RATE IN CHEMICAL KINETICS

In Section 1.1 we discussed rate in a general way, particularly in cases where time was involved. We now turn our attention to rate in chemical kinetics and, in particular, consider how to define the rate of a chemical reaction. Ideally, this quantity should have the same, positive value, regardless of whether it is defined in terms of a reactant or product species. 

One of the main examples we shall use in this section is a reaction involving hypochlorite ions (CIO ) and bromide ions in aqueous solution at room temperature 

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For the sake of completeness, Equ. 2.5i is often taken as the definition of the reaction rate in chemical kinetics. Nevertheless, the true reaction rate, r, is connected with the previously indicated and used rates of growth or consumption, rj or r, through the stoichiometric coefficients Vj... 

Chemical engineering inherited the definition for the reaction rate from chemical kinetics. The definition is for closed systems, like batch reactors, in which most of the classical kinetic studies were done. Inside a batch reactor little else besides chemical reaction can change the concentration of reactant A. In a closed system, for the reaction of... 

Among other contributions of Arrhenius, the most important were probably in chemical kinetics (Chapter 11). In 1889 he derived the relation for the temperature dependence of reaction rate. In quite a different area in 1896 Arrhenius published an article, "On the Influence of Carbon Dioxide in the Air on the Temperature of the Ground." He presented the basic idea of the greenhouse effect, discussed in Chapter 17. 

Rather than the use of instantaneous or initial rates, the more usual procedure in chemical kinetics is to measure one or more concentrations over the timed course of the reaction. It is the analysis of the concentrations themselves, and not the rates, that provides the customary treatments. The concentration-time data are fitted to an integrated form of the rate law. These methods are the subjects of Chapters 2, 3, and 4. 

Although thermodynamics can be used to predict the direction and extent of chemical change, it does not tell us how the reaction takes place or how fast. We have seen that some spontaneous reactions—such as the decomposition of benzene into carbon and hydrogen—do not seem to proceed at all, whereas other reactions—such as proton transfer reactions—reach equilibrium very rapidly. In this chapter, we examine the intimate details of how reactions proceed, what determines their rates, and how to control those rates. The study of the rates of chemical reactions is called chemical kinetics. When studying thermodynamics, we consider only the initial and final states of a chemical process (its origin and destination) and ignore what happens between them (the journey itself, with all its obstacles). In chemical kinetics, we are interested only in the journey—the changes that take place in the course of reactions. 

Because reactants are used up in a reaction, the concentration of R decreases as time passes thus, A[R] is negative. The minus sign in Eq. la is included to ensure that the rate is positive, which is the normal convention in chemical kinetics. If we follow the concentration of a product P, we express the rate as... 

In chemical kinetics an empirical relationship is used to relate the overall rate of a process to the concentrations of various reactants. A common form for this expression is... 

In chemical kinetics, one finds linked sets of differential equations expressing the rates of change of the interacting species. Overall, mathematical models have been exceedingly successfiil in depicting the broad outlines of an enormously diverse variety of phenomena in nature. Some scientists have even commented in surprise at how well mathematics works in describing nature. So successful have these mathematical models been that their use has spread from the hard sciences to areas as diverse as economics and the analysis of athletic performance [3]. 

The terms rate, speed, and velocity are all synonymous in chemical kinetics, though this is not so in mechanics. It takes different periods of time to complete different reactions. The neutralization reaction between acids and bases, mentioned earlier as an example of homogeneous reactions, takes place almost instantaneously at room temperature and under atmospheric pressure. However, it takes many days for iron to rust under these conditions. Thus, the rates of reactions that may take place under the same conditions of temperature and pressure may differ very significantly. When carbon or sulfur or phosphorus bums in... 

Some economies are possible if equilibrium is assumed between selected compartments, an equal fugacity being assignable. This is possible if the time for equilibration is short compared to the time constant for the dominant processes of reaction or advection. For example, the rate of chemical uptake by fish from water can often be ignored (and thus need not be measured or known within limits) if the chemical has a life time of hundreds of days since the uptake time is usually only a few days. This is equivalent to the frequently used "steady state" assumption in chemical kinetics in which the differential equation for a short lived intermediate species is set to zero, thus reducing the equation to algebraic form. When the compartment contains a small amount of chemical or adjusts quickly to its environment, it can be treated algebraically. 

Chemical kinetics deals with quantitative studies of the rates at which chemical processes occur, the factors on which these rates depend, and the molecular acts involved in reaction processes. A description of a reaction in terms of its constituent molecular acts is known as the mechanism of the reaction. Physical and organic chemists are primarily interested in chemical kinetics for the light that it sheds on molecular properties. From interpretations of macroscopic. kinetic data in terms of molecular mechanisms, they can gain insight into the nature of reacting systems, the processes by which chemical bonds are made and broken, and the structure of the resultant product. Although chemical engineers find the concept of a reaction mechanism useful in the correlation, interpolation, and extrapolation of rate data, they are more concerned with applications... 

Basic Concepts in Chemical Kinetics—Determination of the Reaction Rate Expression... 

Fractional and Other Order Reactions in Constant Volume Systems. In chemical kinetics, one frequently encounters reactions whose orders are not integers. Consider a reaction involving only a single reactant A whose rate expression is of the form... 

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