Unit 8: Reaction Rates
Introduction
A match is a chemical reaction ready to go, but unless a little heat is added by friction the
reaction will not start. Water can be made with hydrogen and oxygen, but just mixing the
gases is not enough, a catalyst must be used. Kinetics is the study of the rates of reactions.
Understanding the reaction rate is just as important as understanding if the thermodynamics
of a reaction—the energy calculations—are favorable (see unit 7). Some reactions, like the
match, are ready to go but are stable until enough energy is added, other reactions have
driving forces that keep the reaction going forward, and other reactions need a third-party to
negotiate the terms of the reaction like the catalytic reaction of hydrogen and water. This unit
is about rates of reaction, how concentration affects the rate of reaction, catalysts, and the role
of an activated complex in every reaction.
Fire
A fire is a good example of our intuitive understanding of the factors governing a the rate of a
reaction. If you want a fire to burn fiercely and rapidly, then you need lots of wood, heat, and
oxygen. This is why one of the first things done before starting a fire is to gather lots of wood
—then you’ll have a big fire. But, as seen on TV shows so often, starting the fire requires little
bits of wood called kindling, because the match to light the fire is not going to burn the pieces
of wood. Kindling is small, it exposes a lot of the wood’s surface match flame, it also changes
the heat from the match to a temperature change because the mass is low. Still, again in the TV
shows, often all the kindling does is smoke and smolder, until someone blows gently on the
kindling pile. This adds extra oxygen, increasing its concentration. Now the fire can start.
First the little kindling pile, then some sticks, then the logs, and finally the roaring fire.
This scenario introduces the key elements of reaction rate. 1) higher concentrations, like the
added oxygen, lead to greater rates of reaction; 2) some energy is needed to get the reaction
started even if it is exothermic, which is why a match is needed to start a fire even though it
does just fine after it is started; and 3) there are factors that change the concentration and
increase the rate of reaction, like using kindling instead of logs of wood.
the reaction rate is ∆[H2]/∆t or ∆[I2]/∆t or –½ ∆[HI]/∆t.
Concentration vs Time
H2 + I2 ➔ 2 HI
2M –
∆ time
∆ time
∆ [H2] or
∆[I2]
1M–
Rate = 1 ∆[HI]
2 ∆t
∆ [HI]
Concentration (M)
Reaction Rate
Rate is a term usually used to
show the change in something
over change in time. The rate of
travel is the change in distance
over time, and the rate of interest
on your savings is change in
dollars over time. The rate of
reaction, or reaction rate, is the
change in molar concentration of
reactants or products over
change in time. On a graph
concentration vs. time, the rate
of reaction is the slope of the
line. For example, in the reaction
H2 + I2 ➔ 2HI,
Key
—
H2 —
I2 —
HI
Rate = – 1 ∆[H2]
1 ∆t
= – 1 ∆[I2]
1 ∆t
0M–
Time (sec, min, hours, etc.)
On the graph the change in the concentration of the product HI is increasing twice as fast as
the H2 and I2 are disappearing. The coefficients of the balanced equation shows the same
doubling of HI: H2 + I2 ➔ 2HI. In order for the rate of reaction to be the same regardless of
whether a product or reactant concentration is used, the inverse of the coefficient is multiplied
by the change in concentration over change in time; that is if the concentration is twice as large
then the rate will be multiplied by 1/2 to balance the larger change in concentration.
Moreover, the change for the production of products will be positive, because the final
concentration is larger than the starting concentration. But the change in the disappearance of
the reactants will be negative, because the final concentration is smaller than the starting
concentration. Therefore, the rate based on the reactant concentrations is made positive by
multiplying by –1.
Example, “List the rates of reaction for the chemical equation 2Al + 3O2 ➔ 2Al2O3, in terms of
the product and the reactants.”
Rate = – 1 ∆[Al]
Rate = – 1 ∆[O2]
Rate = 1 ∆[Al2O3]
2 ∆t
3 ∆t
2
∆t
Example. “Write the rate of reactions based on products and reactants for the balanced
chemical equation : C2H6 + 5⁄2 O2 ➔ 2 CO2 + 3 H2O
Rate = – ∆[C2H6]
Rate = – 2 ∆[O2]
Rate = 1 ∆[CO2]
Rate = 1 ∆[H2O]
∆t
5 ∆t
2
∆t 3
∆t
Determining Rate of Reaction
To determine the rate of a reaction the experimental data is collected and then the changes in
concentration over time are calculated to give the rate.
For example, “Given the following data determine the average rate of reaction during the first
15 seconds for 2N2O5 ➔ 4NO2 + O2. Show how to calculate the same rate with the products
and the reactant.”
Time
(s)
[N2O5]
mol/L
[NO2]
mol/L
[O2]
mol/L
0.0
0.55
0.00
0.00
15
0.41
0.28
0.07
Rate = – 1 ∆[N2O5] = – (0.41 - 0.55) = 0.0047 M/s
2 ∆t
2•(15 - 0)
Rate = 1 ∆[NO2] = (0.28 - 0) = 0.0047 M/s
4 ∆t
4•(15 - 0)
30
0.31
0.48
0.12
Rate = ∆[O2] = (0.07 - 0)
∆t
(15 - 0)
=
0.0047 M/s
45
0.23
0.64
0.16
All calculations of the rate give the same answer.
But if the rate was calculated at a different time the rate of reaction is slower. For the last 15
seconds the rate of formation of oxygen, O2, is: Rate = ∆[O2] = (0.16 - 0.12) = 0.0027 M/s.
∆t
(45 - 30)
This is because the amount of reactant is decreasing and the rate of reaction is dependent upon
the concentration of the substance measured. This means that the rate of reaction is usually
given as the beginning rate when the concentration changes are largest. In our example we
used an average rate of reaction based on the initial conditions and the first measured value. The
rate would be faster if the first measurement was closer to the beginning of the experiment, say
the first 5 seconds. Using calculus it is possible to get the slope of a single point on the curve
and determine the instantaneous reactioin rate. Usually, the average reaction rate is sufficient for
most problems and experiments, but keep in mind that the rate is an average and that the rate
becomes slower over time.
Pressure instead of Concentration.
Many reactions happen in the gas phase like the reaction used above, 2N2O5 ➔ 4NO2 + O2, .
Instead of concentration, it would be possible to measure amount of each substance in terms of
pressure. This is because all gases follows the ideal gas law in typical reaction conditions and
the formula for the ideal gas law can be manipulated so that molar concentration is
proportional to pressure.
Ideal Gas Law: PV = nRT rearrange to give P = n n/V is molarity so
RT V
P• 1 = Molarity, M
RT
For each gas in the container there is a partial pressure, which is the pressure of only that gas
in a container; whereas, the total pressure in the container is the sum of all the partial pressures
of the substances in the container. To determine the rate of reaction from the partial pressure,
the partial pressure measurements must be multiplied by 1/RT to convert them to molar
concentrations, which can then be used to determine the reaction rate.
Factors that Change the Reaction Rate
Concentration or pressure, temperature, and a catalyst are factors that determine the reaction
rate. The concentration or pressure changes seem obvious based on the previous discussion
because of their direct relationship to rate: rate = ∆[concentration, M] = 1 ∆ P .
∆t RT ∆t
But to understand the reasons for the change, we need a model of the behavior of free moving
particles as gases, liquids, or those in solution.
Kinetic Molecular Theory
Kinetic energy is the energy of motion, and is the energy of the motion of the atoms,
molecules, and ions of matter. Kinetic molecular theory, KMT, states that particles of matter
are in constant and random motion regardless of their state of matter. KMT also proposes that
the motion of particles is directly proportional to temperature, such that, at high temperatures
the particles (on average) are moving faster. Moreover, with regard to gases, KMT
hypothesizes that particles of are too small for their volume to interfere with the properties of a
gas and that the distance between the particles of a gas is so great that the intermolecular
forces are insignificant between the particles.
So at -100°C on the graph almost no particle reach
1000 m/s, but at 600°C many particles have
velocities of 1000 m/s or more .
Maxwel
Te
nu
Maxwell-Boltzmann Distribution
The movement of particles are
random and constant, so particles in a
container do not all have the same
velocity (speed and direction). The
Maxwell-Boltzmann Distribution
graphs the number of particles at
specific velocity at different
temperatures. Each temperature
curve shows a peak near the average
energy, which corresponds to the idea
that temperature is a measure of the
average kinetic energy, since higher
temperatures have higher average
kinetic energies. But what is most
important for rate of reaction is that
high temperature curves show more
and more particles with high energy.
vel
http://commons.wikimedia.org/wiki/File:MaxwellBoltzmann_distribution_1.png
Collision Theory
Collision theory assumes that colliding particles are responsible for the reactions between
substances. Collision theory proposes that a reaction can only occur between particles if three
conditions are met: 1) particles must collide for a reaction to happen, 2) colliding particles
have sufficient energy to initiate the reaction, 3) the particles must be “aimed” or orientated in
a specific way for the reaction to occur.
Collision Theory
Particles must Collide
Collisions Must be of
Sufficient Energy
Particles must have
Appropriate Orientation
H2 + I2 ➔ 2HI
Lines, —, represent amount
of kinetic energy
Factors Affecting Reaction Rate
A reaction will increase in rate when the concentration, pressure, and temperature increase.
With collision theory we can explain the increase in rate due to increase in the number of
particles as measured by concentration or pressure and the increase in the rate of reaction with
the increase in temperature. If there are more particles in a reaction container then the
likelihood of a collision goes up. It also increases the odds that the collision will take place
with sufficient energy and in the correct orientation. If the temperature increases then the
number of particles with sufficient energy to cause a reaction will increase, as shown in the
Maxwell-Boltzmann distribution.
Activated Complex
When a match sits in a box the chemical energy is ready and willing to react, but it stays stable
until the little heat of friction is added. Like in many reactions some energy must be added
before the reaction can begin. The activation energy is the amount of energy needed start a
reaction. In the graphs of an exothermic and endothermic reaction, the activation energy is the
energy needed to get the reaction started.
➡➡Energy ➡➡
➡➡Energy ➡➡
Exothermic Reaction
**
↑
Ea
↓
⎯
Reactants
Products
Reaction Progress
Endothermic Reaction
**
↑
Ea
Reactants
Products
↓
⎯
Reaction Progress
Ea is the activation energy for a reaction. ** is the energy of the activated complex
Once an exothermic reaction starts the activation energy is supplied by the reaction itself,
which is why a match remains lit without adding more friction. For an endothermic reaction
the energy to overcome the activation energy must come from the surroundings, so the
container and whatever else is connected to the reaction mixture become colder as they lose
energy.
**
H2 + I2
Energy
Activated Complex
An activated complex a combination
of the atoms in the reactants that is
halfway between full bond breaking
of the reactants and full bond forming
to make products. This species has the
highest energy of any combination of
atoms from the reactants that leads to
the products. The collision theory
helps explain the nature of the
activated complex: if the particles are
not arranged to form the activation
complex then the collision does not
lead to products, and if the collision
occur with enough energy then the
bond breaking and bond forming of
the complex cannot occur.
** = Activated Complex
2HI
Reaction Progress
Catalyst
A catalyst is a substance that causes a reaction to increase in rate without being consumed by
the reaction. Cells require enzymes, which are proteins, to act as catalysts in biological
processes, and many industrial processes are not possible without a catalyst. When hydrogen
peroxide is added to a cut, it begins foaming or bubbling as it produces oxygen that will kill
bacteria in the wound. The catalase in blood acts as a catalyst and speeds up the
decomposition of the hydrogen peroxide. The catalytic converter in a car usually contains
platinum, palladium, or rhodium as a catalyst, to changes toxic gases in the exhaust fumes into
more benign substances, like NO into N2 and O2.
↕Ea
Reactants
(catalyzed)
Products
Reaction Progress
➡➡Energy ➡➡
➡➡Energy ➡➡
A catalyst works by providing a new pathway for the reactants to form products so the
activated complex is different than the activated complex of the uncatalyzed reaction. The
reaction rate increases because the new pathway has a lower activation energy so the sufficient
energy required by collision theory is lower and more particles can combine successfully. A
graph of a catalyzed reaction shows a “tunnel” through the barrier from the reactants to the
products.
Exothermic Reaction
Endothermic Reaction
↑
Ea
Products
(catalyzed)
Reactants
↓
⎯
Reaction Progress
Summary
The rate of a reaction, or reaction rate, is the change in molar concentration over time and can
be calculated from the data provided by an experiment. The rate of a reaction can be
calculated with either data from the reactants or from the products but it must be equal for
any substance used. For this reason rates are adjusted to be equal. For the model reaction,
aA + bB ➔ cC + dD, the reaction rate = – 1 ∆[A] = – 1 ∆[B] = 1 ∆[C] = 1 ∆[D] .
a ∆t
b ∆t
c ∆t d ∆t
The reaction rate is an average rate from the initial point where data was collected to the final
point that data was collected, so the formulas above calculate average reaction rate. Using
calculus a reaction rate at a point can be calculated which is called the instantaneous reaction
rate.
Collision theory explains the factors affect a reaction. Collision theory states that 1) particles
must collide for a reaction to happen, 2) collisions must have sufficient energy for the reaction
to happen, and 3) only collisions with particles “aimed” or oriented in the correct geometry
will lead to a reaction.
Increasing concentration increases a reaction, because it increases the number of collisions,
which must lead to a greater number of successful collisions. Since the partial pressure of a
gas is related to the concentration of the gas in a container (P/RT = n/V = Molarity), then
increasing pressure also increases the reaction rate. Temperature is a measure of the average
kinetic energy of the particles, so some particles can have high energy and some can have low
energy. When the temperature increases the number of particles with high energy increases,
this causes more collisions between particles with sufficient energy and reaction rate will
increase.
The activation energy for a reaction is the little bit of energy that is needed to make the reaction
proceed to products. Like the friction for striking a match or the dropping of nitroglycerin, the
activation energy will start an exothermic reaction, but the energy that is produced by the
reaction will continue to supply the needed activation energy so the reaction can continue. For
endothermic reactions, the activation energy is supplied by the surroundings that become
colder as energy is removed. The activated complex is the species produced by the activation
energy. It is a combination of the reactant and product with the bonds half broken and half
formed.
A catalyst is a substance that increases the rate of reaction when it is present and is unchanged
at the end of the reaction. Enzymes are used in many cellular processes and industry makes
extensive use of catalysts. A catalyst provides another pathway for a reaction and another
lower activated complex. Because the pathway has a lower activation energy, there are more
successful collisions and the reaction rate increases.
Reaction Rates
8. Chemical reaction rates depend on factors that influence the frequency of collision of
reactant molecules. As a basis for understanding this concept:
a. Students know the rate of reaction is the decrease in concentration of reactants or the
increase in concentration of products with time.
b. Students know how reaction rates depend on such factors as concentration, temperature,
and pressure.
c. Students know the role a catalyst plays in increasing the reaction rate.
d.*Students know the definition and role of activation energy in a chemical reaction.