The genesis of this paper started with a request from a former student, Thomas Kuntzleman, now a professor of chemistry. He asked if I would consider submitting my thoughts about ‘big ideas’ in chemistry. In his email he attached a paper that I had written for the Journal of Chemical Education six years earlier 1. That article was submitted the year after I retired and was a response to a submission questioning the utility of the Principle of Le Châtelier.
In that article I alluded to the absence of ‘big ideas’ in chemistry. In fact I stated that for me the Principle of Le Châtelier and the concept of electronegativity were the two most important ideas in chemistry. That statement reflected the point I had reached at the end of my teaching career. About ten years before I retired I had started working on a general chemistry storyline and in doing so developing my own textbook. By the time I retired I had a textbook in progress that students could buy from our bookstore as well as Power Point handouts for the remainder of the sequence.
The first chapter in this textbook was titled ‘A Different Kind of Introduction’. It served as an introduction for the three ‘introductory’ chapters that followed. The first of these gave a survey of an important topic with a significant chemical component: global warming. The next chapter was about certain ‘big ideas’ in chemistry. The last of the introductory chapters presented some ‘learning tools’ that I had developed over the years.
The ‘big ideas’ chapter presented 9 big ideas in human terms. It was stated that these be would transformed into specific big ideas of chemistry. When I looked at these again, now seven years later, I wasn’t satisfied with how they were stated. Nor was I happy with how each was explained. Lastly, I noticed that there was something fundamental that was missing. If these were indeed ‘big ideas’ in chemistry and not just ‘big ideas’ for learning general chemistry, how these ideas extended into the other areas of chemistry needed to be stated explicitly. In other words, these ideas had to have ‘legs’. I believe that both students and practitioners need to be aware of these extensions.
What follows below is an updated version of my original ‘big ideas’. I do not claim this to be an exhaustive list nor do I believe that it cannot be improved upon. But I do think it might serve as good starting point to work from to get the notion of big ideas into chemistry.
Each big idea will be stated first compactly in ‘human terms’. For me this continues to ‘connect’ well. This will be followed by a short exposition of that idea as it would be presented to the student in the introductory chapter. The same big idea in chemical terms follows. This will allow for an immediate comparison. This would however appear at an appropriate point in the course and would be prefaced by a restatement of the human big idea. A second exposition, now in chemical terms and directed toward concept development, follows; there is necessarily some repetition of what was in the preceding section. Both of these expositions ‘for the student’ are representative of how I would have endeavored to convey this idea to the student. The analogies and examples necessarily reflect my peculiarities and prejudices. I am certain that numerous other ways, some undoubtedly better, would accomplish the same goal. I would highly encourage that endeavor to be one of another goal of this paper.
Up to this point the big idea has been addressed to the student. What follows after this is commentary for the audience of this paper. First is a detailing of how this idea can be further developed in general chemistry, in some instances what I did in my course. The ‘legs’ into other areas of chemistry of the big idea will complete the discussion. Because I also taught biochemistry the ‘legs’ discussion unavoidably will focus on applications of these big ideas to that subdiscipline of chemistry.
Before I start I need to clarify how certain words will be used. Humans will be referred to as individuals as well as a species. Likewise matter will be used as a general term and chemical, substance or chemical substance will be used as more specific terms.
1-Student: There are certain fundamental rules as to what constitutes ‘human’
The most significant absolutely universal commonality of all humans is that we are all born. There are also some fundamental parts for humans: head, 2 arms, 2 legs, 1 heart, 1 liver. You get the idea. There are also some rules as to how the parts are put together. As the kids song goes: toe bone connected to the foot bone, foot bone connected to the heel bone, heel bone connected to the ankle bone… There are things that are allowed and just as importantly things that are not. Would it surprise you that all the elements were ‘born’ in some very special ‘wombs’ and that matter ‘evolved’ over time to what we encounter now? Since there are rules for all the matter, living and non-living, it would make sense that there are rules for how the fundamental building blocks of matter are put together.
1-Audience: There are certain fundamental rules to how matter is organized
It may surprise you to know that matter was born. There are also some fundamental parts for matter. You have already heard these words: protons, electrons, neutrons. There are very precise rules as to how these parts are ‘connected’. Some kinds of arrangements are allowed, others are not.
In general chemistry: I believe that the greatest weakness in the presentation of the general chemistry is the absence of a story line. And if you have a story to tell, it demands a compelling introduction. That is not typically what you get in Chapter 1 or on day 1! After starting my ‘textbook’ (as detailed above) I go to the Big Bang. I build matter; I pretend to be a physicist for a couple of days. I do not play fast and loose with the facts: matter is built as a consequence of gravity, increases in temperature, and the formation of more stable elements given the prevailing conditions. (As an aside the phrase ‘prevailing conditions’ is used throughout the course in relating the status of matter to the status of the surroundings, most significantly energy). In this approach nuclei come first. It is my belief that the stand alone placement of ‘nuclear chemistry’, usually in one of the final chapters of most textbooks, is inappropriate. A ‘natural’ place for it arises if one takes this route. Stable and unstable nuclei are discovered as are the ‘general’ rules for nuclear stability in terms of what elements are still present on earth and their origins (due to long half lives from the time of the formation of the second generation star).
At the end of this trip the following generalization can be made: variations in the number of neutrons in a nucleus result in some nuclei being stable whereas others are less stable to some degree or other. Shortly after this in the course the following generalization can be added: variations in how electrons are arrayed result in some electronic arrangements being stable whereas others are less stable to some degree or other. I think it is beneficial to compare directly nuclear and electronic ‘stability’.
Legs: the obvious extensions of this idea in later chemistry courses are all of quantum mechanics and nuclear chemistry. That is where the finer details and the mathematical rigor can be layered on.
2-Student: Humans belong to families and communities and these families and communities overlap.
Human families come in all sizes. You may be an only child or you may have several siblings in your nuclear family. You may be an only child but have lots of cousins in your extended family. On the other hand you could have several siblings and no cousins. So both nuclear and extended families can be large or small. Do you look more like members of your family or your classmates? Are you surprised by these similarities? Human families are connected by genes and social relationships. You are related to your father and to your mother but they are not related to each other (that is a social relationship called mating). Sometimes family relationships overlap. Let’s say you have a cousin and this cousin has another cousin. Is that person also your cousin? Depends on which side of the family that cousin comes from, doesn’t it? The relationship can be either “genetic’ or “social”. There are a variety of human social relationships: being in the same class, club or music group. You can also have relatives in these social groups. So there is always the possibility of overlap. You should expect that chemicals also can belong to a number of different ‘families’ depending upon what is in common; there is also the possibility of overlaps in some of these families.
2-Audience: Elements, and substances made from elements, can belong to families and other groups, small and large
The manner in which the periodic table is organized highlights relationships between the elements. Elements in the same column are related to each other ‘genetically’; they have what are called common outer electronic configurations. In fact these columns are referred to as families and some have specific family names such as the halogens. There are a group of families on the left side of the periodic table that can be thought of as belonging to one ‘tribe’; these are called metals. A group of families on the right side belong to another ‘tribe’; these are called nonmetals. Not surprisingly the elements in between these two tribes, called metalloids, have characteristics that are ‘hybrids’. Surprised? Family relationships exist beyond the elements to a variety of chemical substances. We can say that a chemical belongs to numerous different families depending on how we define the connection, and whether this connection is “genetic” or “social”. Students learning chemistry often think that they are being deliberately confused (or tricked) when a substance they studied in one family is brought up in a completely different family. Be ready to deal with important substances that have very interesting ‘family lives’.
In general chemistry: In my approach this big idea emerges from a thorough study of three things: 1) the chemical properties of the elements in forming different families of compounds specifically oxides, hydrides, the products of oxides reacting with hydrides (acids and bases) and salts; 2) the physical properties (melting point [MP], boiling point [BP], and water solubility of the previous compounds); 3) the physical properties of elements such as ionization energy, atomic size and so forth. The manner in which electronegativity first appears in my story line is unconventional. It arises from the study of the formulas of oxides and hydrides, the order of the elements in the formula and oxidation numbers. The manner in which this is done is detailed elsewhere (2). The more conventional definition of electronegativity is layered on later.
Legs: There are obvious legs in general chemistry, some already mentioned above such as acids and bases; this extends into inorganic chemistry and additional ways to classify acids and bases and other substances. This idea obviously extends into organic chemistry with the different functional group families and into biochemistry with different biomolecules. The rejoinder to students about not being tricked applies to instructors as well. One must carefully state what is the common ‘trait’ defining a chemical group especially when the members of the group appear to be quite disparate.
3-Student: Humans have different extrinsic (shapes and sizes) and intrinsic (intelligence and artistic ability) characteristics. These determine what humans are capable of doing. The most important characteristic of humans is intelligence.
Humans come in a variety of ‘forms’ and distinguishing features. Some human characteristics effect what individual humans are capable of, others do not. Size is an attribute that varies greatly among humans. Tall humans have a better chance at being good basketball players; bulkier humans have a better chance of being good offensive lineman in football. On the other hand size is not a factor in determining prowess at card games. The way humans are put together, that is their structure, determines the functions that certain body parts can carry out. You write with your hands, you see with your eyes, you smell with your nose (other things that is). You should expect that chemical substances have these same features: different sizes and shapes; different parts; and the capacity of different parts to do different things.
3-Audience: Chemical substances have defined shapes and sizes because of how atoms in the substance are organized. This results in most substances having different ‘parts’, a consequence, most significantly, of the distribution of charge due to differences in electronegativity of the atoms in the substance.
In building the elements and in learning the structure of atoms you learned that matter seeks the lowest energy level for the prevailing conditions. The same principle will apply as we make more complex matter: maximize attractions and minimize repulsions among the atoms that make up a substance. You already know that the competition for electrons between atoms of different elements is unequal. We’ve called that idea electronegativity. Just like intelligence, electronegativity is special. That idea will now be given a firmer foundation. It is critical to know how to make correct structures and correlate these structures to certain geometric shapes. We can then use electronegativity to ‘highlight’ the different parts of these structures. This in turn will allow us to predict how a substance with this structure can interact with others of its own kind or with other substances. But that is another big idea.
In general chemistry: How to obtain the correct structures of different substances is of critical importance. In my story line the different kinds of matter emerge from looking at the properties of the elements and the compounds of the elements mentioned earlier. I have a flow chart in terms of substances exhibiting certain properties (MP, water solubility, conductivity) that lead to the four major classifications of matter: metallic, ionic, network covalent and molecular covalent (the names of elements and compounds are provided before the details of how these various classes are organized). Exceptions are dealt with later. There is also the ‘reverse’ exercise for students: to look at a formula and classify it. Since most students go on to organic chemistry I place a great emphasis on the correct construction of Lewis structures, an understanding of the corresponding geometries, and especially recognition of the presence and magnitude of polarization in the molecule. With the widespread application of molecular modeling, both the presence and magnitude of the polarization can be dramatically highlighted.
Legs: The elevation of electronegativity to big idea status and its emphasis in general chemistry is warranted by its widespread application in other areas of chemistry. One need only say nucleophilic and electrophilic to recognize its importance in organic chemistry. Also electronegativity differences allow one to predict MP, BP and the relative solubility of organic compounds in water or organic solvents. As a biochemist I would state without qualification that electronegativity is of paramount importance: hydrogen bonding, active sites, catalysis. There are numerous other applications of electronegativity too numerous to mention.
4-Student: Humans, and groups of humans, can move from place to place and change location, but they retain their fundamental human characteristics
That statement seems so obvious but let’s take it a step further which will help to understand the chemical big idea this is paired with. Ice hockey is fast moving game. Unlike other sports, substitutions are made ‘on the fly’. Players jump on the ice as players come off the ice; these are called line changes. There are always the same number of players on the ice for each team (forgetting for the moment penalty situations). There are also the same number of players on each team, some on the bench, some on the ice. The number of players is conserved. One frequently hears the term getting ‘fresh legs’ in the game in describing line changes. This involves replacing an exhausted player with a player that has been resting on the bench. The ‘energy level’ of the players in the game therefore stays fairly constant. It also is conserved. Each player has certain fundamental skills: primarily skating and shooting the puck. Once you get past these fundamentals the game gets interesting since players with different levels of skills will make a difference! The situation with matter is exactly the same. There are certain constants, things that are conserved. There are also attributes that vary greatly.
4-Audience: Despite obvious differences in appearance and properties whenever matter changes the total mass, the number of atoms and the energy content of the matter remain constant.
You have undoubtedly encountered these earlier in your education as the principles of Conservation of Mass and Conservation of Energy. You’ve seen this idea applied in the numerous balanced chemical equations you have seen. Chemistry is a lot like math and accounting: you have to keep a track of things and make sure that there are the same ‘amounts’ on both sides of the equation, formula or ledger. You should also keep in mind that since atoms contain electrons, and as you have already experienced, electrons are exchanged, you will also have to sometimes keep a track of the number of electrons and the charge on the two sides of chemical equation.
In general chemistry: The application of this big idea is obvious in terms of balanced equations: complete, net, ionic or redox. It is also essential to stoichiometry.
Legs: the quantitative extension of this big idea to all areas of chemistry is obvious.
5-Student: Humans interact with other humans and can exchange things; the motivations and strengths of these interactions can vary depending on the humans involved.
There are two parts here. The first is the basis of the interaction; the second is the nature of the interaction. The basis of an interaction is why it occurs and just as importantly why it may not occur. It is reasonable to say that humans have a tendency to get along with other humans with whom they have more in common. That’s the premise of all dating sites; it’s match.com after all. The motivation here is to exchange love. There are all sorts of motivations for humans interacting: business, pleasure, common activity. The nature of an interaction is its character. Some interactions are equal in character for instance several people working on a project and everyone pitching in the equally. Others are very unequal, slavery for instance; all the work is done for someone else. Some interactions are weak. They come and go, for instance a greeting or wave to someone you recognize. Some are strong, like a 50 year marriage. A few, like the human interaction called murder, are irreversible. The interactions of chemicals pretty much cover the same ground. Water ‘precipitates’ in the form of rain, snow, hail and then evaporates with heat – it comes and it goes. On the other hand a piece of wood burns in a fire – it’s gone forever. You should notice that heat or energy is involved in both these examples. That is a very important consideration when matter interacts.
5-Audience: Chemical substances can interact with themselves and with other substances in a completely reversible manner or can react with other substances in a partially reversible or irreversible manner. In all cases, there has to be an appropriate driving force that causes the interaction or reaction.
We use the term interaction to cover all the possible ways in which substances can come together. These interactions can be weak or strong. Weak interactions come and go. Strong interactions, more often called reactions, sometimes go ‘all the way’ although they also can go only part of the way. For humans it was mentioned that there had to be a motivation, a basis, for an interaction, for instance seeking love. For chemical substances the basis of an interaction is called a driving force. That depends on the strength of the match between substances: no match, no driving force, no interaction; weak match, weak driving force, interaction; strong match, strong driving force, reaction.
In general chemistry: The wording here is very careful. It covers phenomena where weak forces are in play: primarily phase transitions and solubility. It covers interactions that come into play to facilitate partial reactions: weak acids and bases, complex ions, weak solubility. It also covers irreversible reactions. The fundamental difference is the nature of the driving force. Therefore I develop this big idea in several ‘phases’. The first phase occurs when intermolecular attractions are covered; this is right after the building of molecular covalent substances when their properties are investigated. The second phase occurs when equilibrium is investigated, especially the weak acid-base equilibria. The big idea only becomes fully developed after energy concepts, most significantly the strengths of bonds, has been established. The consequences are different here because the driving force is so much stronger and leads to a scrambling of bonds. I think it important to have the notion of chemical ‘reactivity’ treated as a gradient from none to boom. That allows for a collateral treatment of differences in energy between ‘reactants’ and ‘products’.
Legs: this big idea goes hand in hand with the previous one in terms of its applicability to other areas of chemistry, many in the same areas.
6-Student: Humans are generally in a state of harmony but respond in a variety of ways when that harmony is disrupted
Most of the time life just goes along and follows a regular routine: take in fuel, get rid of waste, recharge with sleep, repeat. Of course there are other things happening. But this represents what biologists call homeostasis, a balance. However once in a while things can happen that upset this balance. These can be small or large but are all perturbations. Headaches are a common perturbation. Most humans don’t tough it out; they take aspirin or some other medication that reduces the pain. More serious illnesses require more serious responses. Communities of humans can also be perturbed. When flood waters rise, or tornadoes or fires approach humans move to shelters away from the danger. And most often they move back when the danger has passed. Similarly chemical substances if left alone are in a similar ‘balance’. Homeostasis in chemistry is called equilibrium. Take a look around at all the ‘contented’ chemical substances you are surrounded by! But just like humans when substances or collections of substances are perturbed they can respond. This is accomplished in a variety of ways. Chemicals like humans are very adaptable.
6-Audience: Equilibrium and the Principle of LeChatelier.
This chemistry to human analogy is a tough one. There are some things that are similar: both humans and substances can be in equilibrium states; and both humans and chemical substances respond to perturbations. But the nature of the equilibrium and the response to perturbations are very different. For instance in the example of the flooding, if the humans behaved like substances not all would leave when the flooding started; in fact some from high ground would move into the flooded area and people would randomly be moving back and forth between high ground and the flooded area! The number of people in the flooded area would be less (the response to the perturbation) but these would constantly be different people! The problem is twofold: 1) substances can’t make decisions like humans; 2) substances at equilibrium have to be treated as very large populations that can randomly move between two different states. This will require a careful approach.
In general chemistry: I believe it important to be honest with the student about the shortcomings of the analogy. Equilibrium, equilibrium equations and even more so solving equilibrium problems are major challenges for many students. Perhaps it is because of the poor ‘overlap’ with common human experience mentioned above. I also believe word choice is important. I prefer the use of the term perturbation over stress or other options. It is a more global word; it is also neutral whereas stress is negative. As an aside I believe that how we use certain words sometimes gets in the way of a clear and consistent message (the careless use of ionization and dissociation comes to mind). But that is another topic.
After the concept of equilibrium in simple chemical systems has been established I make the connection to other ‘equilibria’ and how these respond to perturbations. There is homeostasis from biology. This is especially appropriate since the majority of the clientele in the course is biologically inclined. There are wonderful examples for individual organisms, a population of an organism, and entire natural environments and how these respond when there are perturbations. Global warming is another excellent topic with lots of chemical examples, for instance the levels of carbonates in sea water. For my course this is where there is a further refinement and rigor for ideas that were raised at the beginning of the course.
Legs: As a biochemist there is a very selfish reason for having students thoroughly understand how this idea works. It is absolutely essential to understanding how biochemical pathways work in terms of push and pull. I want students who eventually wind up in my biochemistry course to have a deep appreciation for this. The practical applications of the equilibrium idea and how to shift the equilibrium are everywhere. Much of what constitutes chemical engineering is an application of this big idea.
7-Student: Small changes or shifts for humans and human communities can have major consequences for both individual humans and human communities.
This big idea probably doesn’t make a lot of sense to you as it is stated. It needs to be explained with an example. Here is one that is pretty easy to grasp nowadays. There is an election for Congress and one party is in the majority in the House of Representatives, let’s say 220 Republicans to 215 Democrats (there are a total of 435 representatives in the House). After the election there is a gain of 5 seats by the Democrats and the new composition of the House is 215 Republicans to 220 Democrats. Do you think the legislation being pushed, and the actions of the House will stay the same or change? Come on! A small change in numbers has caused a potentially large change overall. In this case the chemistry analogy overlaps perfectly. A small change in the number of chemical units that have one property to chemical units that have a different property can change the behavior of the entire chemical community.
7-Audience: The overall behavior of a chemical system depends on the ratios of chemically related species of the system. Small changes at certain points can cause big changes in the overall behavior of the system.
You might think that this is the same as the previous big idea. Part of it is since this is also about equilibrium. The difference is that at certain points in a dynamic chemical system there is a possibility for dramatic change. Although the change is small, either in a physical quantity such as temperature, or in the balance of chemical species, the appearance and behavior of the system is completely different. The best example that you are familiar with is what happens to water around the freezing point. At 0.1oC water is a liquid and you can swim in it (for a short time or with a wet suit). At -0.1oC water is a solid and you can skate on it (after you have let it get to a certain thickness). That’s a 0.2o change in temperature, a small change, but one that results in a dramatic difference. This idea is critical for you to appreciate since it means that there are certain critical ‘tipping points’ for chemical systems.
In general chemistry: It is important to have this idea in place when one starts to layer on the mathematics involved with equilibria, notably with weak acids and bases. I sometimes flippantly call this big idea ‘the effect of ratios, powers and logarithms’. For example consider an equilibrium equation with two species in the numerator and one in the denominator, the general form for weak acids and bases. Take a little from one of the species in the numerator, you have to take the same from the other species in the numerator AND you have to add that to the species in the denominator. This is exactly like the House of Representatives example: take out a Republican, you have to add a Democrat; and at the ‘equivalence point’ the change is dramatic! The small change is ‘magnified’. The same thing happens when this relationship is converted to logarithmic form as in the Henderson – Hasselblach equation. If one of the species in the log term ratio goes up, the other goes down. The dramatic changes of course occur at the points where the species in the equilibrium are close to being equal. Phase changes are another example of this idea. Indicators are an excellent way of demonstrating this idea: the system is showing one color and on the addition of the tiniest drop of a reagent are showing another color.
I believe it to be of critical importance, for reasons to be further detailed in the section that follows, that students are able to view chemical systems as consisting of a mix of species that have an ‘average’ property. For instance at the pKa of a monoprotic weak acid the average charge is -0.5. Half of the acid species are protonated and have 0 charge; the other half have a charge of -1. There are no species with a charge of -0.5, but the system can be treated as having a charge of -0.5.
Legs: My bringing this idea to big idea status had its origins in my teaching of biochemistry. It came from attempting to get students to have a molecular understanding of how hemoglobin, which carries oxygen to tissues, works. The primary reason why oxygen is picked up by hemoglobin at the lungs and dropped off at the tissues is a small change in pH between the two regions (the tissues, due to metabolism, are more acidic). The following is a distilled version of what happens on the molecular level. The amino acid histidine has a side chain that is ionizable with a pKa around physiological pH. There are numerous histidines in each hemoglobin molecule and these are located in key places. With the change in pH (more acidic) more of these histidines are protonated when the hemoglobin arrives at the tissues. That causes some of the hemoglobins to change shape to a form that cannot bind oxygen as well and therefore the oxygen is released (the actual process is quite elegant with some additional aspects that also involve the binding of carbon dioxide such that it can be removed from the tissues and sent to the lungs). The ‘bottom line’ so to speak is that there are more hemoglobin species that bind oxygen poorly than those that bind oxygen strongly at the tissues but both species are present. Likewise when the hemoglobin arrives back at the lungs the pH change is reversed and there are more hemoglobins that bind oxygen strongly than those that bind hemoglobin poorly. At both the lungs and the tissues the oxygen binding properties of hemoglobin can be treated as a weighted average of the species present. Thus there are two very different binding curves that can be displayed graphically. The difference in oxygen binding at the partial pressures of oxygen at the lungs and at the tissues can be displayed dramatically. I attempted to do an analysis of the ‘charge differential’ on the histidines in a similar manner to that mentioned above for a weak acid base pair. I was absolutely astounded and dumbfounded that most students could not think in terms of populations of chemical species, could not understand that no species actually carried a fractional charge and could not determine a fractional charge from proportions of two species. That led me to emphasize this idea in the teaching of my general chemistry course.
There are numerous other places in biochemistry that warrant and benefit from thinking in terms of average properties of populations of chemical species. This idea pops up in analysis of complex mixtures in analytical chemistry and in the population of different species in spectroscopy, notably NMR.
8-Student: Humans seek to maximize both security and freedom
It sure is nice living in a neighborhood that is peaceful with supportive parents and neighbors that are friendly and helpful. This sure beats being in a part of the world that is strife torn. It is actually easy to measure the human drive for security – it is called immigration. People move from places where they feel less secure to places where they think they will do better. The same applies to the notion of freedom. As kids we try to get away with as much as we can; if we have exceedingly easygoing parents, we get away with more than what we should. Sometimes a person’s exercise of what they consider to be their freedom goes too far. Nowhere in any human community is the “freedom” to kill others in the community accepted. That is because this type of “freedom” would jeopardize the security of the community. So freedom and security are related – ideally we would like to maximize both. However, we recognize that we have to balance security and freedom. Living in a hospital every minute of your life gives you a lot of security about your health – attention is immediately available. But it really limits your freedom. You shouldn’t be surprised that matter seeks to find the same balance between freedom and security.
8-Audience: ΔG = ΔH –TΔS
This big idea starts with what is one, if not, the most important equation in all of science. Don’t worry, we won’t derive it! Instead we’ll make sense of why it works. Let’s start from our human analogy. The ‘security’ part is going to be correlated to the H, the enthalpy, in the equation. Chemically H is correlated to the strength of bonds; the stronger the bonds, the more security. That works. The freedom part is correlated with S, the entropy. Notice that S is connected to T which is temperature in Kelvin. That certainly makes sense. We know that as substances go from solids to liquids to gases with an increase in temperature that there is greatly enhanced freedom of motion. The ‘compromise’ between stronger bonds and more freedom of motion is represented by G, called the free energy. The negative sign makes sense if you think about the fact that you have to compromise security with freedom. If one goes up the other has to go down. A positive sign would suggest that you could have both. We know that is not the case. Most importantly with the negative sign the math works in terms of how the quantities are defined.
It is instructive at this point to consider the two ‘extremes’. Very high melting solids have very strong bonds and little or no freedom of motion. Gases with very low boiling points such as the noble gases have minimal attractions and maximum freedom of motion. The rest of matter is somewhere in between.
The Δ (delta) you already recognize as symbolizing change. Our human big idea was ‘humans seek to maximize both security and freedom’. Seeking is looking for something. Matter does the same thing although not consciously. We can however envision matter, given the right circumstances, ‘investigating’ other ways of organizing itself such that it ends up with a better combination of bonds and freedom of motion. Combination could mean better bonds and less freedom or poorer bonds but more freedom or other combinations as long as the change overall is favorable. That favorable change would mean of course that excess energy is released. Going in the opposite direction would mean that energy is added.
In general chemistry: The elaboration for the student is more detailed here than for the other big ideas. That is because the overlay of the human big idea with an abstract mathematical relationship requires it. In addition since the ‘contradictory’ math in terms of negative enthalpy changes and positive entropy changes (both favorable) follows soon after, it is important to work on internalizing this very central idea for the student. I do not do internal energy or enthalpy separately and then bring in free energy later. I think these, especially the textbook treatments of the difference between internal energy and enthalpy, obfuscate things unnecessarily. The question is what do you want the student to know and use?
I do not care for the slavish determination of ΔH or ΔG or ΔS values by reference to tables – that is accounting. Instead I want students to be able to apply the following two generalizations: matter tends to more polar bonds and matter tends to more states and more diffuse states. These generalizations can be ascertained by a study of bond energy, enthalpy of formation and entropy tables. For instance the study of heats of formation values for ionic solids will produce the expected conclusion that ionic solids composed of higher charged ions have lower energy than solids composed of lower charged ions. Well chosen similar comparisons of ‘numbers’ for enthalpy and entropy values similarly lead to the generalizations stated above. Using those generalizations students are reasonably successful in predicting the sign and relative magnitude of ΔH or ΔG or ΔS values for a variety of chemical transformations. Once again a fundamental understanding of electronegativity differences comes in to play.
Legs: This big idea has also been nourished by my teaching biochemistry. The operative energy change in all biochemical transformations is ΔGo, free energy change adjusted for pH 7. I teach the rationale for each of the steps in major biochemical pathways by connecting the changes in the nature of the metabolites to the changes in free energy in terms of both enthalpy and entropy changes. Surprisingly many biochemical transformations have a strong entropy driving component. Coupled with the Principle of LeChatelier it makes for a deeper and more fulfilling understanding of the flow of metabolites through pathways and also very nicely establishes the points at which biological control should be manifested.
Although the energy connection is not a major emphasis in organic there is no reason why it cannot be added in terms of predicting which transformations would be more likely.
9-Student: Humans can live under conditions that may be less than ideal. Humans can ‘transition’ to more ideal conditions given appropriate stimulation or motivation
You might think that this is another way of phrasing the previous big idea, but it is not. Many students have a hard time distinguishing between these two chemistry big ideas. Here is how to see the difference. Let’s say you live in a strife torn place. You know that things are better somewhere else. But there are also factors that make you reluctant to leave. There are family connections; there is the fear of having to learn a new language; there is always inertia, a reluctance to take the risk. Something has to ‘push’ you to finally decide to make the decision. You have to harness the energy to go. That last sentence actually directly hits the connection to how matter behaves. It takes an energy shove to go from a less stable to a more stable state but once something gets going, there is a momentum that keeps it going.
9-Audience: Matter can be locked into certain higher energy states that are metastable under those prevailing conditions. Given an appropriate activation matter can transition to a lower energy, more stable state.
Very early on we discovered a guiding principle relating matter and energy: prevailing conditions determine the state of matter [this is established in the evolutionary story of the creation of the elements starting from the Big Bang]. If there were no counteracting processes the previous big idea would dictate that all the elements would combine in such a way that matter overall would be in its most stable state. That would mean that we would exist as carbon dioxide, water and some minerals! That is why we are extremely fortunate for this big idea. Biological processes, primarily photosynthesis, as well as certain geological processes, counteract the tendency of matter to go to its most stable state. There are for instance some very long lived metastable ‘chemical systems’ that are hundreds, some even thousands of years old: redwoods, bristlecone pines. Yet chopped down, put in a pile and ignited, they too return to carbon dioxide and water and minerals and give off a lot of energy as they burn. There are many chemical substances that are stable under the prevailing conditions but if the conditions change, or there is a stimulus provided, the transition to more stable states can occur, sometimes very dramatically.
In general chemistry: The natural extension from the statement of the big idea is to introduce activation energy as a concept. The ‘hump’ to go over can be added to energy diagrams already in place [I use those for H, S and G and for bond energies]. It is important to establish that a certain reaction can go both ways. Photosynthesis and respiration (combustion of glucose) are excellent examples. For photosynthesis activation plus continued energy input is required whereas for respiration only activation is needed. Starting with activation energy and the Arrhenius equation naturally leads to an investigation of kinetics.
Legs: Kinetics of course is important in organic in terms of rate limiting steps in mechanisms and is a central topic in physical chemistry. I would argue for a postponement of the finer points of mechanisms and determination of rate constants and the rest of the mathematical treatment of kinetics until later in the chemistry curriculum. My experience is that it is a level of abstraction that is challenging for many of the students in general chemistry most of whom will benefit more from a greater emphasis on getting structures and energy concepts right.
As the reader has no doubt noticed I put a very heavy emphasis on electronegativity and energy. Both are vessels that can carry explanations for a lot of chemical phenomena. The two are present in some form in at least half of the big ideas, perhaps more. Electronegativity, as already mentioned, arrives very early in a nonconventional way. As for energy I never ever talk about changes in matter without talking about either an energy rationale for that change or what is happening in terms of energy. I do not have a separate thermodynamics chapter. It is embedded in the story line as a second theme to story of matter.
Although I am quite strident about the importance of electronegativity and energy, I am less firmly committed to the other big ideas. Perhaps there are others. Perhaps there are better ways of stating the ones I have given. Perhaps there are better analogies than the ones I have presented. Regardless, I offer this as a starting point for having a serious discussion about thinking about big ideas in chemistry and then working to incorporate those ideas into how we teach chemistry.
This submission would never have seen the light of day without the encouragement and careful editing of Thomas Kuntzleman. He is also responsible for the addition of a big idea that was not in my original inventory (#4) in explicit form.
- Schultz, E. J. Chem. Educ. 2010, 87, 472-473
- Schultz, E. J. Chem. Educ. 2005, 82, 1649-1655