Elementary Kinetics

INTRODUCTION

Reaction rates

Kinetics is the study of chemical reaction rates. In other words, it is the study of how fast different chemicals react with one another to form new products. Kinetics is needed as a field of study because different chemical reactions occur at different rates. Some chemical reactions happen very quickly once the chemicals involved (called the reactants) are mixed together, while other reactions are relatively slow. For example, a very common kitchen biochemistry experiment involves mixing baking soda (sodium bicarbonate) with household vinegar (a diluted solution of acetic acid):

Na+HCO3–	+	CH3COOH		NaCH3COO–	+	CO2	+	H2O
baking soda		vinegar		sodium acetate		carbon dioxide		water

If you have ever tried this at home, you know that once these reactants are mixed, the solution really begins to fizz as carbon dioxide gas bubbles are released. The reaction proceeds quickly and is over in a minute or so. On the other hand, some reactions occur more slowly. For example, over years, rubber (a polymer chain of isoprene molecules) becomes cracked and brittle, in part because the ozone found in our atmosphere breaks the long polymer into small molecules:

cis-1,4-polyisoprene	+	O3		levulinic acid
natural rubber		ozone		breakdown product

Finally, the rates of some chemical reactions can be changed by the action of catalysts. Catalysts are substances that are able to speed up a chemical reaction. The catalytic converter on your automobile is a good example. When gasoline is not completely burned in your car engine, one of components of the exhaust is carbon monoxide, a toxic gas. Emissions of carbon monoxide are greatly reduced by sending the exhaust through a catalytic converter, which contains expensive platinum metal:

			(Pt)
CO	+	O2		CO2
carbon monoxide		oxygen		carbon dioxide

A structural model of chymotrypsin, an enzyme catalyst. Chymotrypsin greatly accelerates the breakdown of proteins during digestion in the small intestine.

Although this reaction can happen without the platinum, it happens much more slowly. The platinum helps the reaction proceed quickly by holding atomic oxygen (O) so that it can react with the CO. It is important to notice that the platinum is not at all changed by the reaction.

Catalysts dramatically increase the rates of reactions, but are never themselves used up in the reactions they catalyze. Enzymes in our bodies are another good example of catalysts.

Kinetics and thermodynamics

Why do some reactions happen slowly while others happen quickly? First of all, the reaction needs to be physically possible. Although reactions are a matter of probability and no reaction is truly impossible, some molecules are very unlikely to react with one another, even if they spend a lot of time together. The likelihood of a chemical reaction happening can be determined by another field of study called thermodynamics. For a reaction to have a reasonable chance to proceed, the free energy of the products needs to be lower than the free energy of the reactants. In other words, some of the energy stored in the reactant molecules is released when they are formed into products. You may have seen an energy diagram of a chemical reaction, which shows the free energy levels of the reactants and the products.

The free energy difference between the reactants and the products is called DG, or the Gibbs Free Energy of reaction, and it is calculated by the formula:

Energy diagram for a spontaneous reaction.

If the DG is negative, meaning the products are at a lower energy than the reactants, then the reaction is thermodynamically favorable, meaning it has a reasonable likelihood of proceeding. The DG does not indicate how fast this reaction will happen. In the reaction diagram, the blue line represent the energy path of the reaction.

Notice that as the reaction proceeds, the reactants actually have to reach a higher energy state before they can reach the low energy state of the products. The reactants have to scale an "energy wall," called the Energy of Activation (DG^‡). The higher the DG^‡, the taller the wall. As you might suspect, a taller wall is more difficult to scale, and thus reactions with a high DG^‡ proceed more slowly. On the other hand, reactions with a lower DG^‡ proceed faster. Reactions with a lower DG^‡ have a faster reaction rate, and are said to be kinetically favorable.

Why is there a chemical reaction energy wall? One reason is that in a chemical reaction, old bonds in the reactant molecules have to be broken (and breaking things always takes some force!) so that new bonds can be formed. Some bonds are just harder to break than others. Think of it as branches on a tree. A thin twig snaps easily under a little force, but a thick, well-established limb will break only if a large amount of pressure is applied.

Another reason for the energy wall is geometric strain. As two molecules react, they form one larger molecule that is literally bent out of shape. This halfway point between reactants becoming products is known as the transition state. It is shown as the top of the wall in the energy diagram. The transition state is an important concept the study of enzymes.

The more strain on the reactants during the transition state, the more difficult it will be for the products to form (and the slower the reaction proceeds). This is like buying a child's toy or piece of furniture that has "some assembly required" stamped on the box. Sometimes, the pieces snap together easily, and you are done in no time. Other times, you wonder how you will ever squeeze "tab A" into "slot B." Just like in a chemical reaction, the more strain you have to put on the pieces to get them together, the more difficult it is to assemble the product.

Phosphate ion resonance adds stability.

Yet another reason reactants have a hard time scaling the energy wall is that some reactant molecules are particularly stable and thus strongly resist breaking apart. This is an important concept in biochemistry. Some molecules are strengthened through resonance stabilization, a phenomenon in which electrons are distributed among several atoms so that the bonds and electronic charges can be drawn in several different arrangements. A good example of this is the phosphate ion, which distributes negative charges and a double bond over its four P–O bonds. There is no good way to draw the actual phosphate ion, but the structure of the ion can be approximated by drawing all the possible resonance structures on paper.

It is important to remember that the ion does not change back and forth between these four forms but is rather a combination of all of them. The greater the number of possible resonance structures, the greater the stability of the compound.