8.3.2: Temperature and Reaction Rates

Temperature is another important factor when we consider reaction rates. This makes sense if you remember that the vast majority of reactions involve collisions and that the effects of collisions are influenced by how fast the colliding objects are moving. We know intuitively that heating things up tends to make things happen faster. For example, if you want something to cook faster you heat it to a higher temperature (and cooking, as we know, is just a series of chemical reactions). Why is this so? If we consider the reaction of hydrogen and oxygen, discussed in Chapter 7, which is a highly exothermic reaction—explosive, in fact. Yet a mixture of hydrogen and oxygen is quite stable unless energy is supplied, either by heating or a spark of electricity.

The same is true of wood and molecular oxygen. The question is: What is the initial spark of energy being used for?

The answer lies within one of the principles that we have returned to over and over again: When atoms form bonds, the result is a more stable system, compared to the energy of non- bonded atoms. But not all bonds are equally stable; some are more stable than others. Nevertheless, energy is always required to disrupt a bond—any bond. If a reaction is to take place, then at least one of the bonds present in the reactants must be broken, and this requires energy.

Imagine two reactants approaching each other. As the reaction starts to occur, the first thing that happens is that at least one bond in a reactant molecule must start to break. It is the initial, partial-bond-breaking step that requires an input of energy from the molecule’s surroundings, and the amount of energy required and available will determine if the reaction occurs. If the amount of energy in the environment is not enough to begin the breaking of bonds in the reactants (for example, in the burning of wood, large amounts of energy are required for the initial bond breaking), then the reaction will not occur without an energy “push”. Wood does not just burst into flames (at least at standard temperatures)—and neither do humans.¹⁶⁰ The burning wood reaction, wood + O₂ ⇄ H₂O + CO₂, does not occur under normal conditions, but if the temperature increases enough, the reaction starts. Once the reaction starts, however, the energy released from the formation of new bonds is sufficient to raise the local temperature and lead to the breaking of more bonds, the formation of new ones, and the release of more energy. As long as there is wood and oxygen available, the system behaves as a positive and self-sustaining feedback loop. The reaction will stop if one of the reactants becomes used up or the temperature is lowered.

It is the activation energy associated with reactions that is responsible for the stability of our world. For example, we live in an atmosphere of ~20% oxygen (O₂). There are many molecules in our bodies and in our environment that can react with O₂. If there were no energy barriers to combustion (i.e., reaction with O₂), we would burst into flames. Sadly, as Salem witches and others would have attested (if they could have), raise the temperature and we do burn. And once we start burning, it is hard to stop the reaction. As we have said before, combustion reactions are exothermic. Once they have produced enough thermal energy, the reaction doesn’t need that spark any more. But that initial spark needs the addition of energy (such as the kind provided by a detonator) for explosions to occur.

If we plot energy versus the progress of the reaction, we can get a picture of the energy changes that go on during the reaction. Remember that the reaction coordinate on the x-axis is not time; we have seen that reactions go backwards and forwards all the time. For a simple one- step reaction as shown in the figure, the highest point on the energy profile is called the transition state. It is not a stable entity and only exists on the timescale of molecular vibrations (femtoseconds). The energy change between the reactants and the transition state is called the activation energy. This is the energy that must be supplied to the reactants before the reaction can occur. This activation energy barrier is why, for example, we can mix hydrogen and oxygen

and they will not explode until we supply a spark, and why we can pump gasoline in an atmosphere that contains oxygen, even though we know that gasoline and oxygen can also explode. The amount of energy that must be supplied to bring about a reaction is a function of the type of reaction, some reactions (acid base) have low activation energies and correspondingly high rates, and some (rusting) have high activation energies and low rates.

↓ transition state

Now it should be easier to understand how increasing temperature increases the reaction rate—by increasing the average kinetic energy of the molecules in the environment. Recall that even though individual molecules have different kinetic energies, all of the different populations of molecules in a system have the same average kinetic energy. If we consider the effect of temperature on the Maxwell–Boltzmann distribution of kinetic energies, we see right away that at higher temperatures there are relatively more molecules with higher kinetic energy. Collisions between these high-energy molecules provide the energy needed to overcome the activation energy barrier, that is, the minimum energy required to start a chemical reaction. As the temperature rises, the probability of productive collisions between particles per unit time increases, thus increasing the reaction rate. At the same time, it is possible that raising the temperature will allow other reactions to occur (perhaps reactions we have not been considering). This is particularly likely if we are dealing with complex mixtures of different types of molecules.

The rate equation does not appear to contain a term for temperature, and typically we have to specify the temperature at which the rate is measured. However, because the rate changes with temperature, it must be the rate constant that changes. Sure enough, it has been determined experimentally that the rate constant is k can be described by the equation

k= Ae^–Ea/RT,

where k is the rate constant, E_a is the activation energy, T is the temperature, and R and A are constants.¹⁶¹ This is known as the Arrhenius equation. As you can see, k is directly proportional to the temperature, and indirectly proportional to the activation energy E_a. The constant A is sometimes called the frequency factor and has to do with the collision rate. A changes depending on the specific type of reaction (unlike R, the gas constant, which does not change from reaction to reaction). One way of thinking about the rate constant is to consider it as a representation of the probability that a collision will lead to products: the larger the rate constant, the more frequently productive collisions occur and the faster the reaction.

The activation energy for a reaction also depends upon the type of reaction that is occurring. For example, a Brønsted–Lowry acid–base reaction has a very low activation energy barrier. In these reactions the only thing that is happening is that a proton is being transferred from one electronegative element to another:

H—Cl + H—O—H ⇄ Cl^– + H3O⁺

(draw this out to better see what is happening).

The reaction is rapid because the Cl—H bond is highly polarized and weak. In a sense, it is already partially broken. Also, these reactions usually take place in water, which interacts with and stabilizes the growing charges. Low-energy collisions with water molecules are sufficient to finish breaking the Cl—H bond. We say that acid–base reactions like this are kinetically controlled because they occur upon mixing and do not require heating up or extra energy to proceed. Essentially all collisions involving the HCl molecule provide sufficient energy to break the H—Cl bond. This is also true for almost all proton-transfer reactions. However, for most other types of reactions, simply mixing the reactants is not enough. Energy must be supplied to the system to overcome this energy barrier, or we have to wait a long time for the reaction to occur. In fact, most organic reactions (those in which carbon is involved) are quite slow. Why the difference? The answer should be reasonably obvious. There is simply not enough energy in the vast majority of the collisions between molecules to break a C—H, C—C, C—N, or C—O bond. If you take organic chemistry lab, you will discover that large portions of time are spent waiting as solutions are heated to make reactions happen faster. As we mentioned before, this is quite fortunate. As we mentioned before, this is quite fortunate, since we are (basically) organized by chance and natural selection, from collections of organic reactions. If these reactions occurred spontaneously and rapidly, we would fall apart and approach equilibrium (and equilibrium for living things means death!). You may already see the potential problem in all of this: it is generally not advisable to heat up a biological system, but we certainly need biological systems to undergo reactions. Biological systems need different reactions to proceed in different places and at different rates, without being heated up. For this, biological systems (and many other types of systems) use a wide range of catalysts, the topic of our next section.

Questions to Answer

• When a reaction releases energy, where does the energy come from?
• There is a rule of thumb that increasing the temperature by 10°C will double the rate for many reactions.
• What factor in the Arrhenius equation is always changing?
• Explain why the reaction rate increases when the temperature increases.

References

¹⁶⁰ http://en.wikipedia.org/wiki/Spontaneous_human_combustion

¹⁶¹ R is known as the gas constant; it turns up in many different equations. For example, the ideal gas law PV=nRT (the units depend on the equation where it is used). R is also related to the Boltzmann constant kB, (or k, yet another confusing use of symbols, since the Boltzmann constant is in no way related to the rate constant (k), or the equilibrium constant (K)).