Chemical energy thread: Readings. These readings were designed for students to read online before class, in a flipped classroom environment.

Transcription

1 Chemical energy thread: Readings These readings were designed for students to read online before class, in a flipped classroom environment.

2 ENERGY AT THE SUB-MOLECULAR LEVEL We have developed the concepts of mechanical energy by looking at the motion of physical objects at the human level. This has led us to the ideas of something that is associated with motion that we call kinetic energy -- the energy of movement (½mv 2 ), and potential energy -- the energy of interaction (and relative place or position). It turns out that as we turn to a consideration of the molecular and atomic level, these concepts still apply, though with some additional factors. Resistive forces and thermal energy One of the things that we learned was that our macroscopic mechanical energy -- kinetic plus potential -- was only conserved if resistive forces (friction, viscosity, drag) could be ignored. If they could not be ignored, the total mechanical energy was drained -- lost as the motion went on. And from considerations of examples with a rapid loss of mechanical energy, we concluded that the lost energy actually went somewhere -- into raising the temperature of the interacting matter. We started to see that increased temperatures correspond to the increased (chaotic) motion of the molecules of the matter. With this perspective, the apparent loss of mechanical energy due to resistive forces can be seen as still conserving mechanical energy, just transforming it from a coherent motion (all the molecules of the object moving in the same direction) to a random and incoherent one (all the molecules of the object moving every which way). But the atomic/molecular perspective doesn't only restore our conservation of mechanical energy. It also transforms the way we think about energy. Kinetic and potential energy in an atom or molecule As you know from your chemistry class, atoms are made up of small dense nuclei (protons and neutrons) that contain most of the atom's mass, and light, fast moving electrons that determine the atom's size. Electrons, protons, and neutrons don't behave like tiny billiard balls. Rather, they have complex properties that are both particle-like and wave-like. Once nuclei and electrons combine to build up an atom, the motion of the atom is, in most circumstances, well described by the classical Newtonian framework we have been studying. Indeed, the Newtonian framework is indispensable for efficient ways to simulate biological processes that involve a large number of atoms or molecules via so called Molecular Dynamics Simulations. But within the atom, and in the binding interactions of atoms into molecules by the sharing of electrons, the rules of quantum physics must be used. In quantum physics, electrons and nuclei still have kinetic and potential energies that add up to a total energy, but at any given instant of time one can't say that an electron has a particular position or velocity -- and as a result one can't say that it has a particular potential or kinetic energy. Electrons (and other objects for which quantum effects are significant) have to be thought of as being capable of being in multiple places and states at the same time described by probabilities. So despite the fact that we describe the potential energy of an electron and its

3 associated kinetic energy. we can't usually think of electrons in the same way as any classical particle moving in a potential well. In addition to the "being in multiple places at once", there are a couple of additional funny factors that have to be added: quantized energy levels and barrier penetration. Quantized energy levels Because electrons behave at some level like waves, the waves have to "fit" into possible orbits. One result is that not all states are allowed for electrons in an atom or molecule. There are certain discrete "energy levels" that are permitted by the laws of quantum physics. The same thing is true of atoms bound into molecules -- though there the effect is less important, since the spacing of the levels depends inversely on the size. It's most important for electrons, less important for molecules. But it provides some valuable tools since the absorption and emission of light is restricted to going between allowed levels and that gives a distinct pattern of absorption and emission that are characteristic of individual atoms and molecules. We'll study this in detail in our analysis of light. Barrier penetration One of the properties of describing motion in terms of energies is that it was easy to determine the endpoints. When the KE goes to 0 so does the velocity so the object stops. Furthermore, the object will never be found in a region in which the KE is negative. In atomic and sub-atomic physics this is not strictly true. An electron can be found in a region where its KE would be negative and it can penetrate through a barrier that would be an absolute wall classically. The probability that this happens goes down -- very fast -- as the barrier gets larger, so don't expect to walk though a wall any time soon! Chemical processes that are important for biology are often prevented from happening by a potential energy barrier. The presence of various catalysts can be used to change the height of the barrier to turn a reaction off or on. Quantum barrier penetration plays some role in determining reaction rates. Transferring energy: Collisions and photons We've mostly looked at situations in which mechanical energy is either conserved or lost to hidden internal degrees of freedom -- the thermal motion of atoms and molecules. But when we consider the motion of atoms and molecules themselves, we have to consider explicitly the way they can exchange energy with other objects in their environment. There are two primary mechanisms by which they do this: collisions with other objects and the absorption or emission of electromagnetic energy -- photons. Atomic and molecular collisions When two moving atoms or molecules collide, they can exchange energy. A nice example of how this works is given in the simulation of molecular interactions from the CLUE project. When two atoms or molecules collide one of the results can be the excitation of the inner electronic motions, putting the molecule in an excited energy state. Sometimes, a collision can lead to a chemical reaction -- a rearrangement of the binding of the atoms. Of course the total

4 energy (mechanical and internal) and momentum of the molecules have to be conserved and this constrains what can happen. Photons Electromagnetic energy -- light, radio waves, X-rays -- also has quantum properties. It can be described as made up of little packets of energy with the energy proportional to the frequency. Molecular states can be changed by the absorption of electromagnetic energy. For example, the absorption of photons by molecules of chlorophyll is the way the energy of the sun is transformed to fuel all life on earth. The absorption of light by molecules of rhodopsin is the basic chemical mechanism by which our bodies create signals that we can interpret as vision.

5 ATOMIC AND MOLECULAR FORCES While chemical bonds and chemical reactions are critical for the functioning of an organism, the longer range interaction forces between atoms and molecules also play a huge role in biology. For example, it is well known in biology that the shape of a molecule determines how it functions. A genetic change that changes a molecule's shape can change its function dramatically. A significant part of this is the electrical attraction between molecules. Let's consider a few questions about the interaction of molecules. If atoms are electrically neutral (with an equal number of protons and electrons in each atom), what makes them stick together to form molecules and larger structures? Conversely, if something makes atoms attract each other, what makes them stay some distance apart, instead of moving all the way together? Why don't molecules (and everything made of molecules) implode? How can we model this interaction quantitatively? And what does all of this have to do with energy? For the answers, read the follow-on pages on Interatomic forces, Molecular bonding, and Hydrogen bonding.

6 INTERATOMIC FORCES Electric potential energy between charges We know from Coulomb's law that two charged objects attract or repel each other with a force proportional to 1/r 2, i.e. inversely proportional to the distance squared. So when the charges get closer together, the force of attraction or repulsion gets stronger. A lot stronger: if you cut the distance between the charges in half, the force will be multiplied by four. We can also describe this in terms of potential energy. Let's say two charges attract. Their electric potential energy falls as 1/r as shown at the right. As the charges get closer to each other, their potential energy gets more negative. This makes sense, because as they move closer together, they would accelerate, and therefore gain more kinetic energy, which means they're losing potential energy. It also makes sense because you would have to do work to split them apart. Not only that, but the slope of the potential energy gets steeper as the charges get closer together, indicating that the force pushing them together is stronger. Now let's say two charges repel. The functional form is the same -- 1/r -- but the sign of the product of the charge is now positive rather than negative, so the situation is reversed. As the charges are pushed closer together, their potential energy increases. (This time, go through the reasoning on your own in reverse, to convince yourself that this makes sense.) Again, the slope of the potential energy gets steeper as the charges get closer together, since the force is still stronger when the charges are closer (even though this force is now a repulsion rather than an attraction). As you know, we can set the "zero" point of potential energy anywhere we want; all that really matters is the change in potential energy as something goes from point A to point B. In other words, we could draw a horizontal zero line at any PE position in the graphs above! But there is

7 one very reasonable choice which we will generally make: Let's set the potential energy to be zero when the two charges are so far away from each other that they don't noticeably interact - "infinitely" far apart. Why do we only introduce two electrostatic interactions? Because the electrostatic potential energy, just like any potential energy from multiple interactions can be simply added up (and it's a scalar so its not as difficult to add up as vector forces). Electric potential energy between neutral objects: Van der Waals forces The explanation above shows why ions, which are charged, attract or repel, but doesn't explain how neutral atoms attract each other. Atoms have an equal number of protons and electrons, so the net charge is zero. So they don't experience electric forces. OR DO THEY? Recall how a rubbed balloon stuck to the wall, even though the wall was neutral. (See the PheT simulation.) What was going on there? Let's say the balloon had a net negative charge. Then the negative charges (electrons) in the wall are repelled by the negative charges in the balloon, and they move (slightly) farther away. Now the part of the wall closest to the balloon has a (slightly) positive net charge, and the negative charge in the balloon is attracted to this positive charge. Though it is much less dramatic than a balloon sticking to a wall, the same process also happens if two neutral objects are brought close to each other. Lets look at this at the atomic scale, and consider a pair of neutral atoms. Atoms are neutral overall, but as you know from chemistry, they are made up of a positive nucleus on the inside, and electrons on the outside. Imagine you're an atom, approaching another atom. You might find that, at a given time, the electrons in that other atom are not distributed completely symmetrically about the nucleus. As a result, when you get close enough, the part of the other atom that happens to be closest to you might look positive or negative. Let's say it looks negative (like the balloon). Then your electrons get repelled to the other side, and the side of you closest to the other atom becomes more Image from CLUE (Chemistry, positive, and you are attracted to the other atom. Or let's say Life, the Universe, and the other atom (on the side closest to you) looks Everything) positive. Then your electrons get attracted to that side, and the side of you closest to the other atom becomes more negative, and once again, you are attracted to the other atom. Either way, the result is an attraction. This net attractive force is known as a Van der Waals force (or specifically a London dispersion force) which you may have heard about in your

8 chemistry class. Here's an animation of this phenomenon, along with some questions to consider. Like Coulomb's law, we expect the Van der Waals force to get stronger as the atoms get closer together, and weaker as they get farther apart. Except much more so! This attraction between atoms is only significant if the atoms are really close; otherwise they just look neutral. How can we model this quantitatively? If we have two bare charges, we know the electric potential goes like 1/r. If we have one bare charge and a dipole (neutral but with + and - charges not in the same place) the potential falls like 1/r 2. If we have two dipoles, the potential falls like 1/r 3. The fact that our dipoles are not fixed but fluctuating, sometimes looking like dipoles, sometimes not, makes the result fall off even faster -- like 1/r 6. That's why Van der Waals forces are only noticeable on atomic scales or when two objects actually touch. Interatomic repulsions But there must be more to the story. If atoms just attracted each other, and this attraction continued to get stronger as they got closer together, then everything would eventually attract to everything, and all matter would collapse. So there has to be something that prevents atoms from getting too close. While the van der Waals attraction can be at least qualitatively explained by physics you have already learned - charges and induced dipoles, the interatomic repulsion relies on physics you have not learned about yet in this intro physics class. Lets simply state that interatomic repulsion has to be even stronger than the attraction at very short distances (preventing all matter from collapsing), but weaker than the van der Waals attraction at larger distances. But what could possibly yield a larger PE at short distances (and a smaller PE at long distances) than at PE that changes as 1/r 6? We had not emphasized this before: while the sixth power makes the potential very small very quickly with increasing distance r, it also makes the potential very strong at very small distances! So to generate a potential that is even stronger at small distances and even weaker at large distance all we have to do is go to a higher "power"! Let's just say we choose as our interatomic repulsion potential a function that goes as 1/r 12 (NOTE: While the physics of the repulsion potential is beyond what we learned in physics so far, you may have learned the physics behind the repulsion potential in your chemistry class! The Pauli exclusion principle states basically that you can't have two electrons in the same state (with the same spin orientation) at the same time. This principle is the basis for putting electrons into different orbitals, which gives different elements their chemical properties. The Pauli exclusion principle provides the answer to our puzzle: atoms can't get too close together, or they'll run into the problem of having two electrons in the same state.)

9 A model for the atom-atom potential was constructed by John Lennard-Jones ( ). It is therefore known as the Lennard-Jones potential and it is a reasonable approximation for the regions that atoms typically explore in biological systems. (Atoms don't get close enough to each other to see the details of the short ranged repulsion at biological temperatures.) The Lennard-Jones potential includes two parts: an attraction proportional to 1/r 6, and a repulsion proportional to 1/r 12. We can write this as PE = A/r 12 - B/r 6, where A and B are constants whose values depend on the specific types of atoms. (The positive term represents repulsion, and the negative term represents attraction.) To see what this looks like, you can try graphing it on a graphing calculator or spreadsheet, and experiment with different values of A and B. What you get is shown in the figure at the right. Let's see what we can conclude from this graph. At large r, the potential energy graph looks flat. The slope is just about zero. Thus, atoms that are far apart feel just about no force. This is a very short ranged interaction! If you double the distance between two atoms, the potential energy associated with their attraction is divided by 64 (= 2 6 ). At small r, the graph climbs very steeply down as you approach the origin, indicating that there is a very strong repulsive force at close range.

10 CHEMICAL BONDING Our simple model of interatomic forces has more implications than just the idea that neutral atoms attract due to mutual polarizations and repel when they get too close. It can actually provide a simple model of chemical bonding. Although most real chemical bonds are more complex than this (and rely heavily on the quantum character of electrons), this simple model gives a decent qualitative idea of how things work and interpreting the atom-atom PE graph provides a basis for understanding some of the more sophisticated (and subtle) representations of chemical reactions. In our discussion of interatomic forces we learned that the typical potential energy between two atoms includes two parts: an attractive part that falls off rapidly with increasing distance (proportional to 1/r 6 ), and a repulsive part that is very short ranged and dominates when the atoms try to get too close. The commonly used Lennard-Jones model of this repulsion goes like 1/r 12, so the total PE is modeled by the equation where A and B are constants whose values depend on the specific types of atoms. To see what this looks like, you can try graphing it on a graphing calculator or spreadsheet, and experiment with different values of A and B. The shape of the PE curve looks like the graph shown in the figure at the right. At large r, the potential energy graph looks flat. The slope is just about zero. Thus, atoms that are far apart feel just about no force. At small r, the graph slopes very steeply down and to the right, indicating that there is a very strong repulsive force at close range. Since the strong positive repulsion dominates at short distances, while the longer range negative attraction dominates at longer distances, in between the graph has to turn around. As the atoms come towards each other from far away, the potential energy slopes downward going negative, and then becomes repulsive and goes positive. Somewhere in between, it has to reach a

11 minimum potential energy, before going back up again. The slope of the graph at this point is zero, so two atoms located at this distance experience no force. The attractive and repulsive forces balance exactly. This is a stable equilibrium: if you move the atom away from this point in either direction, it will experience a force pushing it back towards the equilibrium point. Therefore, atoms that have this potential energy interaction can form stable molecules! The value of r, where the potential energy is at a minimum, tells us the bond length for that particular bond. Here's a simulation of two atoms coming together and forming a bond. (In this simulation, the atoms don't stay together! Why not? What would need to happen for them to stay together?) An example of a pair of atoms in a bound state is shown in the figure at the right by the heavy black line. This represents a particular case of a state of the total mechanical (kinetic plus potential) of the atoms' relative motion. Note that we have chosen the zero of our potential so that the total energy of the bound atoms is NEGATIVE. "Negative relative to what?", you might ask. Relative to our "zero" potential energy, which we take to be when the atoms are far apart and at rest. So there is LESS total mechanical energy when atoms are bonded together than when they are separated. This has two important consequences: 1. If atoms start out bonded together, you have to ADD energy just to get them back to "zero" potential energy, i.e. to pull them far apart. "Breaking" the bond requires an input of energy. 2. In reverse: If a bond is formed (between atoms which were previously separate), the result is less potential energy than they started with, but by the principle of conservation of energy, we know this energy had to go somewhere else (it doesn't just disappear). Thus, when bonds are formed, energy is released. (Where does the energy go

12 when a bond is formed? We'll get into some answers to this question later on, but in the meantime, think about this question and try to come up with some possible answers yourself.) You might also notice that we haven't put the energy line at the very bottom of well to indicate that the two atoms have zero KE and are therefore at rest. In quantum physics objects can never be perfectly at rest: there is always some motion, even at the lowest possible energy (ground state) of the system. The "bond length" measured for various bondings is an average. The atoms actually jiggle a bit about the bond length. What is also important is that not every total energy is allowed. In the example shown at the right, only 5 particular energies are allowed (and all the E's are negative combined to the separated atoms showing that the system is bound). The Lennard-Jones potential (and the more accurate Morse potential) is only a simplified model for atom-atom interactions. When one has strong bonds where the electron orbitals are shared and even modified, a model describing the interaction as occurring between atoms is not really sufficient. A better description explicitly needs to consider the structure of the atom, separating it into a nucleus and electrons. But these potential models allow us to talk about the energy balances involved when chemical reactions happen in a simpler way. It describes the transfer of energy accurately, even if the mechanism is not quite correct.

13 CHEMICAL ENERGY In your chem and bio classes, you've heard of "chemical energy" - the energy associated with chemical reactions. What is it? You already know about kinetic and potential energy; is "chemical energy" now a totally separate type of energy to keep track of? Actually, deep down, chemical energy is kinetic and potential energy: the electric potential energy associated with the electrical interactions between electrons, protons, atoms, and molecules the kinetic energy of electrons moving around inside atoms All chemical reactions can be described in terms of kinetic and potential energies, in the same way that the motion of throwing a ball in the air can be described this way. However, for practical reasons, this isn't always the most convenient way to think about chemical reactions. It's not so easy to measure the positions and velocities of electrons and molecules (to measure kinetic and potential energy directly), and it's much easier to measure energy through macroscopic techniques such as calorimetry. So it can still be useful to think about "chemical energy" as its own concept. (These are the energies that you looked up in tables in your chemistry class, and the energy you saw in diagrams with lots of arrows in your biology class.) But just remember that energy is energy! "Chemical energy" isn't different from "energy in physics" or anything else; it's all the same energy. In our discussion of Chemical bonding, we used a potential energy model of atom-atom interactions to explain why: Atoms can bond with other atoms to form stable molecules; When bonds are formed, energy is released; Breaking bonds requires an input of energy. You may have seen these statements in your chemistry class as rules to be followed, but now you can relate them to the rest of your understanding of energy. Now let's apply this to chemical reactions. Two main things happen in chemical reactions: making bonds and breaking bonds. Some amount of activation energy needs to be added in order to break bonds. When other bonds are formed, energy is released. In chemistry, you've probably seen diagrams that look like this:

14 (Source: Wikipedia) The vertical axis is the energy. The horizontal axis is the "reaction coordinate". This can correspond to the position of one or more of the atoms involved in the reaction, though in chemistry, we're not usually so concerned about which atom(s) it is; the important thing is just that the reaction progresses from left to right. To determine the net energy change for the reaction, we can compare the initial and final energies. If the total energy input required to break the bonds is greater than the total energy released by making bonds, then there is a net input of energy, and the reaction is endothermic. If the total energy released by making bonds is greater than the total energy input required to break the bonds, then there is a net output of energy, and the reaction is exothermic. That's all well and good, but we know that energy is always conserved, so there can't be an overall increase or decrease in energy. Where does this energy come from? And where does it go?

15 Molecules have kinetic energy: they're moving around, rotating, and vibrating. (The amount of kinetic energy that they have is related to their temperature, which we'll learn about soon.) So the source of energy that gets a reaction started might be kinetic energy: a reaction could start when two molecules collide with each other at some speed. If a reaction is endothermic (meaning that there is a net input of energy into the reaction, so we have more total chemical potential energy then we did before), the molecules could end up with less kinetic energy than they started with, which we observe as a decrease in temperature. Another possibility (which makes photosynthesis possible in plants) is that certain molecules can absorb energy from light. (We'll learn much more about light next semester!) There are several possibilities for where the energy could end up afterwards, including: Kinetic energy at the molecular level. We observe this as the system getting hotter. Kinetic energy at the macroscopic level. For example, when fireworks explode, a chemical reaction releases energy, which results in the fragments moving outward in all directions at higher speed. In biological systems, chemical reactions are usually coupled together (e.g. the long series of reactions that make up respiration or photosynthesis), and do not reach equilibrium. (If you reach equilibrium, you're dead!) So the energy output from one reaction becomes the energy input for another reaction. When you think of energy at the molecular scale in biology, you probably think of ATP. And ATP can be very confusing! You know from biology that ATP gets broken down into ADP and phosphate, and energy is released. Yet this seems to contradict everything you know about bonding from chemistry and physics: energy is released when bonds are made, not when bonds are broken! What's up with that??? The answer is that breaking the phosphate bond in ATP isn't the only thing happening there! Breaking this bond requires an input of energy, just like breaking any other bond. However, the phosphate then combines with water and forms another bond, which releases energy. Forming this bond releases more energy than it took to break the ATP bond, so the net effect is a release of energy. You won't always hear the water mentioned, since it's less biologically interesting, but it is crucial to understanding where this energy comes from!