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Chemical Kinetics
Thermodynamics teaches us about the energetics and favorability of
reactions but not whether they are fast or slow. For that we need to
understand kinetics , the study of rates of reactions and the physical factors
that influence those rates. Reactions that are thermodynamically favorable
can take millions of years to reach equilibrium. In fact, the velocities of
favorable reactions vary over about 15 orders of magnitude. The speed of
reactions is critically important for living systems, which must ensure that
they occur rapidly enough to be consistent with the rates at which cells
grow and divide. Consequently, cells have evolved strategies to accelerate
reactions so that they occur on a biological timescale. In this chapter, we
will examine the factors that influence reaction rates, and in later chapters,
we will explore the strategies that living systems use to increase and control
those rates.
Reaction rates are determined by the frequency, orientation, and energy
with which molecules collide
Every molecule has a characteristic size, shape, and distribution of electrons.
As 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 a product (or deplete a 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.
- describe the factors that determine reaction rates.
- identify nucleophiles, electrophiles, and leaving groups.
- use arrow pushing to represent reaction mechanisms.
- draw and interpret reaction energy diagrams.
- draw transition states.
- write a rate expression for a simple chemical reaction and explain how the rate is related to ΔG‡.
After this chapter, you should be able to
To understand the physical factors that determine reaction rates.
Objectives
Goal
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 areas of
the reactant molecules, a property determined by the shapes and sizes 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, namely
the velocity of reactant molecules and the 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
Figure 1 Reaction rates depend on multiple factors
reaction rate
=
concentration of reactant molecules
velocity of reactant molecules
cross-sectional area of reactant molecules
probability that molecules collide in the right orientation
probability that molecules collide with enough energy to react
x x x x
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.
Box 2 Interpreting the arrow-pushing formalism
A B A (^) B H Cl H Cl
B (^) A A^ B Cl H H^ Cl
O
H H
O
H H
A B (^) A B
O
H H
O
H H
A B A^ B
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 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 target atom.
An arrow pointing from a double or triple bond to an atom means that one of the bonds breaks, and those electrons form a new lone pair on the target atom.
An arrow pointing from a lone pair to a bond means the lone pair electrons are used to increase the bond order of the target bond (e.g., a single bond becomes a double bond).
Nu E
H O H
Nu E
H O H
Nucleophile Electrophile
(A)
Nu E LG Nu E LG
H N H O
H
H
H N O H
H
H
Nucleophile Electrophile Leaving group
(B)
Figure 2 Nucleophile,
electrophile, and leaving group
describe specific atoms in reaction
mechanisms
(A) Shown is a generic reaction of a
nucleophile with an electrophile (top) and
a specific example involving a reaction
between hydroxide and a hydrogen ion
(bottom). (B) Shown is a generic reaction
involving a leaving group (top) and a
specific example involving a reaction
between amide (NH 2 −) and water (bottom).
Let us apply these concepts to the reaction of carbonic acid (H 2 CO 3 ) with
water to yield bicarbonate and hydronium ion, as discussed in Chapter 3.
The reaction mechanism is described using two arrows (Figure 3). One
arrow points from the lone pair of electrons on the water molecule to a
hydrogen atom on carbonic acid. This arrow conveys the idea that the
oxygen from water is using its lone-pair electrons to form a bond with
the hydrogen atom. Since hydrogen can only form one bond at a time, it
must break its existing bond to oxygen. Breaking the existing O-H bond
is represented by the second arrow, which points from the O-H bond
in carbonic acid to the oxygen atom in the same O-H bond. This arrow
conveys the idea that the O-H bond is breaking and that the electrons from
that bond are being retained by carbonic acid’s oxygen as a lone pair. In this
reaction, the oxygen in water is a nucleophile and the hydrogen in carbonic
acid is an electrophile, as the oxygen in water is using its electrons to form
a new bond and hydrogen is the recipient of those electrons. Finally, the
remainder of the carbonic acid molecule (HCO 3 −) serves as a leaving group,
as it results from the cleavage of the carbonic acid O-H bond; it takes a pair
of electrons with it.
O
C
O
O
H
H
O
H
H
O
C
O
O
H
O
H
H
H
Leaving group
Nucleophile
Electrophile
Figure 3 Using arrow pushing
to describe the mechanism of
carbonic acid dissociation
Box 3
As we will see in Chapter 5 and as shown below, proteins are made from individual amino acid monomers
that are connected by peptide bonds (colored in red). The side chains of each amino acid are represented as
“R 1 ”, “R 2 ”, etc.
Proteins are broken down to amino acids in cells by hydrolysis. Hydrolysis is any reaction in which water
reacts with another species to break an existing bond in that species while forming a new bond to the oxygen
Applying arrow pushing to peptide bond hydrolysis
O
N H R (^4)
H N
R (^5)
O
O
N H R 2
H N
R (^3)
O
R (^1)
Breakout Shown below is the first step of peptide bond hydrolysis, a reaction used by all living
systems to break down proteins. Which atom is the electrophile?
A. The red oxygen.
B. The black oxygen.
C. Nitrogen.
D. Carbon.
E. The red hydrogen.
N
H
O
O H
H
forms a bond to a hydronium ion (Arrow 5). The bond that previously existed between this hydrogen and
the oxygen in hydronium breaks, and the electrons from that bond form a new lone pair on the blue oxygen
atom (Arrow 6).
The next step involves the cleavage of the carbon-nitrogen bond. Note that the atoms in this mechanism have
been recolored for clarity. Arrow 7 shows that a lone pair on the negatively charged oxygen forms a bond
to the carbon atom, creating a double bond. Arrow 8 shows that the carbon-nitrogen bond breaks, with the
electrons from that bond forming a new lone pair on nitrogen. At this point hydrolysis of the peptide bond
has occurred, but in the cell the reaction is not yet complete.
Completion involves another proton transfer. As before, this transfer occurs via two reactions involving
water, as shown below. In one reaction, a lone pair from an oxygen atom in a water molecule forms a new
bond to the red hydrogen atom (Arrow 9), and the bond between the red hydrogen and red oxygen breaks,
with the electrons from the bond forming a new lone pair on oxygen (Arrow 10). In the other reaction, the
lone pair on nitrogen forms a new bond with a hydrogen atom in hydronium (Arrow 11), and the bond
between the hydrogen and oxygen in hydronium breaks, with the electrons from the bond forming a new
lone pair on oxygen (Arrow 12). These final proton transfers are energetically highly favorable and drive the
entire sequence of events that culminate in the hydrolysis of the peptide bond.
N
O
H O H
H
N
O
O
H H
H
7
8
O
O
H (^) O H
H
O
O
O
H
H
H
H N O
H H
H H
H N O
H
H H
H
9
10
11
12
Reaction energy diagrams describe changes in Gibbs free energy as
reactants are converted to products
Another way to represent a reaction mechanism is to depict the change
in Gibbs free energy as individual reactant molecules react to produce a
single set of products. The horizontal axis in the reaction energy diagram
is the reaction coordinate , which is a measure of the extent to which the
reactant molecule(s) has proceeded through energetically distinct steps in
its conversion into a product molecule(s). The reaction coordinate should
not be confused with the time it takes for the reaction to proceed or with
progressive changes in the composition of a mixture of many molecules.
Molecules are represented in reaction energy diagrams as points whose
vertical positions indicate their Gibbs free energy, with more-stable (lower-
energy) species closer to the bottom of the diagram. The difference between
the left-most and right-most points along the vertical axis equals ΔG°rxn (the
difference in free energy under standard conditions between reactants and
products; Chapter 3). Figure 4 shows a reaction energy diagram representing
a thermodynamically favorable reaction (i.e., ΔG°rxn is negative, as depicted
in red) because the free energy of the products is lower than that of the
reactants. Notice that the free energy does not simply decrease along the
reaction coordinate as starting material is converted to product. Rather,
the free energy (G°) increases to a maximum, representing the transition
state (to be discussed below), before decreasing to a level below that of the
reactants. Bonds are being broken and formed as the reaction proceeds,
with different molecules appearing and disappearing during progress along
Figure 4 Using a reaction energy
diagram to represent changes in
free energy in a reaction pathway
Shown is the reaction diagram for a
thermodynamically favorable reaction. The
difference in energy between the reactants
and products equals ΔG°rxn, and since the
reaction is favorable, the products are at a
lower energy than the reactants. The highest
energy state over the course of the reaction
pathway is the transition state, and the
energy difference between the transition
state and the reactants is represented by
ΔG‡.
Course of reaction (reaction coordinate)
G°
∆G°rxn
∆G ‡
Reactants
Products
Transition state
Breakout Which arrow-pushing mechanism would produce the product shown in red?
O
O O
H
H
Product:
(G) Two of these are correct.
O
O O
H
H
O
O O
H H
O
C
O
H
O H
O
O O
H
H
O
O O
H H O
C
O
H
O H
(A)
(D)
(B)
(E)
(C)
(F)
the concentration of the reactants. The greater the ΔG‡, the lower the
concentration of the transition state.
Since chemical reactions proceed to product by going through the
transition state, the rate of a chemical reaction is directly proportional to
the concentration of the transition state at any given moment. Thus, the
reaction energy diagram is a powerful tool for analyzing chemical reactions
because it allows us to assess a reaction’s rate as well as its thermodynamic
favorability. Reactions with very large ΔG‡^ values are said to have high
energy barriers or activation energies, exemplifying the idea that the
reaction occurs slowly because a lot of energy is needed for the reactants to
transform into the transition state. In other words, a reaction with a highly
favorable (highly negative) ΔG°rxn can be extremely slow if ΔG‡^ for the
transition state is very high.
Box 4
Although transition states cannot be observed directly, their structures can be inferred from the reaction
mechanism. To draw a transition state from an arrow-pushing mechanism:
- Inventory the bonds that are being made and broken in one reaction step.
- Draw a single structure in which each of these changing bonds is partially formed. Represent partially
formed bonds using dashed lines. You should find that the dashed lines in your drawing form a
continuous path from one atom to another in the transition state; they are never discontinuous, and
they never branch.
- Assign formal charges in which partially formed bonds represent half a bond, and use δ−^ and δ+^ notation
to represent “half ” charges. You will notice that atoms whose formal charges change during the reaction
will have these partial charges. For example, an atom that is negative in the reactant and neutral in the
product would be partially negative (δ−) in the transition state. This is intuitive given that transition states
represent species that exist in between the reactant and product. Overall charge is conserved between
the reactant, product, and transition state, so the “half ” charges in the transition state will always total
the overall charge found in both the reactant and product.
- Lastly, structures of transition states must be denoted as such by drawing them within brackets and
marking them with the double dagger symbol (‡).
The transition state for the first step of peptide bond hydrolysis is shown below. The bond that breaks during
the reaction is shown in red and the bond that forms is shown in blue.
Transition states can be represented as chemical structures
N
H
O
O H
H
N
H
O
O
H H
transition state products
−
reactants
N
H
O
O
H H
bond
breaking
bond forming
Reaction rate is determined by reactant concentrations and the rate
constant
We are now ready to describe the rate of a reaction in terms of reactant
concentrations and a rate constant. We can express the rate of a single-step
reaction that proceeds via a single transition state as follows:
rate = k [R 1 ][R 2 ]
Where [R 1 ] and [R 2 ] are the concentrations of reactants R 1 and R 2 and k is
the rate constant. The rate constant is a term that describes all of the factors
other than reactant concentrations that affect the rate of a reaction (Figure
6).
The rate constant is related to ΔG‡^ according to the Arrhenius equation
(shown below as a proportionality) in which e is the base for the natural
logarithm (≈ 2.718), R is the gas constant, and T is the temperature in
Kelvin:
We draw two important conclusions from this relationship. First, the
rate constant is inversely related to ΔG‡; as ΔG‡^ becomes larger, the rate
constant becomes smaller. We can understand this relationship intuitively,
as large values of ΔG‡^ are associated with transition states that are difficult
to attain (Figure 7). The second conclusion is that the rate constant varies
with temperature.
Figure 7 The rate constant k and ΔG‡^ correlate with reaction rate
Fast reactions Slow reactions
k is large k is small
∆G‡^ is small (^) ∆G ‡^ is large
rate constant (k)
∆G‡
0
0
increasing rate
k e
−∆G‡ R T
reaction rate
=
concentration of reactant molecules
velocity of reactant molecules
rate constant (k)
cross-sectional area of reactant molecules
probability that molecules collide in the right orientation
probability that molecules collide with enough energy to react
x x x
reaction rate
=
concentration of reactant molecules
x
x
Figure 6 The rate constant accounts for all factors affecting rate other than reactant concentration
reactions enables cells to harness free energy to drive growth, metabolism,
movement, propagation, and other features of living systems in a highly
controlled and controllable manner.
Summary
The rate of a reaction is determined by the frequency with which reactant
molecules collide and the probability that those molecules collide in the
correct orientation and with enough energy to react. The rate at which
molecules collide is influenced by reactant concentration, molecular
velocity, and reactant cross-sectional area. Temperature increases both
molecular velocity (and thus collision frequency) and the probability that
molecules collide with enough energy to react; consequently, reactions
proceed more rapidly at higher temperatures.
Arrow pushing is a formalism that is used to visually represent the
movement of valence electrons that occurs during a reaction (i.e., the
reaction mechanism). Generally speaking, arrow-pushing diagrams use
curved arrows to represent the movement of electron pairs, with arrows
beginning at the source of the electrons (i.e., a lone pair or bond) and
pointing toward the destination of those electrons (i.e., an atom or a bond).
Nucleophile refers to an atom that donates a pair of electrons to form a
bond to another atom to which it was not previously bonded. Similarly,
electrophile refers to the atom to which a nucleophile forms a new bond.
Generally speaking, nucleophiles carry negative charge (full or partial),
and electrophiles carry positive charge (full or partial). The formation of a
new bond between a nucleophile and electrophile often displaces a group
of atoms, called a leaving group, which separates from the electrophile and
forms a second molecule.
A reaction mechanism can also be described using reaction energy diagrams
in which Gibbs free energy is plotted versus the reaction coordinate. The
reaction coordinate is a hypothetical measure of the progress of a reaction
involving one set of reactant molecules as they transform into product
molecules. The energy difference between the products and reactants on
a reaction energy diagram is defined as ΔG°rxn. Each step of a reaction
is indicated by a local maximum on the reaction energy diagram. These
maxima represent the energy of the transition state, which is the highest-
energy species that forms during each step of a reaction. Bonds are breaking
and forming during the transition state, and as such, we show bonds that
are changing using dashed lines in graphical representations of transition-
state structures. Because bonds break during the transition state, essentially
all reactions have an activation energy, ΔG‡, which describes the amount
of energy needed to initiate the reaction. ΔG‡^ is the difference in energy
between the reactants and the transition state. Since energy is always
absorbed during the formation of the transition state, the sign of ΔG‡^ is
always positive.
The rate of a reaction can be described quantitatively using a rate expression
that expresses reaction rate in terms of reactant concentrations. Rate
expressions contain a rate constant k that is inversely related to ΔG‡; therefore,
reactions with large rate constants have small ΔG‡^ values. Reactions with
Practice problems
- Which of the following are reasons why the reaction rate increases with temperature? Select all that
apply.
- Consider the arrow-pushing mechanism shown below:
- Consider the hypothetical one-step reaction shown below.
- The reactants and transition state for a particular reaction are shown below. Draw (a) the arrow-
pushing mechanism that leads from the reactants to the indicated transition state and (b) the
structures of the products that result from the reaction.
i. Collisions between molecules become more frequent.
ii. The reaction cross section increases.
iii. Molecules are more likely to collide with enough energy to react.
a. Which atom is the electrophile? Which atom is the nucleophile?
b. What are the products of this reaction?
a. Write an equation to express the rate of the forward reaction in terms of reactant concentrations.
b. The equilibrium constant for this reaction is measured to be 0.001. Which value is larger, kfor or
krev?
C Cl
H
H
Br H
2 A B
k
for
krev
transition state products
Cl
O
O
H
H
H O
H δ+
Cl δ−
O
O
H
H
O H
H
(Solutions are located on the next page.)
large rate constants have low activation energy barriers and are likely to
proceed quickly. Conversely, reactions with small rate constants have high
activation energy barriers and are likely to proceed slowly. Living systems
use protein catalysts known as enzymes to accelerate and control the rates
of thermodynamically favorable reactions with small rate constants.
