3.3: Potential and Kinetic Energy

One of the most important factors in how, or if, a given material transformation will take place is the energy change associated with it. Energy is a term that is commonly employed in everyday vernacular, often in a vague or qualitative way, giving many students an unwarranted comfort with it.  We need an unambiguous definition, one that lends itself to measurement and quantification. One definition, offered by many well-meaning middle-school science teachers, goes something like: “energy is the capacity to do work”. Which is fine, provided we have a common understanding of what “work” is. Unfortunately, work is an even more poorly understood concept than energy for most people. For our purposes, work simply means the movement of an object against an opposing force. Lifting an object off of a table is a perfect example, as would be pulling two magnets apart. Doing such things requires the application of energy (and undoing these things can supply energy, as we will see).

Figure 3-8. Harnessing the kinetic energy of wind, past and present: (left) a color photochrome print of a Dutch windmill that was taken between 1890 and 1900 in Holland (public domain); (right) modern wind turbines can produce large amounts of electricity and are being promoted as renewable sources of energy ("Wind Turbines in Silhouette" by Adrian S Jones is licensed under CC BY-NC-SA 2.0.)

 

When students are asked to identify types of energy, the following responses, in addition to many others, are often offered: sound, light, motion, heat, and electricity. These are indeed all types of energy and with some clever engineering, they can all be harnessed to do physical work. However, it is helpful to simplify the way we look at energy by classifying it into two clearly distinct types: potential and kinetic. The latter is easy to recognize: kinetic energy is the energy possessed by an object by virtue of its motion. The kinetic energy of flowing wind and water has long been harnessed to perform physical work; mills, for example, have historically often been built along rivers to make use of the energy offered by their currents, and wind has long been used to drive water pumps (like the beautiful old windmills that kept Holland dry) and is being increasingly touted as a green and renewable energy source (Figure 3-8). Most of the types of energy listed above actually fall into the category of kinetic energy: sound is a manifestation of a specific type of particulate vibration, what we recognize as heat is due to rapid and chaotic motion of particles, etc. Recognizing potential energy can be trickier. We can define it, perhaps less succinctly than was possible with kinetic energy, as follows: potential energy is energy possessed by an object by virtue of its position or shape. Some examples will help clarify these ideas.

To elaborate on the above definition, potential energy can be possessed by an object owing to its position in a physical field, specifically a gravitational, electrical, or magnetic field. The proverbial boulder on a hill is a classic example of potential energy as it is perched high in earth’s gravitational field. Just sitting there it does no work, but it has the potential to do work simply because of where it is located. Let it start rolling down the hill, for example, and its ability to do work is clear (physical destruction is a form of work!). Similarly, water behind a dam has potential energy because it can, in effect, “fall” by moving through a channel or turbine.  These examples have one thing in common: the potential energy of the original systems is recognizable by the movement that would result from releasing the objects or materials from whatever is holding them in place. Release the boulder and it rolls. Open a channel under the dam and water flows. Thus potential energy can be converted to kinetic energy, and kinetic energy can be directly harnessed to do work such as grinding wheat, pumping water, or smashing a car that happens to be in the wrong place.

 

Figure 3-9. An example of the work that can be done when potential energy is converted into kinetic energy: a rockslide that destroyed a road and boat launch in the North Cascades National Park in March 2010.  ("Rock Slide on Diablo Lake" is licensed under CC BY-NC-SA 2.0.)

 

 

Examples of potential energy that do not employ gravitational fields are also easy to find. If you take two bar magnets and hold them with like poles together, say north-to-north, you can feel the repulsive force between them. In that position they have potential energy that you will see converted into kinetic energy if you release them: one of the bar magnets will “flip”and the poles will realign themselves, north-to-south. The potential energy of the original configuration had nothing to do with gravity, but instead the magnets’ position with respect to each other’s magnetic fields. In effect, the north-to-north arrangement had the potential to do work via the motion of the “flip” when they are released. 

The conversion between potential energy and work operates in both directions: we can turn the above examples on their heads, to illustrate how. Boulders can be lifted, returning them to their precarious perches, using cranes powered by electricity or internal combustion engines. Water will not flow uphill on its own, but we can carry it in a bucket to a higher elevation, i.e., do work on it. In these cases, we are moving objects away from the Earth’s surface, increasing their potential to do work should they be released again. Likewise, magnets that are stuck together can be pulled apart, increasing their capacity to do work should they be released and slam back together.

 

 

Figure 3-10. Setting a mousetrap twists the spring mechanism, thereby storing potential energy in the form of its new shape; that potential energy can be released suddenly, with disastrous consequences for unwary rodents.  Molecules can also be twisted into forms that have higher potential energy. (Image by Charles Rondeau, released under CC 1.0)

 

 

Before moving to examples that have greater chemical relevance to chemical bonding, it is worth looking at the last form of potential energy we referred to above, specifically that possessed by an object by virtue of its shape, or conformation. A couple of familiar examples include springs and rubber bands. Anyone who has shot a rubber band at a friend or sibling knows that, when stretched, it is capable of achieving impressive speeds, and therefore kinetic energy, because its stretched shape endows it with potential energy. In contrast, a spring that is neither compressed nor extended beyond its resting position has no capacity to do work because its shape cannot change on its own. But compress it and the situation changes: it now has potential energy that is entirely due to its new conformation. Its tendency to spontaneously revert to its original form enables it to perform useful work such as accelerating a vehicle or irreversibly rearranging a mouse’s vertebrae (Figure 3-10). While this form of potential energy may seem irrelevant to chemistry, it is most definitely not: the relationship between a molecule’s conformation and its energy is often the key determinant in the shape it will assume. And for many biological molecules such as proteins and enzymes, shape is everything. For example, it is the relaxation of a "compressed" form of a protein called myosin that is responsible for the contraction of muscles, such as those controlling your eyes as they read these words. This and other "molecular machines" operate via a sequence of compression and relaxation of protein molecules, whereby molecules are "worked on" to assume high energy conformations and then relaxing back down to a more stable shape. These cycles are typically powered by the energy released by the reaction of water with ATP (adenosine triphosphate), the so-called "energy carrier" in most organisms. More about that later.

Because matter is ultimately composed of charged particles, the potential energy that arises from electrostatics has particular relevance to chemistry. The key idea here is much the same as we already described with the example of the magnets. Consider two particles, one positively and one negatively charged. As you know, opposite charges attract each other. If we hold these two particles apart they possess potential energy, in a manner that is analogous to holding two masses apart, such as the Earth and that boulder on the hill. In the latter example, the farther the boulder is from the Earth’s surface, the more potential energy it possesses; with the charged particles, the greater the distance between them, the greater the potential energy. Releasing the particles results in their movement towards each other, culminating in their collision and sticking together, just like the magnets we previously described. We can separate the particles, but only by doing work on them, and doing so restores their potential energy.

The notion that the potential energy of the particles increases with the distance between them may seem counterintuitive because the attractive force between the particles gets weaker as they get farther apart. But this is no different than how the potential energy of an object increases with its height; if the height becomes great enough, the gravitational force acting on it becomes weaker, yet the potential to do work increases because the distance the object can fall also increases. To illustrate, we can diagram the energy for a system of two oppositely charged particles (Figure 3-11). As can be seen, the potential energy drops off rapidly as the two charges get close to one another. This is because the amount of work that can be performed by the particles moving toward each other diminishes as they get closer together: they have less distance to travel to reach their destination so the possibility of extracting work out of that movement lessens. This is true despite the fact that the attractive force between them increases as they approach each other. 

 

 

Figure 3-11. Potential energy as a function of the distance between two oppositely charged objects. Note that the potential energy falls off rapidly as the two objects get closer together and reaches a minimum value when they the objects meet.

 

 

 

Let’s take a different view of the information in Figure 3-11. Imagine the two oppositely charged particles are stuck together; the distance between them is zero and their potential energy is at a minimum because no work can be extracted from them if we allow them to move because they can’t - they are as close together as possible. We can separate them, but that requires work. The force necessary to pull the particles apart is greatest at first because the attractive force between them is greatest when they are close together. But as the distance between them increases, it becomes easier and easier to continue pulling them apart. Thus the potential energy continues to increase, but not as rapidly as when we first separated them; the potential energy curve begins to plateau and it will asymptotically approach a limiting value. 

The sort of energy profile depicted in Figure 3-11 is often referred to as a potential energy well. Oppositely charged particles will tend to fall into such wells in an "energy landscape", moving as close as possible to each other and thereby minimizing their potential energy. It is not so different from other, literal, landscapes you have seen firsthand. Rainwater will accumulate in a rutted, potholed terrain at the lowest points: these are spots of least potential energy and water spontaneously flows downhill, leading it to these points. Similarly, the spontaneous movement of oppositely charged particles brings them together. These are simple examples of a profound principle: processes that decrease potential energy tend to be spontaneous, meaning that, once initiated, they do not require any assistance to make them proceed. That boulder, for example, once it begins to roll will continue to roll until something stops it.  Chemical processes, too, can usually be understood in terms of changes in potential energy: reactions that result in decreases in potential energy will proceed spontaneously and, if the decrease in potential energy is large enough, sometimes explosively.