Embed Size (px)
Citation preview
1
Case two for second-order would occur for a reaction involving two reactants:
A + B P
2
Case two for second-order would occur for a reaction involving two reactants:
A + B P
[A][B]t
[A]rate k
3
Case two for second-order would occur for a reaction involving two reactants:
A + B P
The integrated rate law becomes
t[A][B][A][A][B][B]ln 00
0t
0t k)(/
/
[A][B]t
[A]rate k
4
Case two for second-order would occur for a reaction involving two reactants:
A + B P
The integrated rate law becomes
For this more complicated case it is necessary to keep track of two different concentrations.
t[A][B][A][A][B][B]ln 00
0t
0t k)(/
/
[A][B]t
[A]rate k
5
Half-Lives
6
Half-Lives
Half-life: The time required for the concentration of a reactant to decrease to half of its initial concentration.
7
Half-Lives
Half-life: The time required for the concentration of a reactant to decrease to half of its initial concentration.
Zero-order reaction: put in the expression leads to the result:
0t [A][A]2
1t[A][A] 0t k
k20
1/2[A]t
8
First-order reaction: put in the expression
0t [A][A]2
1
t[A][A]ln
t
0 k
9
First-order reaction: put in the expression
leads to the result:
0t [A][A]2
1
t[A][A]ln
t
0 k
kln(2)t1/2
10
Decomposition of N2O5 (first-order kinetics).
11
Measuring the half-life of a reaction is one way to determine the rate constant of a first-order reaction.
12
Measuring the half-life of a reaction is one way to determine the rate constant of a first-order reaction.
A common example of the use of the half-life concept is the decay of radioactive isotopes.
13
Measuring the half-life of a reaction is one way to determine the rate constant of a first-order reaction.
A common example of the use of the half-life concept is the decay of radioactive isotopes.
Example:
eXeI 13154
13153
01
14
Measuring the half-life of a reaction is one way to determine the rate constant of a first-order reaction.
A common example of the use of the half-life concept is the decay of radioactive isotopes.
Example: This is a beta-decay where denotes an electron. 131 is the mass number = number of protons +
number of neutrons; 53 is the atomic number.
eXeI 13154
13153
01
e01
15
Radioisotope usage to image the thyroid gland.
-I131The thyroid gland absorbs ions, which undergo beta decay that exposes a photographic film.
(healthy) image Tc99)(unhealthy image I131
16
17
18
Theory of Chemical Reaction Rates
19
Theory of Chemical Reaction RatesThe effect of temperature
20
Theory of Chemical Reaction RatesThe effect of temperature
The Arrhenius Equation
21
Theory of Chemical Reaction RatesThe effect of temperature
The Arrhenius Equation
Nearly all reactions proceed faster at higher temperatures.
22
Theory of Chemical Reaction RatesThe effect of temperature
The Arrhenius Equation
Nearly all reactions proceed faster at higher temperatures. As a rough rule – the reaction rate doubles when the temperature is increased by
10 oC.
23
How do reactions get started?
24
How do reactions get started? Many chemical reactions get started as a result of
collisions among reacting molecules.
25
How do reactions get started? Many chemical reactions get started as a result of
collisions among reacting molecules. According to the collision theory of chemical
kinetics, we would expect the rate of reaction to be directly proportional to the frequency or rate of molecular collisions.
26
How do reactions get started? Many chemical reactions get started as a result of
collisions among reacting molecules. According to the collision theory of chemical
kinetics, we would expect the rate of reaction to be directly proportional to the frequency or rate of molecular collisions.
seccollisionsofnumberrate
27
How do reactions get started? Many chemical reactions get started as a result of
collisions among reacting molecules. According to the collision theory of chemical
kinetics, we would expect the rate of reaction to be directly proportional to the frequency or rate of molecular collisions.
This relation explains the dependence of rate on concentration.
seccollisionsofnumberrate
28
The preceding proportionality is oversimplified in one important respect.
29
The preceding proportionality is oversimplified in one important respect. A chemical reaction does not occur simply on encounter of two reactant molecules.
30
The preceding proportionality is oversimplified in one important respect. A chemical reaction does not occur simply on encounter of two reactant molecules.
Any molecule in motion possesses kinetic energy. When molecules collide, part of their kinetic energy is converted to vibrational energy.
31
The preceding proportionality is oversimplified in one important respect. A chemical reaction does not occur simply on encounter of two reactant molecules.
Any molecule in motion possesses kinetic energy. When molecules collide, part of their kinetic energy is converted to vibrational energy. If the kinetic energies are large, then the molecules will vibrate so strongly that some chemical bonds will break – which is the first step towards the formation of products.
32
If the kinetic energies are small, the molecules will merely bounce off each other and nothing will happen.
33
If the kinetic energies are small, the molecules will merely bounce off each other and nothing will happen.
In order to react, the colliding molecules must have a certain minimum kinetic energy – called the activation energy Ea.
34
If the kinetic energies are small, the molecules will merely bounce off each other and nothing will happen.
In order to react, the colliding molecules must have a certain minimum kinetic energy – called the activation energy Ea.
Activation energy: The minimum energy with which molecules must collide to react.
35
NO + O3 NO2 + O2
36
aE
NO + O3 NO2 + O2
37
We can think of the activation energy as the barrier that prevents less energetic molecules from reacting.
38
We can think of the activation energy as the barrier that prevents less energetic molecules from reacting.
In a normal reaction in the gas phase, there is a tremendous spread in the kinetic energies of the molecules.
39
We can think of the activation energy as the barrier that prevents less energetic molecules from reacting.
In a normal reaction in the gas phase, there is a tremendous spread in the kinetic energies of the molecules. Normally, only a small fraction of these molecules – the very fast moving ones – can take part in a reaction.
40
The speeds of the molecules follow the Maxwell-Boltzmann distribution.
41
Energy level diagram for a chemical reaction.
42
Energy level diagram for a chemical reaction showing fraction of gas phase molecules that have the required energy to reach products.
43
Since a higher temperature gives rise to a greater number of energetic molecules – the rate of product formation is greater.
44
Arrhenius Equation
45
Arrhenius Equation Arrhenius showed that the rate constant of a
reaction can be written as
RTEA a / ek
46
Arrhenius Equation Arrhenius showed that the rate constant of a
reaction can be written as
where k is the rate constant
RTEA a / ek
47
Arrhenius Equation Arrhenius showed that the rate constant of a
reaction can be written as
where k is the rate constant Ea is the activation energy
RTEA a / ek
48
Arrhenius Equation Arrhenius showed that the rate constant of a
reaction can be written as
where k is the rate constant Ea is the activation energy
R is the gas constant (8.314 JK-1 mol-1)
RTEA a / ek
49
Arrhenius Equation Arrhenius showed that the rate constant of a
reaction can be written as
where k is the rate constant Ea is the activation energy
R is the gas constant (8.314 JK-1 mol-1) T is the temperature (Kelvin scale)
RTEA a / ek
50
Arrhenius Equation Arrhenius showed that the rate constant of a
reaction can be written as
where k is the rate constant Ea is the activation energy
R is the gas constant (8.314 JK-1 mol-1) T is the temperature (Kelvin scale) A is related to the collision frequency and is called the frequency factor (pre-exponent factor)
RTEA a / ek
51
A second form of the Arrhenius equation, which is useful for the determination of Ea, is obtained by taking the natural log of both sides of the Arrhenius equation.
52
Math Aside: Review of log properties.
53
Math Aside: Review of log properties.
Some useful properties of logs that occur frequently.
54
Math Aside: Review of log properties.
Some useful properties of logs that occur frequently.
1 )ln( e
55
Math Aside: Review of log properties.
Some useful properties of logs that occur frequently.
1 )ln( e
ln(Y) ln(X) ln(XY)
56
Math Aside: Review of log properties.
Some useful properties of logs that occur frequently.
1 )ln( e
ln(Y) ln(X) ln(XY)
ln(Y) ln(X) ln(X/Y)
57
Math Aside: Review of log properties.
Some useful properties of logs that occur frequently.
1 )ln( e
ln(Y) ln(X) ln(XY)
ln(Y) ln(X) ln(X/Y) ln(X)m )ln(Xm
58
Math Aside: Review of log properties.
Some useful properties of logs that occur frequently.
1 )ln( e
ln(Y) ln(X) ln(XY)
ln(Y) ln(X) ln(X/Y) ln(X)m )ln(Xm
Y )ln( Y )Yln( ee
59
From the Arrhenius equation we have:
)( /RTEAlnln a ek
60
From the Arrhenius equation we have:
)( /RTEAlnln a ek
)( /RTElnlnAln a ek
