be associated with standard state entropies So, and the difference in the horizontal lengths of the reactant and product regions with ∆So.
Other published demonstrations have similar goals to the Box, but have different strengths and emphases, especially as they relate to temperature, the standard states, and activation energy.3,4
Thermochemical and Thermodynamic Demonstrations: In Gen Chem 1, questions frequently arise asking how a system can get warmer when energy comes out in an exothermic reaction, or how a system can get cooler when energy goes in in an endothermic reaction. The demonstration can address these questions clearly. An exothermic reaction is demonstrated with the balls starting out as reactants on the high enthalpy shelf. A slight bit of shaking (low temperature) enables the balls to move from the high shelf to the low enthalpy products side, and when they do they bounce higher indicating a higher temperature, at least for a few bounces. Similarly, an endothermic reaction is demonstrated with the balls starting on the low enthalpy side. Significant shaking is required to have any bounce to the high enthalpy shelf, but when they do, the amplitude of the bouncing is reduced indicating a lower temperature, at least for a few bounces. A video of these Gen Chem 1 demonstrations is available in the supplemental material.
These demonstrations reinforce two key concepts: 1) in an exothermic reaction the reactants are in a higher energy arrangement of the atoms than the products, and those arrangements have nothing to do with the initial temperature, and 2) it is the release (or absorption) of energy when going from reactants to products that leads to the observed temperature changes.
In Gen Chem 2 the demonstration is primarily about equilibrium and how it changes with temperature. Students may learn the Boltzmann distribution that tells them that two states, I and j, are populated relative to each other as described in eq 1,
(1)
where the p's are the populations, the ϵ's are the energies, k is the Boltzmann constant, and T is the temperature. Grouping together degenerate (or nearly degenerate) states for the products and reactants leads to eq (2) below,
(2)
where the N's represent the number of "ways" the atoms can be arranged and still be identified as products or reactants. While students may not see these specific equations until a Physical Chemistry course, the qualitative aspects of these equations are suitably understandable, and they do see other applications in the sections of their textbooks on the Distributions of Molecular Speeds5 and the Arrhenius Equation6.
These mathematical descriptions are reflected in the demonstration when it shows that at higher temperatures (more vigorous bouncing) the bouncy balls wind up on the higher shelf more often. Additionally, the longer the horizontal shelf the more time a bouncy ball will stay in the region of that shelf, i.e. in the state that that shelf represents. Also, in the extreme of high temperature, the low energy state is still occupied but only in proportion to the number of ways the low energy state can exist relative to the sum of all the ways the system can exist.
Possibly the most useful application of this demonstration is in showing how it predicts the direction of reactions starting from standard states at different temperatures and consequently reflects the sign of ∆Go and whether Keq is greater than or less than 1. These applications are summarized in Figure 3 immediately below.
Figure 3. All key organizations of the partition in the box and the expected distribution of the bouncy balls under different shaking (temperature) conditions. The conclusions one would make about Keq are also included.
In each of these examples, standard states of products and reactants are represented by having the same number of bouncy balls in each region of the box. Then if the amount of bouncing (i.e. the temperature) is such that causes a net transfer of balls from the reactants side to the products side, you conclude ∆Go < 0 and Keq > 1. Similarly, if the temperature is such as to cause a net transfer of balls from the products side to the reactants side, you conclude ∆Go > 0 and Keq < 1. One should then be able to shake the Box more or less vigorously with different partitioning pieces and reproduce the general features of the dependence of ∆Go on temperature commonly found in textbooks,7 or in plots8 as in Figure 4, where ∆Ho and ∆So are taken as constants with respect to temperature so one can focus just on their signs.
With the Box oriented as in the top row of Figure 3, the demonstration is reflecting a reaction with ∆Ho < 0 and ∆So < 0. With a small amount of shaking, balls will go from the reactants shelf to the products shelf even though the reactants region is longer than the products region, indicating that ∆Go < 0 and Keq > 1. But at very high temperatures, the balls will be evenly distributed through the box, and since the reactants region is bigger than the products region, there will have been a net transfer of balls from the products to the reactants side, so ∆Go > 0 and Keq < 1. This is reflected by the "∆Ho < 0, ∆So < 0" line in Figure 4.
Turning the Box around from the previous orientation so that it is oriented as in the second row in Figure 3, the demonstration is reflecting a reaction with ∆Ho > 0 and ∆So > 0. With a small amount of shaking, balls will go from the products shelf to the reactants shelf, even though the products shelf is longer, indicating ∆Go > 0 and Keq < 1. But at very high temperatures, the balls will be evenly distributed through the box, and since the products region is bigger than the reactants region, there will have been a net transfer of balls from the reactants to the products side, so ∆Go < 0 and Keq > 1. This is reflected by the "∆Ho > 0, ∆So > 0" line in Figure 4.
With the Box oriented as in the third row of Figure 3, the demonstration is reflecting a reaction with ∆Ho < 0 and ∆So > 0. With a small amount of shaking, balls will go from the reactants shelf to the products shelf, indicating that ∆Go < 0 and Keq > 1. At very high temperatures, the balls will be evenly distributed through the Box, and since the products region is bigger than the reactants region, again there will have been a net transfer of balls from the reactants to the products side, and again, ∆Go < 0 and Keq > 1. This is reflected by the "∆Ho < 0, ∆So > 0" line in Figure 4.
Turning the Box around from the previous orientation so the Box is oriented as in the bottom row in Figure 3, the demonstration is reflecting a reaction with ∆Ho > 0 and ∆So < 0. With a small amount of shaking, balls will go from the products shelf to the reactants shelf, even though the products shelf is longer, indicating that ∆Go > 0 and Keq < 1. And at very high temperatures, the balls will be evenly distributed through the Box, and since the reactants region is bigger than the products region, again there will have been a net transfer of balls from the products to the reactants side, and again, ∆Go > 0 and Keq < 1. This is reflected by the "∆Ho > 0, ∆So < 0" line in Figure 4.
A video of the demonstration for the second row of Figure 3 is available in the supporting information. But it should be noted that once students understand the demonstration with one set of conditions, they seem to be able to extrapolate to the others; so it may not be necessary to reorganize and redemonstrate to cover all the situations.
Figure 4. ∆Go vs T for four general thermodynamic conditions. The ∆Ho and ∆So values are not necessarily the same in the different conditions. For each line ∆Ho is defined as the intercept and ∆So is defined as the slope.
Conclusion: While this demonstration does not provide quantitative results for the reactions, and is most clear when comparing extremes of temperature, students find it useful in understanding key thermodynamic concepts, especially the relation of ∆Go and Keq, and their dependence on temperature. In semesters prior to making the Box, attempts to verbally describe such a device in class seemed to have limited, if any, success. With only a verbal description of the Box, students did poorly in class at predicting the demonstration's results for the different reaction types, and questioning individual students about understanding the model rarely got more than a polite "kind of" or "not really". In semesters where the physical Box was used, students did very well in class at answering questions about the demonstration's results for the different reaction types, and no student has ever reported that it was confusing. Indeed, several students have remarked (without provocation) that they have continued to think about the Box in P-Chem and in studying for GREs or MCATs, and one heading into high school teaching asked to take it with them.
And while thermodynamic ensembles are unlikely to be covered in a General Chemistry course, it may be of interest for upper-level courses that this Box can be viewed as a cell in a Canonical Ensemble. That is, the number of particles (proportional to the number of bouncy balls) and the temperature (related to the identical shaking of the reactants and products) are fixed, but the distribution of particles between products and reactants, and consequently the energy of a cell, is distributed around an average that reflects the equilibrium.
Associated Content: A video describing demonstrations for use in Gen Chem 1 explaining temperature changes in endothermic and exothermic reactions can be found at https://youtu.be/FWmF_A0pKCU. A video describing demonstrations for use in Gen Chem 2 explaining why equilibrium constants change as they do with temperature at different combinations of ∆H and ∆S can be found at https://youtu.be/CljFM9OW-dU.
References:
1. Bain, K.; Towns, M,H. Investigation of Undergraduate and Graduate Chemistry Students' Understanding of Thermodynamic Driving Forces in Chemical Reactions and Dissolution. J. Chem. Educ. 2018, 95, 512-520.
2. see for instance- Overby, J.; Chang, R. Chemistry, 14th ed.; McGraw Hill, 2022; pp 781-783.
3. Reversible Reactions Simulation (3.15). PhET Interactive Simulations, University of Colorado, https://phet.colorado.edu/en/simulations/reversible-reactions (accessed 2023-02-15). This online demonstration resembles the Box and portrays the key elements of reversible reactions. It differs from the Box, however, in that it depends on elastic collisions with the abscissa as a linear dimension, and the temperature is determined by molecular speeds which fluctuate throughout the demonstration and are different for the reactants and products, even at equilibrium.
4. Greaves, R. J.; Schlecht, K. D. Gibbs Free Energy. J. Chem. Educ. 1992, 69, 417-418. This demonstration can show most of what the Box can do but does not allow one to see the temperature changes of an exothermic or endothermic reaction, and it depends on having some arbitrary activation energy built into the device. And with three active dimensions it may also be difficult to scale to a lecture-size presentation.
5. see for instance- Overby, J.; Chang, R. Chemistry, 14th ed.; McGraw Hill, 2022; pp 207-209.
6. see for instance- Overby, J.; Chang, R. Chemistry, 14th ed.; McGraw Hill, 2022; pp 596-600.
7. see for instance- Overby, J.; Chang, R. Chemistry, 14th ed.; McGraw Hill, 2022; pp 795-801.
8. see for instance- Moore, J.; Zhou, J.; and Garand, E. D20.5 Temperature Dependence of Gibbs Free Energy. In Chemistry 109 Fall 2021; University of Wisconsin, 2021. https://wisc.pb.unizin.org/chem109fall2021ver02/chapter/temp-dependence-... (accessed 2023-02-15).