My answer to the question “What is Color?”

The Alan Alda Center for Communicating Science holds a contest each year to explain a complex scientific idea in under 300 words.  Those 300 words have to convey meaning (and here’s the hard part) to a 5th grader.  This year’s question was “What is Color?”  The finalists have been named and can be read and (in the case of the video entries) seen here.

My (non-finalist) entry is below.  I am posting it because I spent a fair bit of time writing it, so I both want it to see the light of day and receive feedback in the comments section or on twitter (@SGPrilliman).  So I hope you enjoy it and let me know what you think!  Make sure you check out the finalists at the link above.

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What is color? That’s a really important question. When scientists say “That’s a really important question” it means “this isn’t going to be easy” so hang on!

Sometimes light behaves like a wave on the ocean. In this case color is the distance between the peaks of the waves. For red light, the distance from one peak to the next is 600 nanometers (one nanometer is one billionth of a meter). For blue light, the distance from one peak to the next is 400 nanometers. Light behaving as a wave explains why “Blu-ray” disks hold more video than DVD’s. The smaller the wavelength of the laser inside, the closer the grooves can be on the disk, the more data it holds.

That seems okay, right? But in the early part of the 20th Century it became clear that sometimes light was better described as a particle, not a wave. When light behaves like a particle, color is a measure of the energy of the particle. Red light particles have less energy than blue light particles. This is why cooler stars look red, hot stars look blue, and in-between temperature stars (like our sun) look yellow.

So which is it? Is color a measure of the distance between peaks in the waves, or is it a measure of the energy of light particles? The problem is, light is both a particle and a wave, so color is both the distance between waves and a measure of the energy of the particle.

Do you understand? Neither do I. Having two answers to one question is messy, but those are the best kind. Simple answers are boring. Messy answers lead scientists like me and future scientists like you to keep asking questions and developing a deeper understanding of our complex universe.

 

 

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Which of these things is not like the other? Enthalpy of formation, enthalpy of atom combination and bond energy

I have had many questions about the difference between enthalpy of formation (ΔHf) values and enthalpy of atom combination (ΔHac) values.  I’ve also been told there is not much about ΔHac­ values on the internet (which is fine because it would probably be wrong).  Two deal with both issues simultaneously I’m writing this blog post. There are many ways to calculate the change in enthalpy (ΔH) of a chemical reaction.  This is because enthalpy (H) is a state function – the path taken from start to finish does not matter, only the starting materials (reactants) and ending materials (products). The most common ways of calculating ΔH are:

  • Experimentally (from doing the reaction and measuring the heat)
  • Estimating with bond energies (broken bond absorb energy, formed bonds release energy)
  • Using an equation based on the enthalpy of formation (ΔHf): ΔH=ΣΔHf(products) − ΣΔHf(reactants)

ΔHf values are based on the reaction of taking a compound’s elements as they exist at room temperature and atmospheric pressure and measuring the heat released or absorbed when the compound is formed.  In other words, the ΔHf for liquid water is the ΔH of the reaction

H2 (g) + ½ O2(g) →  H2O(l)             ΔH=ΔHf = − 286 kJ/mole

Notice that we have H2 and O2 in the reactants here because oxygen exists as O2 gas  and hydrogen exists at H2 gas molecules at room temperature and atmospheric pressure.  To make liquid water from its element, those elements have to be broken up into atoms then recombined into the compound. Most people use ΔHf values because it gets you the right answer and because… that’s what everyone else does.  Enthalpy of formation values have become one of those things you do not because you really understand it or because it’s the best way but because that’s how it’s always been done.

It turns out there is a better way to do this which is with enthalpy of atom combination values, ΔHac.  The ΔHac values are a measure of the change in enthalpy going from gas phase atoms to a compound.  For liquid water, the corresponding reaction is:

2H (g) + O(g) →  H2O(l)                 ΔH=ΔHac = − 970 kJ/mole

Why?  What difference does it make?  In terms of plugging into the equation, none.  It’s still products minus reactant values.  The units are kJ/mole, so you still have to multiply by the stoichiometric coefficient.  Why bother then? It’s worth bothering because the ΔHac values actually reveal the total bond energy present in 1 mole of a substance.  For gas phase water, the ΔHac value is – 926 kJ/mole, which is two times the O to H bond energy value of 463 kJ/mole.  The extra 44 kJ/mole for liquid water is the hydrogen bonding energy. The enthalpy of formation values do not give you the bond energy.  Enthalpy of formation values only tell you the relative enthalpy change going from the substances elements, which are almost always either molecules or solids.  As such, the enthalpy of breaking down the bonds in those elements is folded into ΔHf, making the value itself useless.  ΔHac values can be plugged in the equation and have intrinsic value. Bond energy is the real concept worth emphasizing here.  Most people don’t understand bond energy and, as a practicing chemist, bond energy is the far more useful concept for understanding new situations, if for no other reason than it doesn’t require tracking down obscure ΔHf or ΔHac­ values.  I’m pretty sure I used ΔHf values once in my entire physical chemistry graduate career.

One more example: carbon dioxide. ΔHac for CO2 = −1609 kJ/mole ΔHf for diamond: −394 kJ/mole What does the ΔHf tell you about bonding in CO2?  Basically nothing because mixed into that number is the breaking of bonds from graphite and O2.  Meanwhile, the ΔHac value tells you that the bond energy of the C to O double bond in CO2 is 805 kJ/mole.

Comments?  Typos?  Still confused?  Tell me in the comment section.

Here is the reference for the paper that first proposed using ΔHac values: Gillespie, R. J., Spencer, J. N., Moog, R. S.  “An Approach to Reaction Thermodynamics through Enthalpies, Entropies, and Free Energies of Atomization.”  J. Chem. Educ., 1996, 73 (7), p 631. http://pubs.acs.org/doi/abs/10.1021/ed073p631

AP Chemistry Big Idea 2

I’mImage starting a series of blog entries on the Big Ideas of the College Board’s new AP Chemistry Curriculum [link] with Big Idea 2 because it’s a little easier to tackle off the bat than Big Idea 1.  Big Idea 2 states:

“Chemical and physical properties of materials can be explained by the structure and the arrangement of atoms, ions, or molecules and the forces between them.” – APCCF

A theme throughout this Big Idea is that students can move back and forth between particulate level representations, symbolic representations and macroscopic observations (which is Science Practice 1).  In other words, Johnstone’s triangle − the idea that expert students can move back and forth between the various representations − becomes very important.

For example, if the student is given LiBr as the formula of a substance they are expected to determine that it will be an ionic compound (LO 2.17), which means it will be a brittle solid (LO 2.19) that dissociates when it dissolves in water because of attraction between the ions and polar water molecules (LO 2.14), forming a solution that conducts electricity (LO 2.19 again).  Given NH3 as a formula a student is expected to determine it will be a molecular compound that dissolves in water because it is polar and forms hydrogen bonds with water (LO 2.15) but does not conduct electricity because it does not form ions but remains discreet molecules containing one N and three H atoms.  The student could also be asked to work with or draw pictures of all of this (LO 2.8) or design an experiment to determine the type of bonding present in an unknown solid (LO 2.22).  In other words, they would have to know you could try to dissolve the compound in water and, if it dissolved, test the conductivity to determine whether the compound is molecular or ionic.

Forces play a large role in the Big Idea, and it’s clear that student need to be able to differentiate between various strengths of forces and the directionality of those forces.  I’m particularly intrigued here by learning objective 2.3:

“The student is able to use aspects of particulate models (i.e., particle spacing, motion, and forces of attraction) to reason about observed differences between solid and liquid phases and among solid and liquid materials.”

I could see a question such as “Why can you move your hand through air and liquid water but not NaCl.  Justify your answer by discussing the interparticle interactions in each substance.”  Air is a mixture of gas molecules and water is composed of H2O molecules.  In the case of air the interaction between particles are weak dispersion forces, easily overcome by the motion of your hand.  In water the interparticle attraction is still relatively weak hydrogen bonds, but enough that you can feel the viscosity. For solid NaCl however, the particles are much closer together than in air or liquid water and more strongly attracted to one another because each ion is a full +1 charge and they are stacked in a lattice structure.  This means the particles cannot easily move when you wave your hand at them and viola!, it behaves as a solid.

The one part of this Big Idea I am still trying to wrap my head around teaching is LO 2.25 which deals with alloys:

“LO 2.25 The student is able to compare the properties of metal alloys with their constituent elements to determine if an alloy has formed, identify the type of alloy formed, and explain the differences in properties using particulate level reasoning.”

The part of me that studied a little materials science in graduate school feels this is too much for AP/general chemistry level knowledge.  I also don’t have a good way to teach this yet. The key word is yet!  I am going to work on a POGIL activity that addresses alloys, which I will post and discuss on this blog.  Please feel free to bug me if I haven’t done it yet.

Comments, questions, and (polite) arguments are encouraged.  Please leave me a note in the comments below.

The covalent bond and why I’m cranky about it

The covalent bond is central to the study of chemistry.  It’s not the only kind of bonding (compounds can exhibit ionic bonding as well, and metallic elements and alloys exhibit metallic bonding), but covalent bonds hold together non-metal atoms into the elegant and beautiful structures we call molecules that constitute the bulk of our field.  No covalent bond means no molecules.  No molecules means pretty much everything is physics.

Like most chemists, I am kind of touchy about how to describe a covalent bond.  My best description is that it is a force between two atoms created by the mutual attraction for shared electrons. Those electrons are only shared because of the laws of quantum mechanics which places them (mostly) in a position between the atoms they hold together. Unfortunately, the notion that a bond is actually a force, not a physical thing, is hard to think about.  How do you draw a force? We have mostly settled on using lines between atoms to signify that this force exists between them.  Many molecular models use sticks to hold atoms together into molecules. This is leads the novice into thinking about atoms held together by sticks, not forces, which leads (in part) to my next problem.

Many students will tell you that breaking a bond releases energy, but the opposite is actually true.  Many people blame the biologists for this because of the emphasis on the hydrolysis of ATP which releases energy.  ATP hydrolysis does cleave an O to P bond but it also forms hydrogen bonds, and the formation of those hydrogen bonds are the reason that energy gets released.

However much blame the biologists receive (or deserve), there is another reason for this misconception. Breaking a bond is not like breaking a stick at all.  Because a covalent bond is an attractive force, you must put energy in to overcome that force.  The correct analogy here is pulling magnets apart, not breaking a stick.  Sadly, because students focus not on bonds as a force (which we say) but rather as bonds as sticks (which we show them), the concept gets messed up in the process of trying to learn it.

I try to emphasize this in class by putting magnets in the hands of my students on the first day we discuss covalent bonds. Whether or not this helps is arguable given them number of students who tell me the wrong answer on exams when I ask about whether or not breaking bonds releases or absorbs energy. However, it is desperately important for teachers and students to think about these issues when covering this most central of chemical concepts.

Significant donuts: error, precision and significant digits

On my significant digits activity in class last week I asked the following question

“If you are doing an experiment with a balance that only reads to the tenths place, is it better to use samples with masses of approximately 5 g or 500 g?  Explain and provide examples. “

My answer to this (the one that, you know, I think is straightforward) is that 500.0 g contains four significant digits and 5.0 g contains two significant digits.  Because more significant digits implies more precision, 500.0 g is the better mass to use in the experiment.

In the past no one has ever really pushed me on this, but four or five of my students have this year, and good for them.  They could have just memorized “my answer” but instead they want to understand.  Which is awesome.

Here’s one way to think about it.  Let’s say you buy two packages of donuts.  The first is supposed to contain 10 and cost $1 (we’re talking little donuts here).  The second box contains 100 and costs $10.  You buy your boxes and take them home, but the first box only contains 9 donuts and the second box only contains 99 donuts.

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Which one are you more upset about?  Most people (unless you over think it) will say the 9 donuts bothers you more because in 10 donuts you really miss the one donut.  In 100 donuts you don’t miss it as much.

In both cases you were cheated out of 10 cents worth of donut, but in the first box this is 10% of your investment, in the second box this is 1% of your investment.  In other words, it’s the percentage difference between the expected and the actual number of donuts that matters.

Now back to masses.  If a scale reads 5.0 g, it really means 5.0 ± 0.1 g.  The difference between the expected mass (5.0 g) and the real mass (which could be between 5.05 or 4.95) is 0.1/5.0 = 2%.  For the 500.0 g mass it’s 0.1/500.0 = 0.02%.  As the mass of the object increases, the uncertainly in our measurements decreases as a percentage of the mass.

All of this gets at what we really mean when we say “significant digits”.  The more significant digits a value has, the more precisely it is known relative to the error that comes from the instrument used to obtain it.  If you use a beaker to measure 10 mL of water you have about a 20% error, so we would call that 10 mL.  You might have 12 or your might have 8 mL.  If you use a pipet, you get a ± 0.02 mL error, so we record that 10.00 mL.

Here’s the point: The rules of significant digits give us the freedom to not have to think about the exact error in every measurement. Why? Because we know that all of the error fits inside the last digit in our value and we leave it at that.

Thoughts?  Discussion?  Please comment below.

Can the internet explain the difference between a molecule and a compound?

Every year I teach my students the difference between the words “molecule” and “compound”.  The difference is that these two words refer to two different concepts on two different size scales.  A molecules is a collection of 2 or more atoms held together by a strong force in a set structure.  Water (H2O), the oxygen in air (O2), the nitrogen in air (N2) and table sugar (C12H22O11) are common substances we encounter that are composed, at the atomic level, or molecules.

We will later will call this force a covalent bond, but that’s later on in the course.  A compound, however, is a pure substance that has a set ratio of two or more elements.  Water (H2O) is a compound that, at the atomic level, is composed of atoms.  O2, is composed of molecules but is not a compound.  It only contains atoms of one element, oxygen.   There is another class of compounds, the ionic compounds, that are compounds that do not form molecules at the atomic level.  Sodium chloride (NaCl, table salt) is composed of rows of ions (or a lattice), the ion pairs are not covalently bonded and will come apart (dissociate) when placed in water.  In other words, ionic compounds are compounds that are NOT composed of molecules.

Every year we have to spend some time on this because it is a persistent misconception that molecules and compounds are the same things.  It turns out that this is a much more persistent misconception than I thought.  If you Google “definition of compound and molecule”, you discover many sites that don’t correctly explain the difference between molecule and compound.  This site and this site and this site are just plain wrong.  They all have some variation on the INCORRECT statement that “all compounds are molecules” and/or “but not all molecules are compounds”.  This site (a .edu address!!) makes it sound like ionic compounds are formed from molecules.

In other words, not only should you not trust the internet, but this is one of those misconceptions that is hard to overcome, even for people who regard themselves as “experts”.  I will fully admit that I didn’t have this distinction clear until I was a chemistry teacher myself (and I have a Ph.D. …).

In celebration of the hard slog

It seems that everyone is focused today on Big Ideas and The Next Big Thing.  Maybe it’s because we live in a world of constant technological change that heightens our awareness of it.  Maybe it’s because Twitter and TED talks have put Big Ideas in nice bite sized packages.  It seems that everyone wants to shift the paradigm, change the optics, focus on the “Big Picture”.  Everyone wants to have a big idea that changes the world.

That’s fine. The big problems facing humanity require big ideas to solve.  However, lost in all of this is a recognition and a celebration of the necessity of the hard slog.  I come (and do most of us) from a long line of farmers, a group of people who understand constant, hard work better than almost anyone. I can’t keep the grass out of a 50 square feet of vegetable garden, let alone manage hundreds of acres of farm. But it is my career as an educator that has made me appreciate the importance of sustained hard work, the importance of incremental change and not just major changes and shifts.

Think about it this way. Let’s say you have one bad math teacher in high school for one year.  Over the course of a school year, you are now (50 minutes x 180 class periods/60 minutes per hour =) 150 hours behind someone that had a good math teacher. That is 150 hours of experience that a teacher later has to help you make up, because if they don’t you will fail his or her class too.  As a university professor I often encounter students who know barely any chemistry upon entering my class.  I also get students who are well prepared and can learn an enormous amount from me because their middle school and high school science and math teachers worked hard, every day over a period of years to teach and prepare them for the next level.

There is a great analogy for this in geology.  Mountains are built up because gigantic plates of the earth’s crust run into each other and force land upward.  Over millions of years, however, these same mountains are worn down by wind and rain into mere hills, then plains.  Tiny changes, unobservable as they happen but sustained over long periods of time, are just as important as tectonic forces.

The work of education, of both teaching and learning, is hard work. But it is that hard work that pays off for my students in the end.  It’s not because someone had the next Big Idea.  It’s because people concentrated and motivated themselves to work hard, day in and day out.  As a new school year begins we need to remember that both kinds of change, dramatic shifts and small but persistent changes, are important and need to be recognized.