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Chemical Kinetics 4 Chemical Kinetics To understand the physical Thermodynamics teaches us about the energetics and favorability of reac- Goal factors that determine reac- tions but not whether they are fast or slow. For that we need to understand tion rates. kinetics, the study of rates of reactions and the physical factors that influ- ence those rates. Reactions that are thermodynamically favorable can take Objectives millions of years to reach equilibrium. In fact, the velocities of favorable After this chapter, you should be able to: reactions vary over about fifteen orders of magnitude. The speed of reac- tions is critically important for living systems, which must ensure that they • describe the factors that determine reaction rates. occur rapidly enough to be consistent with the rates at which cells grow and divide. Consequently, cells have evolved strategies to accelerate reactions • identify nucleophile, electrophile, and so that they occur on a biological timescale. In this chapter we will exam- leaving group. ine the factors that influence reaction rates, and in later chapters, we will • use arrow pushing to represent reaction explore the strategies that living systems use to increase and control those mechanisms. rates. • draw and interpret reaction energy diagrams. Reaction rates are determined by the frequency, orientation, and energy • draw transition states. with which molecules collide • write a rate expression for a simple Molecules have a characterize size, shape, and distribution of electrons. As chemical reaction and explain how the rate is related to ΔG‡. such, a reaction between two molecules can only occur when they physically contact each other; they must collide to react. The rate at which molecules react with each other to form product (or deplete reactant) is determined by the frequency with which they collide, the probability that they collide in an orientation that allows the reaction to occur, and the probability that the molecules that collide do so with enough energy for the reaction to take place. Chapter 4 Chemical Kinetics 2 Probability that Probability that reaction concentration of velocity of cross sectional area of = x x x molecules collide in x molecules collide with rate reactant molecules reactant molecules reactant molecules the right orientation enough energy to react Figure 1 Reaction rates depend on multiple factors Not every collision leads to a reaction, but the rate of a reaction depends on the frequency with which reactant molecules collide, which is influenced by the concentration of the reactants (Figure 1). The larger the number of reactant molecules that are confined within a given volume, the greater the probability of their colliding. The rate of reaction is also influenced by the velocity of the reactant molecules, which again influences the frequency of collisions. The rate of reaction also depends on the cross-sectional area of the reactant molecules, a property determined by the shape and size of the molecules involved in the reaction. Reactions can only occur between parts of molecules that are capable of forming new bonds; therefore, the rate of a reaction also depends on the probability that individual molecules collide in the appropriate orientation to react (Figure 1). However, colliding in a productive orientation is not sufficient. Individual molecules also need to collide with enough energy to react. As we have seen, breaking bonds requires energy, and because all reactions involve the breaking of bonds, an input of energy is required to overcome this energetic barrier (or “threshold of free energy” as we will see below). Even for a favorable reaction in which the products are lower in energy than the reactants, some amount of energy is necessary to overcome this energetic barrier and initiate the bond breaking reaction. The rate of a reaction is influenced by temperature, an insight that was formalized by the scientist Svante Arrhenius in the late 1800’s. Temperature increases the frequency with which molecules collide by influencing the velocity of the reactant molecules and the proportion of molecules with sufficient energy to overcome the energetic barrier to react (see Box 1). Therefore, temperature influences two of the five factors in Figure 1, velocity of reactant molecules and probability that molecules collide with enough energy to react. To better understand how the five factors influence the rate of reactions, we need to understand how reactions proceed, that is, the sequence of events or pathway by which reactions proceed. The reaction pathway can be represented in two complementary ways: by a molecular mechanism and by a reaction energy diagram. These representations allow us to derive rules that predict reaction outcomes. An arrow pushing formalism describes reaction mechanisms Put simply, a chemical reaction is a rearrangement of valence electrons that leads to the cleavage and/or formation of bonds. The specific electron movements associated with each reaction are described by the reaction mechanism. Reaction mechanisms show where electrons originate in the reactant and where they ultimately reside in the product. This is represented Chapter 4 Chemical Kinetics 3 Box 1 The Boltzmann Distribution Energy is not distributed evenly among molecules in a system, and if you were to examine each individual molecule at any moment, you would find that some molecules have more energy than others. As a con- sequence, some molecules may have enough energy to react upon colliding, whereas others may not. As temperature increases, however, so does the probability that molecules in the system have enough energy to react. The Boltzmann distribution describes the probability that a molecule will occupy a specific energy level. Shown below are three simple plots of Boltzmann distributions at different temperatures. Each bar rep- resents the probability of a molecule at that temperature having the indicated energy level (the taller the bar, the higher the probability). Bars further to the right indicate higher energy levels. energy needed to react low temperature medium temperature high temperature increasing energy As you can see, at the “low” temperature it is likely that the molecule is at a low energy level, and there is little chance that it has enough energy to react (as indicated by the dotted line). As temperature increases, how- ever, so does the probability that the molecule has enough energy to react. At the “medium” temperature, there is a small chance that a molecule has enough energy to react. At the “high” temperature, the likelihood of a molecule possesses enough energy to react is much higher. graphically using a formalized system called arrow pushing in which the movement of electrons is diagrammed using a series of curved arrows. Arrow pushing diagrams adhere to the following rules: 1. Each arrow represents the movement of one pair of valence electrons. 2. Each arrow begins where the electrons originate (either a lone pair of electrons or a bond) and ends where the electrons are going (either an atom or a bond). 3. An arrow that starts at an atom represents the movement of a lone pair of electrons. 4. An arrow that starts at the center of a bond represents the breaking of that bond. 5. An arrow that ends at an atom represents the formation of a new covalent bond or a new lone pair. 6. An arrow that ends at a bond represents adding of a bond to form a double (or triple) bond. Applying the rules of arrow pushing so that they become second nature requires practice. Box 2 shows examples of mechanisms that are described by individual arrows. Use arrow pushing to draw the reactions shown in the Boxes and then tackle the practice problems. Chapter 4 Chemical Kinetics 4 Box 2 Interpreting arrow pushing formalism Interpretation Generic Example Molecular Example An arrow pointing from a single bond to an atom means that the bond breaks and a lone pair forms on A B A B H Cl H Cl the target atom. An arrow pointing from a lone pair to an atom means that the lone pair electrons form a new bond to the B A A B Cl H H Cl target atom. An arrow pointing from a double or triple bond to an atom means that one of the bonds breaks, and those O O electrons form a new lone pair on the target atom. A B A B H H H H An arrow pointing from a lone pair to a bond means the lone pair electrons are used to increase the bond O O A B order of the target bond (e.g., a single bond becomes A B a double bond). H H H H As we saw in Chapter 2, many molecules contain atoms that carry full or partial charges. Reactions between molecules (small molecules or functional groups on macromolecules) often occur when the electrons from an atom carrying a negative charge (full or partial) forms a bond with an atom in another molecule that carries a positive charge (full or partial). For reactions in which a bond is formed between atoms that were not previously bonded, the electron-rich atom from which the electrons originate is known as the nucleophile and the electron-deficient, atom is known as the electrophile (Figure 2). As their names imply, nucleophiles are attracted to nuclei and electrophiles are attracted to electrons (philos being Greek for love). Another concept that is important in understanding reaction mechanisms is the leaving group. This term is used to describe an atom or portion of a molecule that separates from a molecule as a result of a bond breaking during the course of a reaction. Leaving groups always take both electrons from the broken bond with them as they depart. Nucleophile, electro- Figure 2 (A) Nu E phile, and leaving group describe Nu E specific atoms in reaction mecha- Nucleophile Electrophile nisms (A) Shown is a generic reaction of a nucle- H O H H O H ophile with an electrophile (top) and a spe- cific example involving a reaction between hydroxide and a hydrogen ion (bottom).
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