The rate of a reaction measures how fast the concentrations of the reactants decrease or how fast the concentrations of the products increase. The rate of a reaction is different from its spontaneity. In speaking of chemical reactions, spontaneity has no connotation of speed; it refers only to whether the reaction will occur with the release of free energy as the equation is written and at the specified temperature. The reaction of hydrogen with oxygen is a spontaneous

H₂(g) + ¹/₂O₂(g) H₂O(g)     G = -235 kJ/mol

But a mixture of the two gases can be kept for years at room temperature (298 K) with only imperceptible amounts of water being formed. Only when more energy is added does reaction take place at a measurable rate.

A. Changing the Rate of a Reaction
A reaction will form products more rapidly if the conditions under which the reaction occurs are changed so that more molecules have enough energy to reach the peak of either of the graphs in figure 13.4. There are three ways to increase the size of this set of molecules.

1. Increase the concentration of reactant molecules present
The more molecules present in the reaction vessel, the more likely is a collision. We can increase the number of molecules by increasing the concentration of the reactants. If the reactants are both gases, an increase in pressure decreases the volume and brings the molecules closer together, thus increasing the likelihood of collision.

2. Increase the temperature of the reaction
The rate of a reaction will increase if the number of molecules with enough energy to provide the activation energy of the reaction increases. Figure 13.5 shows the distribution of energies in a collection of molecules at two different temperatures. (We considered the same distribution in Chapter 9). In Figure 13.5, molecules with an energy greater than at point A are sufficiently energetic to provide the activation energy necessary for collision. The screened area under each curve represents the number of molecules at that temperature with an energy greater than A. The screened area is much larger under the higher-temperature curve. Therefore, at the higher temperature, more collisions occur and the reaction proceeds faster. At lower temperatures, these results are reversed and the reaction is slower.

FIGURE 13.5 The distribution of energies in a collection of reacting molecules at two different temperatures.

We store food in a refrigerator because of this effect of temperature on reaction rates. The rates of the reactions that lead to food spoilage are decreased considerably by cooling the food from room temperature to that in a refrigerator. The rates of these reactions are decreased even further by storing food in a freezer. Recent developments in low-temperature surgery have resulted from the application of this principle. By cooling the patient, metabolic reactions are slowed and the operation can be performed more deliberately, with less trauma to the patient.

3. Lower the activation energy required for reaction
We have said that a certain amount of energy, the activation energy, is necessary for reaction. If the activation energy could be lowered (in our bicycling analogy, if the pass were not quite so far above the first valley), more molecules would be able to react. In Figure 13.6, the color line represents a lower activation energy. How can the activation energy of a reaction be lowered? Just as another pass between the valleys might be lower than that originally used, another pathway for the reaction may have a lower activation energy.

FIGURE 13.6 The effect of a catalyst on activation energy. The black line represents energy changes in an uncatalyzed reaction. The colored line shows the energy changes for the same reaction in the presence of a catalyst.

A catalyst can provide such an alternative pathway. A catalyst is a substance that, when added to a reaction mixture, increases the rate of the overall reaction yet is recovered unchanged after the reaction is complete. Suppose a substance C is added to a reaction mixture. If the formation of the product occurs at a faster rate in the presence of C than in its absence and if C is recovered unchanged, then C is a catalyst for the reaction. The colored line in Figure 13.6 shows the energy changes for the same reaction as shown by the black line but in the presence of a catalyst. Activation energy is still required, but it is less than that of the uncatalyzed reaction.

There are many examples of catalysts. Since the mid-1970s, many automobile exhaust systems have been manufactured with catalysts for the reaction

2 CO(g) + O₂(g) 2 CO₂(g)

In the absence of a catalyst, this reaction requires a very high temperature and does not occur significantly at normal exhaust temperatures. The well-being of the public requires that cars stop spewing out large amounts of carbon monoxide. The introduction of a catalyst to the exhaust system of the car makes possible the oxidation of carbon monoxide to carbon dioxide at lower exhaust temperatures, with a considerable improvement in air quality.

The enzymes that trigger biological processes are catalysts. Enzymes have enormous power to change the rates of chemical reactions. In fact, most of the reactions that occur so readily in the living cell would, in the absence of enzymes, occur too slowly to support life.

For example, the enzyme carbonic anhydrase catalyzes the reaction of carbon dioxide and water to form carbonic acid:

CO2 + H2O

carbonic anhydrase

H2CO3

Carbonic anhydrase increases the rate of this reaction almost tenfold over that of the uncatalyzed reaction. Red blood cells are especially rich in this enzyme. For this reason, they are able to absorb carbon dioxide as it is produced in the body and transport it back to the lungs, where it is released as one of the waste products of the body.

Whether catalysts are inorganic like those in automotive emission-control systems or organic like the enzymes of living system, they are remarkably effective because they provide an alternative pathway for a reaction, one that has a lower activation energy.

B. Other Factors That Affect the Rate of a Reaction

1. Surface area
When a reaction is to take place between reactants in two different physical states, the reaction rate is increased if we increase the surface area of the more-condensed reactant. Such reactions include a gas or a liquid with a solid or a gas with a liquid. Consider the reaction between oxygen in the air with cellulose, a reaction we call burning. Cellulose is the main component of wood and of flour. A match will ignite twigs but will not ignite a large log; the twigs have more surface area. If the cellulose is ground to a fine powder (enormous surface area) as in flour, a spark is sufficient to start a very rapid reaction - that is, an explosion. For this reason, flour mills operate under strict regulations designed to prevent static electricity.

Similarly, the reaction between a gas and a liquid will take place more rapidly if the liquid is sprayed in small drops through which the gas passes than if the gas is passed over the surface of a large body of liquid.

2. Light
Some reactions, classified as photochemical reactions, are very sensitive to light. A mixture of the reactants in such a reaction will be stable in the dark indefinitely. When exposed to light of the correct wavelength, the reaction occurs, often at an explosive rate. The reaction of hydrogen with chlorine is one such reaction.

		dark
H2(g) + Cl2(g)no reaction
		light
H2(g) + Cl2(g)2 HCl(g)

The decomposition of nitrogen dioxide into nitrogen monoxide and atomic oxygen is another photochemical reaction. Small amounts of nitrogen dioxide are found in the exhaust gases from gasoline engines. Its decomposition on bright sunny days triggers the series of reactions that causes smog.

Example: The decomposition of hydrogen peroxide is exothermic. The reaction is catalyzed by iodide ion. The equation for the uncatalyzed reaction is 2 H2O2(l) 2 H2O(l) + O2(g) Sketch a possible graph for this reaction, first without a catalyst and then with a catalyst. On both graphs, label the energy of the products and the enthalpy of the reaction. Solution Because the uncatalyzed reaction is exothermic, the enery of the products will be less than the energy of the reactants. The shape of the graph will be like this: . Because the catalyzed reaction is the same reaction as before, the energy of the reactants and the energy of the products will be the same as in the figure above. But, because it is catalyzed, the activation energy will be less as shown here: