You may be familiar with acid-base titrations
that use phenolphthalein as the endpoint indicator. You might
not have noticed, however, what happens when a solution that
contains phenolphthalein in the presence of excess base is
allowed to stand for a few minutes. Although the solution
initially has a pink color, it gradually turns colorless as
the phenolphthalein reacts with the OH- ion in a
strongly basic solution.
The table below shows what happens to the
concentration of phenolphthalein in a solution that was
initially 0.005 M in phenolphthalein and 0.61 M
in OH- ion. As you can see when these data are
plotted in the graph below, the phenolphthalein concentration
decreases by a factor of 10 over a period of about four
Experimental Data for the Reaction
Between Phenolphthalein and Excess Base
Experiments such as the one
that gave us the data in the above table are classified as
measurements of chemical kinetics (from a Greek stem
meaning "to move"). One of the goals of these
experiments is to describe the rate of reactionthe
rate at which the reactants are transformed into the products
of the reaction.
The term rate is often used to
describe the change in a quantity that occurs per unit of
time. The rate of inflation, for example, is the change in
the average cost of a collection of standard items per year.
The rate at which an object travels through space is the
distance traveled per unit of time, such as miles per hour or
kilometers per second. In chemical kinetics, the distance
traveled is the change in the concentration of one of the
components of the reaction. The rate of a reaction is
therefore the change in the concentration of one of the
occurs during a given period of timet.
Rates of Reaction and the Rate Law for a Reaction
The rate of the reaction between
phenolphthalein and the OH- ion isn't constant; it
changes with time. Like most reactions, the rate of this
reaction gradually decreases as the reactants are consumed.
This means that the rate of reaction changes while it is
To minimize the error this introduces into
our measurements, it seems advisable to measure the rate of
reaction over periods of time that are short compared with
the time it takes for the reaction to occur. We might try,
for example, to measure the infinitesimally small change in
concentrationd(X)that occurs over an
infinitesimally short period of timedt.
The ratio of these quantities is known as the instantaneous
rate of reaction.
The instantaneous rate of reaction at any
moment in time can be calculated from a graph of the
concentration of the reactant (or product) versus time. The
graph below shows how the rate of reaction for the
decomposition of phenolphthalein can be calculated from a
graph of concentration versus time. The rate of reaction at
any moment in time is equal to the slope of a tangent drawn
to this curve at that moment.
The instantaneous rate of reaction can be
measured at any time between the moment at which the
reactants are mixed and the reaction reaches equilibrium.
Extrapolating these data back to the instant at which the
reagents are mixed gives the initial instantaneous rate of
Rate Laws and
An interesting result is obtained when the
instantaneous rate of reaction is calculated at various
points along the curve in the graph in
the previous section. The rate of reaction at every point on
this curve is directly proportional to the concentration of
phenolphthalein at that moment in time.
Rate = k(phenolphthalein)
Because this equation is an experimental law
that describes the rate of the reaction, it is called the rate
law for the reaction. The proportionality constant, k,
is known as the rate constant.
Different Ways of
Expressing the Rate of Reaction
There is usually more than one way to measure
the rate of a reaction. We can study the decomposition of
hydrogen iodide, for example, by measuring the rate at which
either H2 or I2 is formed in the
following reaction or the rate at which HI is consumed.
2 HI(g) H2(g)
Experimentally we find that the rate at which
I2 is formed is proportional to the square of the
HI concentration at any moment in time.
What would happen if we studied the rate at
which H2 is formed? The balanced equation suggests
that H2 and I2 must be formed at
exactly the same rate.
What would happen, however, if we studied the
rate at which HI is consumed in this reaction? Because HI is
consumed, the change in its concentration must be a negative
number. By convention, the rate of a reaction is always
reported as a positive number. We therefore have to change
the sign before reporting the rate of reaction for a reactant
that is consumed in the reaction.
The negative sign does two things.
Mathematically, it converts a negative change in the
concentration of HI into a positive rate. Physically, it
reminds us that the concentration of the reactant decreases
What is the relationship between the rate of
reaction obtained by monitoring the formation of H2
or I2 and the rate obtained by watching HI
disappear? The stoichiometry of the reaction says that two HI
molecules are consumed for every molecule of H2 or
I2 produced. This means that the rate of
decomposition of HI is twice as fast as the rate at which H2
and I2 are formed. We can translate this
relationship into a mathematical equation as follows.
As a result, the rate constant obtained from
studying the rate at which H2 and I2
are formed in this reaction (k) is not the same as the
rate constant obtained by monitoring the rate at which HI is
The Rate Law Versus
the Stoichiometry of a Reaction
In the 1930s, Sir Christopher Ingold and
coworkers at the University of London studied the kinetics of
substitution reactions such as the following.
+ OH-(aq) CH3OH(aq) + Br-(aq)
They found that the rate of this reaction is
proportional to the concentrations of both reactants.
Rate = k(CH3Br)(OH-)
When they ran a similar reaction on a
slightly different starting material, they got similar
+ OH-(aq) (CH3)3COH(aq)
But now the rate of reaction was proportional
to the concentration of only one of the reactants.
Rate = k((CH3)3CBr)
These results illustrate an important point: The
rate law for a reaction cannot be predicted from the
stoichiometry of the reaction; it must be determined
experimentally. Sometimes, the rate law is consistent
with what we expect from the stoichiometry of the reaction.
|2 HI(g) H2(g)
||Rate = k(HI)2
Often, however, it is not.
4 NO2(g) + O2(g)
||Rate = k(N2O5)
Some reactions occur in a single step. The
reaction in which a chlorine atom is transferred from ClNO2
to NO to form NO2 and ClNO is a good example of a
+ NO(g) NO2(g) + ClNO(g)
Other reactions occur by a series of
individual steps. N2O5, for example,
decomposes to NO2 and O2 by a
||N2O5 NO2 + NO3
||NO2 + NO3 NO2 + NO + O2
||NO + NO3 2 NO2
The steps in a reaction are
classified in terms of molecularity, which describes
the number of molecules consumed. When a single molecule is
consumed, the step is called unimolecular. When two
molecules are consumed, it is bimolecular.
Reactions can also be classified in terms of
their order. The decomposition of N2O5
is a first-order reaction because the rate of reaction
depends on the concentration of N2O5
raised to the first power.
Rate = k(N2O5)
The decomposition of HI is a second-order
reaction because the rate of reaction depends on the
concentration of HI raised to the second power.
Rate = k(HI)2
When the rate of a reaction depends on more
than one reagent, we classify the reaction in terms of the
order of each reagent.The difference between the molecularity
and the order of a reaction is important.
The molecularity of a reaction, or a step
within a reaction, describes what happens on the molecular
level. The order of a reaction describes what happens on the
macroscopic scale. We determine the order of a reaction by
watching the products of a reaction appear or the reactants
disappear. The molecularity of the reaction is something we
deduce to explain these experimental results.
Model of Chemical Reactions
The collision theory model of chemical
reactions can be used to explain the observed rate laws for
both one-step and multi-step reactions. This model assumes
that the rate of any step in a reaction depends on the
frequency of collisions between the particles involved in
The figure below provides a basis for
understanding the implications of the collision theory model
for simple, one-step reactions, such as the following.
NO(g) NO2(g) +
The kinetic molecular theory assumes that the
number of collisions per second in a gas depends on the
number of particles per liter. The rate at which NO2
and ClNO are formed in this reaction should therefore be
directly proportional to the concentrations of both ClNO2
Rate = k(ClNO2)(NO)
The collision theory model suggests that the
rate of any step in a reaction is proportional to the
concentrations of the reagents consumed in that step. The
rate law for a one-step reaction should therefore agree with
the stoichiometry of the reaction.
The following reaction, for example, occurs
in a single step.
+ OH-(aq) CH3OH(aq)
When these molecules collide in the proper
orientation, a pair of nonbonding electrons on the OH-
ion can be donated to the carbon atom at the center of the CH3Br
molecule, as shown in the figure below.
When this happens, a carbon-oxygen bond forms
at the same time that the carbon-bromine bond is broken. The
net result of this reaction is the substitution of an OH-
ion for a Br - ion. Because the reaction occurs in
a single step, which involves collisions between the two
reactants, the rate of this reaction is proportional to the
concentration of both reactants.
Rate = k(CH3Br)(OH-)
Not all reactions occur in a single step. The
following reaction occurs in three steps, as shown in the
+ OH-(aq) (CH3)3COH(aq)
In the first step, the (CH3)3CBr
molecule dissociates into a pair of ions.
The positively charged (CH3)3C+
ion then reacts with water in a second step.
The product of this reaction
then loses a proton to either the OH- ion or water
in the final step.
The second and third steps in
this reaction are very much faster than first.
|(CH3)3CBr (CH3)3C+ +
+ H2O (CH3)3COH2+
+ OH- (CH3)3COH
The overall rate of reaction
is therefore more or less equal to the rate of the first
step. The first step is therefore called the rate-limiting
step in this reaction because it literally limits the
rate at which the products of the reaction can be formed.
Because only one reagent is involved in the rate-limiting
step, the overall rate of reaction is proportional to the
concentration of only this reagent.
Rate = k((CH3)3CBr)
The rate law for this reaction therefore
differs from what we would predict from the stoichiometry of
the reaction. Although the reaction consumes both (CH3)3CBr
and OH-, the rate of the reaction is only
proportional to the concentration of (CH3)3CBr.
The rate laws for chemical reactions can be
explained by the following general rules.
The rate of any step in a
reaction is directly proportional to the
concentrations of the reagents consumed in that
The overall rate law for a
reaction is determined by the sequence of steps,
or the mechanism, by which the reactants
are converted into the products of the reaction.
The overall rate law for a
reaction is dominated by the rate law for the
slowest step in the reaction.