### Potential-Energy Curves

In order to understand why and how a reaction works, it is necessary to think about what is really happening. Let's use our favorite example, the burning of hydrogen with oxygen to form water. On the molecular level, diatomic H2 and O2 molecules are smashing into each other. If their speed is low, they simply bounce off each other, like two cars hitting bumpers. However, if the speed is high, they might stick together, like cars crashing together. Since temperature is really only an indication of how fast the molecules are moving, they are more likely to stick together at high temperatures. If they do stick together, the molecule H2O2 is temporarily formed. This molecule (peroxide) is not very stable, and tends to break apart into H2O and an extra oxygen. Energy is also released in the form of heat. During the combustion process, the lone oxygen finds another hydrogen molecule and sticks to it, forming another water molecule and releasing more energy. Because the extra energy makes the molecules move faster, another reaction is more likely to happen, which will release even more heat. This chain reaction happens in a fraction of a second, consuming the reactants and producing water.

The diagram immediately to the right of this paragraph is called a potential-energy curve. It represents in a graphical form the series of events we just discussed. The vertical axis is the potential energy of the reacting atoms or molecules (in joules or kilojoules), and the horizontal axis represents time. Since billions of particles react (at different times) during a reaction, we cannot choose one specific time period to represent. Instead, the potential-energy curve proceeds from the reaction's beginning to completion, a cycle repeated by every reacting particle. A specific time on the curve is called the reaction coordinate.

Before the reaction, the O2 and H2 have a given potential energy, represented by plateau A at the beginning of the reaction. To react, they must overcome the repulsive energy between their negatively-charged electron clouds. This barrier is called the activation energy, and is represented by the sharp increase in potential energy shown by C. If the molecules have sufficient energy to join together, they form a temporary molecule called the activated complex. This complex has high potential energy, represented by the peak on the curve. It then breaks apart into water and the extra oxygen atom. These products have lower potential energy than their reactants at the completion of the reaction (D), with the difference in energies being shown at D. The extra potential energy is given off as heat, and the difference is equivalent to ΔH, the heat change of the reaction. This reaction is exothermic, as potential energy is lost and given off as heat. An endothermic reaction is shown to the left below.

If a reaction is reversed, its potential-energy curve is flipped horizontally, as can be seen in the two curves above. In this case, the old ΔH becomes the new activation energy, while the old activation energy is the new ΔH.

We can now explain the reaction behaviors summarized in the previous page. Because nature seeks a lower state of energy (heat, for example, flows from regions of high thermal energy to cooler areas), exothermic reactions are likely to be product-favored. Endothermic reactions add energy, thus making them mostly reactant-favored.

Spontaneity can also be explained through the potential-energy curve, but first we need to briefly discuss temperature conditions. Temperature, as you know, is merely a representation of the average speed of a group of molecules; the higher the temperature, the faster the molecules move, and thus the higher their kinetic energy. Since temperature is an average, some molecules will move faster than others. A very few molecules will have much higher kinetic energy than would be expected. With this in mind, let's look at the activation energy.

If the activation energy is low enough to be met at the standard temperature, the reaction will be spontaneous because almost all molecules have enough kinetic energy to satisfy the activation requirement. As we raise the activation energy (or lower the temperature), fewer and fewer molecules will be able to react. At very high activation energies, very few molecules will have the necessary speed. However, as long as the reaction is product-favored (which usually implies that it is exothermic), the few reactant molecules with high enough speed will be converted to products. If we wait long enough, the reactants will at some point attain the necessary energy and react. Therefore, the activation energy only determines the speed of a reaction, not whether it is product- or reactant-favored. It is essential that the speed of a reaction not be confused with its favorability. Much of the rest of this chapter will deal with reaction speed; favorability will be explained in the "Thermodynamics" chapter. For now, it is enough to assume that most product-favored reactions are exothermic, while most reactant-favored reactions are endothermic. While the rule does not hold for some reactions (such as the dissolution of ammonium nitrate in water, which is both endothermic and product-favored), it is a fairly safe assumption.

Comparing the activation energy and the ΔH value for a reaction can also be useful. If the ΔH value is much higher than the activation energy, the reaction will be fast and self-sustaining, as the reaction of only a few molecules can supply enough energy to start more and begin a chain reaction. For reactions with large activation energies and low ΔH's, the reaction will only be fast at high temperatures, when the combined energy of the surroundings and the ΔH are large enough to overcome the activation energy. At low temperatures, they will be extremely slow and may appear to be reactant-favored. But don't be fooled!

Now that you are familiar with potential energy curves, you can recognize how much these simple diagrams explain: reaction favorability (for the most part), spontaneity and reaction speed, and why reactions tend to run faster at high temperatures. Next, we will shift tracks and explore a mathematical representation of reaction favorability: K, the equilibrium constant.

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