5: Chemical Kinetics, Reaction Mechanisms, and Chemical Equilibrium

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Chemical kinetics is the study of how fast chemical reactions occur and of the factors that affect these rates. The study of reaction rates is closely related to the study of reaction mechanisms, where a reaction mechanism is a theory that explains how a reaction occurs.

5.1: Chemical Kinetics
We can distinguish two levels of detail in a chemical reaction mechanism: The first is the series of elementary processes that occurs for a given net reaction. This is called the stoichiometric mechanism. Frequently it is also possible to infer the relative positions of all of the atoms during the course of a reaction. This sort of model is called an intimate mechanism or detailed mechanism.
5.2: Reaction Rates and Rate Laws
hen we talk about the rate of a particular reaction, we intend to specify the amount of chemical change that occurs in unit time because of that reaction. It is usually advantageous to specify the amount of chemical change in units of moles. We can specify the amount of chemical change by specifying the number of moles of a reactant that are consumed, or the number of moles of a product that are produced, per second, by that reaction.
5.3: Simultaneous Processes
The number of moles of a substance in a system can change with time because several processes occur simultaneously. Not only can a given substance participate in more than one reaction, but also the amount of it that is present can be affected by processes that are not chemical reactions. A variety of transport process can operate to increase or decrease the amount of the substance that is present in the reaction mixture.
5.4: The Effect of Temperature on Reaction Rates
In practice, rate constants vary in response to changes in several factors. Indeed, they are usually the same in two experiments only if we keep everything but the reagent concentrations the same. Another way of saying this is that the rate law captures the dependence of reaction rate on concentrations, while the dependence of reaction rate on any other variable appears as a dependence of rate constants on that variable.
5.5: Other Factors that Affect Reaction Rates
A reaction that occurs in one solvent usually occurs also in a number of similar solvents. For example, a reaction that occurs in water will often occur with a low molecular weight alcohol—or an alcohol-water mixture —as the solvent. Typically, the same rate law is observed in a series of solvents, but the rate constants are solvent-dependent.
5.6: Mechanisms and Elementary Processes
To see what we mean by an elementary process, let us consider some possible mechanisms for the base hydrolysis of methyl iodide. In this reaction, a carbon–iodide bond is broken and a carbon–oxygen bond is formed. While any number of reaction sequences sum to this overall equation, we can write down three that are reasonably simple and plausible.
5.7: Rate Laws for Elementary Processes
If we think about an elementary bimolecular reaction rate law between molecules A and B , we recognize that the reaction can occur only when the molecules come into contact. They must collide before they can react. So the probability that they react must be proportional to the probability that they collide, and the number of molecules of product formed per unit time must be proportional to the number of A−B collisions that occur in unit time.
5.8: Experimental Determination of Rate Laws
The determination of a rate law is a matter of finding an empirical equation that adequately describes reaction-rate data. We can distinguish two general approaches: One approach is to measure reaction rate directly. That is, measure the reaction rate in experiments where the concentrations of reactants and products are known. The other is to measure a concentration at frequent time intervals as reaction goes nearly to completion and seek a differential equation consistent with these data.
5.9: First-order Rate Processes
First-order rate processes are ubiquitous in nature - and commerce. In chemistry we are usually interested in first-order decay processes; in other subjects, first-order growth is common. We can develop our appreciation for the dynamics - and mathematics - of first-order processes by considering the closely related subject of compound interest.
5.10: Rate Laws by the Study of Initial Rates
In concept, the most straightforward way to measure reaction rate directly is to measure the change in the concentration of one reagent in a short time interval immediately following initiation of the reaction. The initial concentrations are known from the way the reaction mixture is prepared. If necessary, the initial mixture can be prepared so that known concentrations of products or reaction intermediates are present.
5.11: Rate Laws from Experiments in a Continuous Stirred Tank Reactor
A continuous stirred tank reactor (CSTR)—or capacity-flow reactor—is a superior method of collecting kinetic data when the rate law is complex. Unfortunately, a CSTR tends to be expensive to construct and complex to operate.
5.12: Predicting Rate Laws from Proposed Mechanisms
Because a proposed mechanism can only be valid if it is consistent with the rate law found experimentally, the rate law plays a central role in the investigation of chemical reaction mechanisms. The discussion above introduces the problems and methods associated with collecting rate data and with finding an empirical rate law that fits experimental concentration-versus-time data. We turn now to finding the rate laws that are consistent with a particular proposed mechanism.
5.13: The Michaelis-Menten Mechanism for Enzyme-catalyzed Reactions
The rates of enzyme-catalyzed reactions can exhibit complex dependence on the relative concentrations of enzyme and substrate. Most of these features are explained by the Michaelis-Menten mechanism, which postulates a rapid equilibration of enzyme and substrate with their enzyme-substrate complex. Transformation of the substrate occurs within this complex. The reaction products do not complex strongly with the enzyme. After the substrate has been transformed, the products diffuse away.
5.14: The Lindemann-Hinshelwood Mechanism for First-order Decay
First-order kinetics for a unimolecular reaction corresponds to a constant probability that a given molecule reacts in unit time. We outline a simple mechanism that rationalizes this fact that assumes the probability of reaction is zero unless the molecule has some minimum energy. For molecules whose energy exceeds the threshold value, we assume that the probability of reaction is constant. However, when collisions are frequent, a molecule can have excess energy only for brief intervals.
5.15: Why Unimolecular Reactions are First Order
The total energy of a molecule is distributed among numerous degrees of freedom. The molecule has translational kinetic energy, rotational kinetic energy, and vibrational energy. When it acquires excess energy through a collision with another molecule, the additional energy could go directly into any of these modes. However, before the molecule can react, enough energy must find its way into some rather particular mode.
5.16: The Mechanism of the Base Hydrolysis of Co(NH₃)₅Xⁿ⁺
The rate law is rarely sufficient to establish the mechanism of a particular reaction. The base hydrolysis of cobalt pentammine complexes is a reaction for which numerous lines of evidence converge to establish the mechanism. To illustrate the range of data that can be useful in the determination of reaction mechanisms, we summarize this evidence here.
5.17: Chemical Equilibrium as the Equality of Rates for Opposing Reactions
The equilibrium constnat that describe the relative concentrations of the species in equilibrium can be extracted from kinetic rate laws.
5.18: The Principle of Microscopic Reversibility
The equilibrium constant expression is an important and fundamental relationship that relates the concentrations of reactants and products at equilibrium. We deduce it above from a simple model for the concentration dependence of elementary-reaction rates. In doing so, we use the criterion that the time rate of change of any concentration must be zero at equilibrium. Clearly, this is a necessary condition; if any concentration is changing with time, the reaction is not at equilibrium.
5.19: Microscopic Reversibility and the Second Law
The principle of microscopic reversibility requires that parallel mechanisms give rise to the same expression for the concentration-dependence of the equilibrium constant. That is, the function that characterizes the equilibrium composition must be the same for each mechanism.
5.20: Problems