OME General Chemistry
Lecture 8: Chemical Reaction Kinetics
Dr. Vladimir Lesnyak
Office: Physical Chemistry, Erich Müller-Bau, r. 111
Email: [email protected]
Phone: +49 351 463 34907
1
Outline
Reaction Rates
1 Definition of Reaction Rate
2 Experimental Determination of Rate
3 Dependence of Rate on Concentration
4 Change of Concentration with Time
5 Temperature and Rate: Collision and Transition-State Theories
6 Arrhenius Equation
Reaction Mechanisms
7 Elementary Reactions
8 The Rate Law and the Mechanism
9 Catalysis
2
Reaction Time
Chemical reactions require varying lengths of time for completion, depending on
the characteristics of the reactants and products and the reaction conditions.
The study of the rate of a reaction has important applications. For example, in the
manufacture of ammonia from nitrogen and hydrogen, we need to know what
conditions will help the reaction proceed in a commercially feasible length of time.
Studying reaction rates helps us to understand how chemical reactions occur. By
noting how the rate of a reaction is affected by changing conditions, we can learn the
details of what is happening at the molecular level.
3
Rates of Reaction
A reaction whose rate has been extensively studied under various conditions:
2N2O5(g) → 4NO2(g) + O2(g)
Questions:
How is the rate of a reaction measured?
What conditions affect the rate of a reaction?
What is the relationship of rate of a reaction to the variables that affect rate?
What happens at the molecular level?
Chemical kinetics is the study of reaction rates,
how reaction rates change under varying conditions,
and what molecular events occur during the overall reaction.
4
Reaction Rates
The rate of any reaction may be affected by:
1. Concentrations of reactants. Often the rate of reaction increases
when the concentration of a reactant is increased.
2. Concentration of catalyst. (A catalyst is a substance that increases the
rate of reaction without being consumed in the overall reaction.)
3. Temperature. Usually reactions speed up when the temperature
increases.
4. Surface area of a solid reactant or catalyst. The rate increases with
increasing surface area.
5
Definition of Reaction Rate
Reaction rate is the increase in molar concentration of product of a reaction
per unit time or the decrease in molar concentration of reactant per unit time.
The usual unit of reaction rate is moles per liter per second, mol/(L·s).
2N2O5(g) → 4NO2(g) + O2(g)
Average rate of formation of O2 =
∆[𝑂𝑂2]
∆𝑡𝑡
The instantaneous rate of reaction
The concentration of O2 increases over
time. The instantaneous rate at a given
time is obtained from the slope of the
tangent at the point on the curve
corresponding to that time.
The slope = ∆[O2]/∆t.
6
Calculation of the Average Rate
2N2O5(g) → 4NO2(g) + O2(g)
Rate of formation of O2 =
∆[𝑂𝑂2]
∆𝑡𝑡
Rate of decomposition of N2O5 = −
∆[𝑁𝑁2𝑂𝑂5]
∆𝑡𝑡
∆[𝑂𝑂2]
1 ∆[𝑁𝑁2𝑂𝑂5]
=−
∆𝑡𝑡
2 ∆𝑡𝑡
The average rate of formation of O2 during the decomposition of N2O5 was
calculated during two different time intervals. When the time changes from
600 s to 1200 s, the average rate is 2.5×10-6 mol/(L·s). Later, when the time
changes from 4200 s to 4800 s, the average rate has slowed to 5×10-7 mol/(L·s).
Thus, the rate of the reaction decreases as the reaction proceeds.
7
Reaction Rate: Problem
A plot of the concentration of a reactant D vs time
1. How do the instantaneous rates at points A and B compare?
2. Is the rate for this reaction constant at all points in time?
8
Experimental Determination of Rate
To obtain the rate, we must determine the concentration of a
reactant or product during the course of the reaction.
One way to do this for a slow reaction is to withdraw samples
from the reaction vessel at various times and analyze them.
More convenient are techniques that can continuously follow
the progress of a reaction by observing the change in some
physical property of the system. These physical methods are
often adaptable to fast reactions as well as slow ones.
9
Experimental Determination of Rate
An experiment to follow the concentration of N2O5
The total pressure is measured during the reaction at 45oC. Pressure values can be
related to the concentrations of N2O5,NO2, and O2 in the flask.
2N2O5(g) → 4NO2(g) + O2(g)
Also: monitoring the decomposition of N2O5 by the intensity of the red-brown
color of NO2. The intensity of absorption at a particular wavelength is measured
by a spectrometer appropriate for the visible region of the spectrum.
Depending on the reaction, other types of instruments are used, including
infrared (IR) and nuclear magnetic resonance (NMR) spectrometers.
10
Dependence of Rate on Concentration
2NO2(g) + F2(g) → 2NO2F(g)
A rate law is an equation that relates the rate of a reaction to the
concentrations of reactants (and catalyst) raised to various powers.
Rate = 𝑘𝑘 𝑁𝑁𝑁𝑁2 [𝐹𝐹2]
rate constant k, is a proportionality constant in the
relationship between rate and concentrations.
The units of k depend on the form of the rate law:
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
𝑘𝑘 =
𝑁𝑁𝑁𝑁2 [𝐹𝐹2]
aA + bB
𝑚𝑚𝑚𝑚𝑚𝑚/(𝐿𝐿 � 𝑠𝑠)
= L/(mol � 𝑠𝑠)
𝑚𝑚𝑚𝑚𝑚𝑚/𝐿𝐿 2
catalyst C
→ dD + eE
Rate = 𝑘𝑘 𝐴𝐴
k varies with temperature!
𝑚𝑚
𝐵𝐵
𝑛𝑛
𝐶𝐶
𝑝𝑝
The exponents m, n, and p are frequently, but not always, integers.
They must be determined experimentally and they cannot be
obtained simply by looking at the balanced equation.
11
Reaction Order
The reaction order with respect to a given reactant species is the exponent of
the concentration of that species in the rate law, as determined experimentally.
Rate = 𝑘𝑘 𝑁𝑁𝑁𝑁2 𝐹𝐹2 → 1st order reaction with respect to NO2 and F2
The overall order of a reaction is the sum of the
orders of the reactant species in the rate law.
Rate = 𝑘𝑘 𝑁𝑁𝑁𝑁2 𝐹𝐹2 → 2nd overall order
2NO(g) + 2H2(g) → N2(g) + 2H2O(g)
Rate = 𝑘𝑘 𝑁𝑁𝑁𝑁
2
𝐻𝐻2 → 2nd order in NO, 1st order in H2, 3rd overall order
Although reaction orders frequently have whole-number values (particularly 1 or 2),
they can be fractional. Zero and negative orders are also possible.
12
Reaction Order: Problem
NO2(g) + CO(g) → NO(g) + CO2(g)
Rate = 𝑘𝑘 𝑁𝑁𝑁𝑁2
2
What is the order of reaction with respect to each reactant species?
What is the overall order of this reaction?
13
Determining the Rate Law
The experimental determination of the rate law for a reaction
requires the order of the reaction with respect to each reactant
and any catalyst.
The initial rate method is a simple way to obtain reaction
orders. It consists of doing a series of experiments in which the
initial, or starting, concentrations of reactants are varied. Then
the initial rates are compared, from which the reaction orders
can be deduced.
14
Initial Rate Method
2N2O5(g) → 4NO2(g) + O2(g)
Initial N2O5
Initial Rate of
Concentration Disappearance of N2O5
Experiment 1 1.0×10‒2 mol/L 4.8 10‒6 mol/(L·s)
Effect on Rate of Doubling
the Initial Concentration of
Reactant
Experiment 2 2.0×10‒2 mol/L 9.6 10‒6 mol/(L·s)
m
Rate Is
Multiplied by
Rate 1 = k[N2O5]m
–1
½
Rate 2 = k(2[N2O5])m = 2mk[N2O5]m
0
1
1
2
2
4
10−6
9×
𝑚𝑚𝑚𝑚𝑚𝑚/(𝐿𝐿 � 𝑠𝑠)
=2
4.8 × 10−6 𝑚𝑚𝑚𝑚𝑚𝑚/(𝐿𝐿 � 𝑠𝑠)
Rate = k[N2O5]1
9.6 × 10−6 𝑚𝑚𝑚𝑚𝑚𝑚/(𝐿𝐿 � 𝑠𝑠) = 𝑘𝑘 × 2 × 10−2 mol/L
9.6 × 10−6 /𝑠𝑠
−4 /𝑠𝑠
𝑘𝑘 =
=
4.8
×
10
2.0 × 10−2
Although reaction orders of greater than 2 are possible, they
are not nearly as common as those less than or equal to 2.
15
Change of Concentration with Time
A rate law tells us how the rate of a reaction depends on reactant concentrations at
a particular moment. But often we would like to have a mathematical relationship
showing how a reactant concentration changes over a period of time.
Knowing exactly how the concentrations change with time for different rate laws
suggests ways of plotting the experimental data on a graph. Graphical plotting
provides an alternative to the initial-rate method for determining the rate law.
Using calculus, we can transform a rate law into a mathematical relationship
between concentration and time called an integrated rate law.
16
Integrated Rate Laws (Concentration-Time Equations):
First-Order Rate Law
aA → products
2N2O5(g) → 4NO2(g) + O2(g)
∆ 𝑁𝑁2𝑂𝑂5
= 𝑘𝑘 𝑁𝑁2𝑂𝑂5
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = −
∆𝑡𝑡
𝑙𝑙𝑙𝑙
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = −
𝑁𝑁2𝑂𝑂5 𝑡𝑡
= −𝑘𝑘𝑘𝑘
𝑁𝑁2𝑂𝑂5 0
𝑙𝑙𝑙𝑙
∆ 𝐴𝐴
= 𝑘𝑘 𝐴𝐴
∆𝑡𝑡
𝐴𝐴 𝑡𝑡
= −𝑘𝑘𝑘𝑘 (1st order integrated rate law)
𝐴𝐴 0
This equation enables to calculate the concentration of N2O5 at any time,
having the initial concentration and the rate constant.
Also, we can find the time it takes for the N2O5 concentration to decrease to
a particular value.
𝑑𝑑 𝐴𝐴
−
= 𝑘𝑘 𝐴𝐴
𝑑𝑑𝑡𝑡
−
𝑑𝑑 𝐴𝐴
= 𝑘𝑘𝑑𝑑𝑡𝑡
𝐴𝐴
𝐴𝐴
− �
𝐴𝐴
0
𝑡𝑡
𝑡𝑡
𝑑𝑑 𝐴𝐴
= 𝑘𝑘 � 𝑑𝑑𝑑𝑑
𝐴𝐴
0
−{𝑙𝑙𝑙𝑙 𝐴𝐴 𝑡𝑡 − 𝑙𝑙𝑙𝑙 𝐴𝐴 0} = 𝑘𝑘(𝑡𝑡 − 0)
17
Second-Order Rate Law
aA → products
∆ 𝐴𝐴
= 𝑘𝑘 𝐴𝐴
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = −
∆𝑡𝑡
2
1
1
= 𝑘𝑘𝑘𝑘 +
(2nd order integrated rate law)
𝐴𝐴 𝑡𝑡
𝐴𝐴 0
Example:
2NO2(g) → 2NO(g) + O2(g)
At 330oC k = 0.775 L/(mol·s). The initial concentration is 0.003 mol/L.
What is the concentration of NO2 after 645 s?
1
𝐿𝐿
1
= 0.775
× 645 𝑠𝑠 +
= 8.3 × 102 𝐿𝐿/𝑚𝑚𝑚𝑚𝑚𝑚
𝑁𝑁𝑁𝑁2 𝑡𝑡
𝑚𝑚𝑚𝑚𝑚𝑚 � 𝑠𝑠
0.003 𝑚𝑚𝑚𝑚𝑚𝑚/𝐿𝐿
𝑁𝑁𝑁𝑁2 𝑡𝑡 = 0.0012 𝑚𝑚𝑚𝑚𝑚𝑚/𝐿𝐿
18
Zero-Order Reactions
aA → products
Rate = k[A]0 = k → the rate of a 0-order reaction
does not change with concentration
The relationship between concentration and time for a 0-order reaction:
[A]t = ‒kt + [A]0 (0-order integrated law)
Example:
Pt
2N2O(g) → 2N2(g) + O2(g)
Many 0-order reactions require some minimum reactant
concentration for the reaction to behave as 0-order.
19
Half-Life of a Reaction
The concept of half-life is also used to characterize a radioactive
nucleus, whose radioactive decay is a 1st order process.
The half-life, t1/2, of a reaction is the time it
takes for the reactant concentration to
decrease to one-half of its initial value.
2N2O5(g) → 4NO2(g) + O2(g)
For a 1st-order reaction the half-life is
independent of the initial concentration:
1
𝑁𝑁2𝑂𝑂5 0
𝑁𝑁2𝑂𝑂5 𝑡𝑡
2
𝑙𝑙𝑙𝑙
= −𝑘𝑘𝑘𝑘
𝑙𝑙𝑙𝑙
= −𝑘𝑘𝑡𝑡1/2
𝑁𝑁2𝑂𝑂5 0
𝑁𝑁2𝑂𝑂5 0
𝑙𝑙𝑙𝑙𝑙/2 = −𝑘𝑘𝑡𝑡1/2
𝑙𝑙𝑙𝑙𝑙/2 = −0.693
0.693 = 𝑘𝑘𝑡𝑡1/2
𝑡𝑡1/2 =
0.693
0.693
=
= 1.44 × 103 𝑠𝑠 = 24 𝑚𝑚𝑚𝑚𝑚𝑚
−4
𝑘𝑘
4.8 × 10 /𝑠𝑠
20
Half-Life of a Reaction
𝑡𝑡1/2
𝐴𝐴 0
=
2𝑘𝑘
𝑡𝑡1/2 =
𝑡𝑡1/2
0.693
𝑘𝑘
1
=
𝑘𝑘 𝐴𝐴
0
(0 order)
(1st order)
(2nd order)
depends on the initial concentration of the reactant:
as a reaction proceeds, each half-life gets shorter
is related to the rate constant but is independent of
concentration of the reactant
depends on the initial concentration: each
subsequent half-life becomes larger as time goes on
21
Graphing of Kinetic Data
It is possible to determine the order of a reaction by graphical plotting of the data for
an experiment. The experimental data are plotted in several different ways, first
assuming a 1st-order reaction, then a 2nd-order reaction, etc. The order of the
reaction is determined by which graph gives the best fit to the experimental data.
1st order:
𝑙𝑙𝑙𝑙
𝐴𝐴 𝑡𝑡
= −𝑘𝑘𝑘𝑘
𝐴𝐴 0
𝑙𝑙𝑙𝑙
𝐴𝐴
= 𝑙𝑙𝑙𝑙𝑙𝑙 − 𝑙𝑙𝑙𝑙𝑙𝑙
𝐵𝐵
𝑙𝑙𝑙𝑙 𝐴𝐴 𝑡𝑡 = −𝑘𝑘𝑘𝑘 + 𝑙𝑙𝑙𝑙 𝐴𝐴
A straight line has the mathematical form y = mx + b
0
2N2O5(g) → 4NO2(g) + O2(g)
ln 𝐴𝐴 𝑡𝑡 = −𝑘𝑘𝑘𝑘 + 𝑙𝑙𝑙𝑙 𝐴𝐴
𝑦𝑦 = 𝑚𝑚𝑚𝑚 + 𝑏𝑏
0
A straight line can be drawn through
the experimental points. The fact that
the straight line fits the experimental
data so well confirms that the rate law
is 1st-order.
22
Graphing of Kinetic Data
We can obtain the rate constant for the reaction from the slope, m, of the straight line:
−𝑘𝑘 = 𝑚𝑚
𝑚𝑚 =
𝑜𝑜𝑜𝑜 𝑘𝑘 = −𝑚𝑚
∆𝑦𝑦
−5.843 − (−4.104) −1.739
=
=
= −4.83 × 10−4 /𝑠𝑠
3600 − 0 𝑠𝑠
∆𝑥𝑥
3600 𝑠𝑠
2nd-order rate law, -∆[A]/∆t = k[A]2, gives the following
relationship between concentration of A and time:
1
1
= 𝑘𝑘𝑘𝑘 +
𝐴𝐴 𝑡𝑡
𝐴𝐴 0
𝑦𝑦 = 𝑚𝑚𝑚𝑚 + 𝑏𝑏
a straight line by plotting 1/[A]t on the vertical
axis against the time t on the horizontal axis
23
Graphing of Kinetic Data: Example
2NO2(g) → 2NO(g) + O2(g)
24
Relationships for 0-, 1st-, and 2nd-Order Reactions
Order
Rate Law
Integrated
Rate Law
0
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑘𝑘
𝐴𝐴 𝑡𝑡 = −𝑘𝑘𝑘𝑘 + 𝐴𝐴
1
2
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑘𝑘[A]
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑘𝑘 A
2
𝐴𝐴 𝑡𝑡
= −𝑘𝑘𝑘𝑘
𝐴𝐴 0
1
1
= 𝑘𝑘𝑘𝑘 +
𝐴𝐴 𝑡𝑡
𝐴𝐴 0
𝑙𝑙𝑙𝑙
Half-Life
0
𝐴𝐴 0
2𝑘𝑘
0.693
𝑘𝑘
1
𝑘𝑘 𝐴𝐴 0
Straight-Line Plot
𝐴𝐴 𝑣𝑣𝑣𝑣 𝑡𝑡
𝑙𝑙𝑙𝑙 𝐴𝐴 𝑣𝑣𝑣𝑣 𝑡𝑡
1
𝑣𝑣𝑣𝑣 𝑡𝑡
𝐴𝐴
25
Temperature and Rate
The rate of reaction depends on temperature, as the rate constant k varies
with temperature. In most cases, the rate increases with temperature.
NO + Cl2 → NOCl + Cl
k = 4.9×10‒6 L/(mol·s) at 25oC
1.5×10–5 L/(mol·s) at 35oC
The change in rate constant with temperature varies considerably from one reaction
to another. In many cases, the rate of reaction approx. doubles for a 10oC rise.
26
Temperature and Rate: Collision Theorie
Collision theory: for reaction to occur, reactant molecules must collide with an
energy greater than some minimum value and with the proper orientation.
The minimum energy of collision required for two molecules to react is the
activation energy, Ea. The value of Ea depends on the particular reaction.
𝑘𝑘 = 𝑍𝑍𝑍𝑍𝑍𝑍
Z - collision frequency,
f - fraction of collisions having energy greater than the activation energy,
p - fraction of collisions that occur with the reactant molecules properly oriented.
Importance of molecular orientation:
NO + Cl2 → NOCl + Cl
NO approaches with its N atom
toward Cl2, and an N—Cl bond forms.
Also, the angle of approach is close to
that in the product NOCl.
NO approaches with its O atom toward
Cl2. No N—Cl bond can form, so NO
and Cl2 collide and then fly apart.
27
Temperature and Rate: Collision Theorie
𝑢𝑢(𝑟𝑟𝑟𝑟𝑟𝑟) =
3𝑅𝑅𝑅𝑅
𝑀𝑀𝑚𝑚
From kinetic theory: at 25oC, a 10oC rise in temperature
increases the collision frequency Z by about 2%.
p, the proper orientation of the reactant molecules, is independent of temperature changes.
The fraction of molecular collisions having energy greater than the activation
energy, changes rapidly in most reactions with even small temperature changes:
𝑓𝑓 = 𝑒𝑒 −𝐸𝐸𝑎𝑎/𝑅𝑅𝑅𝑅
e = 2.718,
Ea - activation energy,
R - the gas constant, 8.31 J/(mol·K)
f decreases with increasing values of Ea → reactions with large activation energies have
small rate constants, reactions with small activation energies have large rate constants.
Example:
NO + Cl2 → NOCl + Cl
Ea = 8.5×104 J/mol,
f = 1.2×10‒15 at 25oC,
3.8×10‒15 at 35oC
28
Temperature and Rate: Transition-State Theorie
Transition-state theory explains the reaction resulting from the
collision of two molecules in terms of an activated complex.
An activated complex (transition state) is an unstable grouping
of atoms that can break up to form products.
NO + Cl2 → NOCl + Cl
O=N + Cl-Cl → [O=N⋅⋅⋅⋅Cl⋅⋅⋅⋅Cl]
O=N + Cl2 ← [O=N⋅⋅⋅⋅Cl⋅⋅⋅⋅Cl] → O=N-Cl + Cl
reactants activated complex products
29
Temperature and Rate: Transition-State Theorie
Potential-energy curve for the endothermic reaction:
NO + Cl2 → NOCl + Cl
For NO and Cl2 to react, at least 85 kJ/mol of energy must be supplied
by the collision of reactant molecules. Once the activated complex
forms, it may break up to products, releasing 2 kJ/mol of energy. The
difference, (85 - 2) kJ/mol = 83 kJ/mol, is the heat energy absorbed, ∆H.
30
Temperature and Rate: Transition-State Theorie
Potential-energy curve for an exothermic reaction
The energy of the reactants is higher than that of the products, so heat
energy is released when the reaction goes in the forward direction.
31
Transition-State Theorie: Problem
1. Which reaction has a higher activation energy for the forward reaction?
2. If both reactions were run at the same temperature and have the same orientation
requirements to react, which one would have the larger rate constant?
3. Are these reactions exothermic or endothermic?
32
Arrhenius Equation
Rate constants for most chemical reactions closely follow the Arrhenius equation:
𝑘𝑘 = 𝐴𝐴𝐴𝐴 −𝐸𝐸𝑎𝑎/𝑅𝑅𝑅𝑅
A - frequency factor, related to the frequency of collisions with proper orientation (pZ)
e = 2.718 (the base of natural logarithms),
Ea - activation energy,
R - gas constant, 8.31 J/(K · mol),
T - absolute temperature
𝐸𝐸𝑎𝑎
𝑙𝑙𝑙𝑙𝑙𝑙 = 𝑙𝑙𝑙𝑙𝑙𝑙 −
𝑅𝑅𝑅𝑅
𝑙𝑙𝑙𝑙𝑙𝑙 = 𝑙𝑙𝑙𝑙𝑙𝑙 +
𝑦𝑦 = 𝑏𝑏
+
−𝐸𝐸𝐸𝐸
𝑅𝑅
1
𝑇𝑇
𝑚𝑚 𝑥𝑥
ln k vs 1/T
for the decomposition of N2O5.
A straight line is then fitted to
the points,
the slope = ‒Ea/R.
Activation energies are typically in the range of 10–100 kJ.
33
Reaction Mechanisms: Elementary Reactions
A balanced chemical equation is a description of the overall result of a chemical reaction.
However, what actually happens at the molecular level may be more involved than is
represented by this single equation. The reaction may take place in several steps.
NO2(g) + CO (g) → NO(g) + CO2(g)
elementary reactions:
intermediate
NO2 + NO2 → NO3 + NO
NO3 + CO → NO2 + CO2
product
Elementary reaction is a single molecular event, such as a collision of molecules,
resulting in a reaction.
The set of elementary reactions whose overall effect is given by the net chemical
equation is the reaction mechanism.
A reaction intermediate is a species produced during a reaction that does not
appear in the net equation because it reacts in a subsequent step in the mechanism.
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Reaction Mechanisms: Molecularity
The molecularity is the number of molecules on the reactant side of an elementary reaction.
A unimolecular reaction is an elementary reaction that involves 1 reactant molecule;
a bimolecular reaction involves 2 reactant molecules;
a termolecular reaction involves 3 reactant molecules.
Higher molecularities are not encountered, because the chance of the correct 4 molecules
coming together at once is extremely small.
NO2(g) + CO (g) → NO(g) + CO2(g)
bimolecular elementary reactions:
NO2 + NO2 → NO3 + NO
NO3 + CO → NO2 + CO2
Bimolecular reactions are the most common.
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Rate Equation for an Elementary Reaction
For an elementary reaction, the rate is proportional to the
product of the concentration of each reactant molecule.
A→B+C
A+B→C+D
A+B+C→D+E
Rate = k[A]
Rate = k[A][B]
Rate = k[A][B][C]
Any reaction we observe is likely to consist of several elementary steps, and
the rate law is the combined result of these steps.
This is why we cannot predict the rate law by looking at the overall equation.
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The Rate Law and the Mechanism:
Rate-Determining Step
The rate-determining step is the slowest step in the reaction mechanism.
2NO2(g) + F2(g) → 2NO2F(g)
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑘𝑘1 𝑁𝑁𝑁𝑁2 [𝐹𝐹2]
k1
NO2 + F2 → NO2F + F (slow step)
k2
F + NO2 → NO2F
(fast step)
NO2 + F2 → NO2F + F
F + NO2 → NO2F
2NO2 + F2 → 2NO2F
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Catalysis
Catalysis is the increase in rate of a reaction that results from the addition of a catalyst.
Catalysts are of enormous importance to the chemical industry, because they allow
a reaction to occur with a reasonable rate at a much lower temperature than otherwise.
Lower temperatures translate into lower energy costs.
Catalysts are often quite specific—they increase the rate of certain reactions, but not
others.
The catalyst must participate in at least one step of a reaction and be regenerated in a
later step.
NO
2SO2(g) + O2(g) → 2SO3(g)
2NO + O2 → 2NO2
NO2 + SO2 → NO + SO3
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Catalysis
Catalyst increases the rate of reaction either by increasing the frequency
factor A or, more commonly, by decreasing the activation energy Ea.
The most dramatic effect comes from decreasing the activation energy.
𝑘𝑘 = 𝐴𝐴𝐴𝐴 −𝐸𝐸𝑎𝑎/𝑅𝑅𝑅𝑅
Comparison of activation energies in the uncatalyzed
and catalyzed decompositions of ozone:
The uncatalyzed reaction:
O3 + O → 2O2
Catalysis by Cl atoms provides an
alternate pathway with lower
activation energy, and therefore a
faster reaction.
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Homogeneous Catalysis
Homogeneous catalysis: a catalyst in the same phase as the reacting species.
NO
2SO2(g) + O2(g) → 2SO3(g)
2NO + O2 → 2NO2
NO2 + SO2 → NO + SO3
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Heterogeneous Catalysis
Some of the most important industrial reactions involve heterogeneous catalysis:
a catalyst that exists in a different phase from the reacting species, usually a solid
catalyst in contact with a gaseous or liquid solution of reactants.
Catalytic hydrogenation of ethylene
C2H4 and H2
molecules diffuse
to the catalyst
The molecules form
bonds to the catalyst
surface. H2 dissociates
to atoms in the process.
H atoms migrate to
C2H4, where they
react to form C2H6.
C2H6 diffuses away
from the catalyst.
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Heterogeneous Catalysis
Surface catalysts are used in the catalytic converters of
automobiles to convert substances that would be atmospheric
pollutants, such as CO and NO, into harmless CO2 and N2.
Automobile catalytic converter
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Enzyme Catalysis
The most remarkable catalysts are enzymes. Enzymes are selective catalysts
employed by biological organisms. A biological cell contains thousands of different
enzymes that in effect direct all of the chemical processes that occur in the cell.
Almost all enzymes are protein molecules with molecular weights ranging to over a
million amu. An enzyme has enormous catalytic activity, converting a thousand or so
reactant molecules to products in a second.
Enzymes are also highly specific, each enzyme acting only on a specific substance,
or a specific type of substance, catalyzing it to undergo a particular reaction.
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Enzyme Catalysis
Enzyme action (lock-and-key model)
The enzyme has an active site to which the
substrate binds to form an enzyme–substrate
complex.
The active site of the enzyme acts like a lock
into which the substrate (key) fits.
While bound to the enzyme, the substrate may
have bonds weakened or new bonds formed to
yield the products, which leave the enzyme.
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Enzyme Catalysis
Potential-energy curves for the reaction of substrate, S, to products, P
The uncatalyzed reaction
of substrate to product.
The enzyme-catalyzed reaction provides a
pathway with lower activation energy
than does the uncatalyzed reaction.
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Key Equations
A 𝑡𝑡 = −kt + A
0
(0 order)
𝐴𝐴 𝑡𝑡
𝑙𝑙𝑙𝑙
= −kt (1st order)
𝐴𝐴 0
1
1
= kt +
(2nd order)
𝐴𝐴 𝑡𝑡
𝐴𝐴 0
𝑡𝑡1/2
𝐴𝐴 0
(0 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜)
=
2𝑘𝑘
𝑡𝑡1/2 =
𝑡𝑡1/2 =
0.693 𝑠𝑠𝑠𝑠
(1 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜)
𝑘𝑘
1
𝑘𝑘 𝐴𝐴
0
(2𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜)
𝑘𝑘 = 𝐴𝐴𝐴𝐴 −𝐸𝐸𝑎𝑎/𝑅𝑅𝑅𝑅
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