The Rate of a Chemical Reaction

Reaction rates are related to chemical equilibrium because, as we will see in Section 15.3, a chemical system is at equilibrium when the rate of the forward reaction equals the rate of the reverse reaction. 

A reaction rate can also be defined as the amount of a product that forms in a given period of time. 

Chemists seek to control reaction rates for many chemical reactions. For example, the space shuttle is propelled by the reaction of hydrogen and oxygen to form water. If the reaction proceeds too slowly, the shuttle will not lift off the ground. If, however, the reaction proceeds too quickly, the shuttle can explode. Reaction rates can be controlled if we understand the factors that influence them. 

The gas-phase reaction between hydrogen and iodine can proceed by other mechanisms, but this mechanism is valid for the low-temperature thermal reaction. 

Whether a collision leads to a reaction also depends on the orientation of the colliding molecules, but this topic Is beyond the scope of this text. 

The rate of a chemical reaction is the speed at which the reacting substances are used up or the speed at which the products are formed. The rate of a reaction depends on the following factors  

The fraction of collisions that occur with sufficient energy to get the reacting molecules over the energy barrier. If the free energy of activation is small, then more collisions will lead to reaction than if the free energy of activation is large. 

The rate of a reaction can also be increased by a catalyst (Section 5.11). 

The first person to measure the rate of a chemical reaction carefully was Ludwig Wilhelmy. In 1850, he measured how fast sucrose, upon treatment with add, hydrolyzed into glucose and fmctose. This reaction occurred over several hours, and Wilhelmy was able to show how the rate depended on the initial amount of sugar present— the greater the initial amount, the faster the initial rate. Today we can measure the rates of reactions that occur in times as short as several femtoseconds (femto = 10 ). The knowledge of reaction rates is not only practically important— giving us the ability to control how fast a reaction occurs—but also theoretically important. As you will see in Section 13.6, the rate of a reaction can tell us much about how the reaction occurs on the molecular scale. 

Similarly, the rate of a chemical reaction is measured as a change in the amounts of reactants or products (usually in concentration units) divided by the change in time. For example, consider the gas-phase reaction between H2(g) and 12(g)  

We can define the rate of this reaction in the time interval ti to t2 as follows  

Since 1 mol of H2 reacts with 1 mol of I2, the rates are defined in the same way. The rate can also be defined with respect to the product of the reaction as follows  

---

Arrhenius equation The variation in the rate of a chemical reaction with temperature can be represented quantitatively by the Arrhenius equation... 

The are many ways to define the rate of a chemical reaction. The most general definition uses the rate of change of a themiodynamic state function. Following the second law of themiodynamics, for example, the change of entropy S with time t would be an appropriate definition under reaction conditions at constant energy U and volume V ... 

Finally, a consideration of equilibrium chemistry can only help us decide what reactions are favorable. Knowing that a reaction is favorable does not guarantee that the reaction will occur. How fast a reaction approaches its equilibrium position does not depend on the magnitude of the equilibrium constant. The rate of a chemical reaction is a kinetic, not a thermodynamic, phenomenon. Kinetic effects and their application in analytical chemistry are discussed in Chapter 13. 

There are many potential advantages to kinetic methods of analysis, perhaps the most important of which is the ability to use chemical reactions that are slow to reach equilibrium. In this chapter we examine three techniques that rely on measurements made while the analytical system is under kinetic rather than thermodynamic control chemical kinetic techniques, in which the rate of a chemical reaction is measured radiochemical techniques, in which a radioactive element s rate of nuclear decay is measured and flow injection analysis, in which the analyte is injected into a continuously flowing carrier stream, where its mixing and reaction with reagents in the stream are controlled by the kinetic processes of convection and diffusion. 

Since the rate of a chemical reaction only depends on the slowest, or rate-determining step, and any preceding steps, species B will not show up in the rate law. 

The power law developed above uses the ratio of the two different shear rates as the variable in terms of which changes in 17 are expressed. Suppose that instead of some reference shear rate, values of 7 were expressed relative to some other rate, something characteristic of the flow process itself. In that case Eq. (2.14) or its equivalent would take on a more fundamental significance. In the model we shall examine, the rate of flow is compared to the rate of a chemical reaction. The latter is characterized by a specific rate constant we shall see that such a constant can also be visualized for the flow process. Accordingly, we anticipate that the molecular theory we develop will replace the variable 7/7. by a similar variable 7/kj, where kj is the rate constant for the flow process. 

In this section we shall examine the analogy between the flow of a liquid and the rate of a chemical reaction. This approach has been developed extensively by Eyring and co-workers and has been applied to a wide variety of deformation processes and systems. 

Enzymatic Catalysis. Enzymes are biological catalysts. They increase the rate of a chemical reaction without undergoing permanent change and without affecting the reaction equiUbrium. The thermodynamic approach to the study of a chemical reaction calculates the equiUbrium concentrations using the thermodynamic properties of the substrates and products. This approach gives no information about the rate at which the equiUbrium is reached. The kinetic approach is concerned with the reaction rates and the factors that determine these, eg, pH, temperature, and presence of a catalyst. Therefore, the kinetic approach is essentially an experimental investigation. 

There is no sharp dividing hne between pure physical absorption and absorption controlled by the rate of a chemic reaction. Most cases fall in an intermediate range in which the rate of absoration is limited both by the resistance to diffusion and by the finite velocity of the reaction. Even in these intermediate cases the equihbria between the various diffusing species involved in the reaction may affect the rate of absorption. 

More often than not the rate at which residual absorbed gas can be driven from the liqmd in a stripping tower is limited by the rate of a chemical reaction, in which case the liquid-phase residence time (and hence, the tower liquid holdup) becomes the most important design factor. Thus, many stripper-regenerators are designed on the basis of liquid holdup rather than on the basis of mass transfer rate. 

For many laboratoiy studies, a suitable reactor is a cell with independent agitation of each phase and an undisturbed interface of known area, like the item shown in Fig. 23-29d, Whether a rate process is controlled by a mass-transfer rate or a chemical reaction rate sometimes can be identified by simple parameters. When agitation is sufficient to produce a homogeneous dispersion and the rate varies with further increases of agitation, mass-transfer rates are likely to be significant. The effect of change in temperature is a major criterion-, a rise of 10°C (18°F) normally raises the rate of a chemical reaction by a factor of 2 to 3, but the mass-transfer rate by much less. There may be instances, however, where the combined effect on chemical equilibrium, diffusivity, viscosity, and surface tension also may give a comparable enhancement. 

Later, in the 1890s, Arrhenius moved to quite different concerns, but it is intriguing that materials scientists today do not think of him in terms of the concept of ions (which are so familiar that few are concerned about who first thought up the concept), but rather venerate him for the Arrhenius equation for the rate of a chemical reaction (Arrhenius 1889), with its universally familiar exponential temperature dependence. That equation was in fact first proposed by van t HofT, but Arrhenius claimed that van t Hoff s derivation was not watertight and so it is now called after Arrhenius rather than van t Hoff" (who was in any case an almost pathologically modest and retiring man). 

Catalysis A process by which the rate of a chemical reaction is increased by a substance (namely enzymes in biochemical reactions) that remains chemically unchanged at the end of the reaction. 

Phase-transfer catalysis (Section 22.5) Method for increasing the rate of a chemical reaction by transporting an ionic reactant from an aqueous phase where it is solvated and less reactive to an organic phase where it is not solvated and is more reactive. Typically, the reactant is an anion that is carried to the organic phase as its quaternary ammonium salt. 

The rate of a chemical reaction can be described in any of several different ways. The most commonly used definition involves the time rate of change in tlie amount of one of the components participating in tlie reaction tliis rate is usually based on some arbitrary factor related to tlie reacting system size or geometry, such as volume, mass, or interfacial area. Tlie definition shown in Eq. (4.6.7), wliich applies to homogeneous reactions, is a convenient one from an engineering point of view. 

Strain can affect the rate of a chemical reaction in different ways. If strain increases, i.e., if the transition state is more strained than the reactant, then the barrier will be higher and the reaction will be slower. On the other hand, if strain is relieved during the reaction, the reaction will be faster. 

A catalyst is a substance whose presence increases the rate of a chemical reaction. The exercise of using catalysts is called catalysis. Today the vast majority of all commercially important chemical reactions involve catalysts, especially in the fields of energy production, petrochemicals manufacture, pharmaceuticals synthesis, and environmental protection. 

The rate of a chemical reaction is influenced by pressure, temperature, concentration of reactants, kinetic factors such as agitation, and the presence of a catalyst. Since the viability of a plant depends not only on reaction efficiencies but also on the capital cost factor and the cost of maintenance, it may be more economic to alter a process variable in order that a less expensive material of construction can be used. The flexibility which the process designer has in this respect depends on how sensitive the reaction efficiency is to a change in the variable of concern to the materials engineer. 

The rate of a chemical reaction is proportional to the concentration of the reactants, and for a reversible isothermal homogeneous reaction ... 

These observations remind us of Chapter 8, in which we considered the factors that determine the rate of a chemical reaction. Of course, the same ideas apply here. We can draw qualitative information about the mechanism of the reaction by applying the collision theory. With quantitative study of the effects of temperature and concentration on the rate, we should be able to construct potential energy diagrams like those shown in Figure 8-6 (p. 134). 

Catalyst Basically a phenomenon in which a relatively small amount of substance augments the rate of a chemical reaction without itself being consumed recovered unaltered in form and amount at the end of the reaction. It generally accelerates the chemical change. The materials ordinarily used to aid the polymerization of most plastics are not catalysts in the strict sense of the word (they are consumed), but common usage during the past century has applied this name tathem. 

The rate of a chemical reaction is always taken as a positive quantity, and the rate constant k is always positive as well. A negative rate constant is thus without meaning. An equation such as Eq. (1-4), which gives the reaction rate as a function of concentration, usually at constant temperature, is referred to as a rate law. The determination of the form in which the different concentrations enter into the rate law is one of the initial goals of a kinetic study, since it allows one to infer certain features of the mechanism. 

A catalyst is a substance that increases the rate of a chemical reaction without being consumed itself. We shall see a lot more of catalysts later, when we consider reaction rates in Chapter 13. However, it is important to be aware at this stage that a catalyst has no effect on the equilibrium composition of a reaction mixture. A catalyst can speed up the rate at which a reaction reaches equilibrium, but it does not affect the composition at equilibrium. It acts by providing a faster route to the same destination. 

What do we mean by the rate of a chemical reaction Informally, we consider a reaction to be fast if the products are formed rapidly, as occurs in a precipitation reaction or an explosion (Fig. 13.1). A reaction is slow if the products are formed over a long period of time, as happens in corrosion or the decay of organic material (Fig. 13.2). Our first task is to set up a precise, quantitative definition of the rate of a chemical reaction. 

Although very corrosive, it can be stored and shipped in steel or common alloys at commercial concentrations. In some chemical processes, it is used simply as an acid while in others it is used as a dehydrating agent to remove water, as an agent to increase the rate of a chemical reaction (catalyst), or as a solvent for reactions in which it remains unchanged. It rarely ends up in the final product. Waste sulfuric acid can be recycled. 

Both concentration and temperature affect the rate of a chemical reaction. This section examines how changes in the concentrations of starting materials and products affect the rate of a chemical reaction. We describe temperature effects in Section 15-1. 

For a better understanding of the effect of changing concentrations on the rate of a chemical reaction, it helps to visualize the reaction at the molecular level. In this one-step bimolecular reaction, a collision between molecules that are in the proper orientation leads to the transfer of an oxygen atom from O3 to NO. As with the formation of N2 O4, the rate of this bimolecular reaction is proportional to the number of collisions between O3 and NO. The more such collisions there are, the faster the reaction occurs. 

The rate or the kinetic equations actually result from the law of mass action which states that, at a constant temperature, the rate of a chemical reaction is directly proportional to the product of the concentrations of the reactants. In order to elaborate, by way of illustration the reaction between hydrogen and chlorine, represented in the following manner, is considered ... 

The rate of a chemical reaction (the chemical flux ), 7ch, in contrast to the above processes, is a scalar quantity and, according to the Curie principle, cannot be coupled with vector fluxes corresponding to transport phenomena, provided that the chemical reaction occurs in an isotropic medium. Otherwise (see Chapter 6, page 450), chemical flux can be treated in the same way as the other fluxes. 

A catalyst is a substance that increases the rate of a chemical reaction without itself being changed in the process. That is, the substance called a catalyst is the same after the reaction as before. During the reaction, it may become a different entity, but after the catalytic cycle is complete, the catalyst is the same as at the start. 

What a catalyst does is change the reaction pathway to one with a lower energy however, one must remember that the rate of a chemical reaction depends on two things the rate constant, which contains energy terms (both enthalpy and entropy), and concentration terms. 

However, some sets of reactants can undergo both a forward and a reverse reaction under the same set of conditions. This circumstance leads to a state called chemical equilibrium. Before we take up equilibrium, however, we have to learn about the factors that affect the rate of a chemical reaction. 

---