Transcript Chapter 22. The rates of chemical reactions

Chapter 22. The rates of
chemical reactions
22.1 Experimental techniques
•
•
Monitoring concentrations:
Depends on the species involved and the rapidity with which their
concentrations changes.
1. spectrophotometry.
2. electrical conductivity
3. pH of the solution
4. redox potential
Determining the compositions of a solution:
1. mass spectrometry
2. gas chromatography
3. emission spectroscopy
4. nuclear magnetic resonance
5. electron spin resonance
Flow method
Stopped flow method
Additional techniques
• Flash photolysis.
(principles…)
• Quenching methods:
1. Chemical Quenching method.
2. Freezing quenching method.
22.2 The rates of reactions
•
The definition of the rate
A + 2B → 3C + D
The rate of consumption of one of the reactants (R) at a given time
is - d [ R] , where R could be reagent A or B.
dt
d[P ]
dt
•
The rate of formation of one of the products (denoted by P) is
•
Following the stoichiometry of the above reaction, one gets
d [ D] 1 d [C ]
d [ A]
1 d [ B]



dt
3 dt
dt
2 dt
Rate of reaction
• Defined as the rate of change of the extent of reaction, ξ.
v
d
dt
• Since the change in the extent of reaction is related to the change in
the amount of each substance J by v d  dn
J
v
J
1 dnJ
v J dt
• When expressed in term of concentration:
v
1 d[J ]
v J dt
note that vj is negative for reactants and positive for products!
• Example: The rate of change of molar concentration of
CH3 radicals in the reaction 2CH3(g) → CH3CH3(g) was
reported as d[CH3]/dt = 1.2 mol L-1s-1 under particular
conditions. What is (a) the rate of reaction and (b) the
rate of formation of CH3CH3?
• Solution:
Rate laws and rate constant
• A rate law is often expressed as a function
v = k [A] [B]
where k is called rate constant.
• In general, rate law cannot be inferred from the chemical reaction
equation.
Example:
H2(g) + Br2(g) → 2HBr(g)
k[ H 2 ][ Br2 ]3 / 2
v
[ Br2 ]  k '[ HBr ]
Reaction order
• The rate law can be written in a generalized form:
v = k [A]a[B]b….
where a is the order of the reaction with respect to the
species A, and b is the order of the reaction with respect to the
species B.
• The overall reaction order is (a+b+….).
• The order of a chemical reaction needs not to be an integral !!!
Example 1: v = k [A]1/2[B]1
Example 2: v = k
(zero order reaction, such as ……)
Determination of the rate law
• Isolation method:
v = k [A]a[B]b
----->
v = k’[B]b
• Method of initial rates:
v = k [A]a
at the beginning of the reaction
v = k [A0]a
taking logarithms gives:
logv = log k + a log[A0]
therefore the plot of the logarithms of the initial rates against the
logarithms of the initial concentrations of A should be a straight line
with the slope a (the order of the reaction).
Example: The initial rate of a reaction depended on the concentration
of a substance B as follows:
[B]0/(mmol L-1)
5.0
8.2
17
30
v0/(10-7 mol L-1s-1)
3.6
9.6
41
130
Determine the order of the reaction with respect to B and
calculate the rate constant.
Solution:
Log([B]0)
-2.30
-2.086
-1.770
-1.523
Log(v0)
-6.444
-6.018
-5.387
-4.886
0
-2.5
-2
-1.5
-1
-0.5
0
-1
-2
-3
Series1
-4
-5
-6
-7
22.3 Integrated rate law
• First order reaction:
A  Product
d [ A]
  k[ A]
dt
The solution of the above differential equation is:
 [ A] 
   kt
ln 
[
A
]
0 

or:
[A] = [A]0e-kt
• In a first order reaction, the concentration of reactants decreases
exponentially in time.
Example: In a particular experiment, it was found that the concentration of
N2O5 in liquid bromine varied with time as follows:
t/s
0
200
400
600
1000
[N2O5]/(mol L-1)
0.110
0.073
0.048
0.032
0.014
confirm that the reaction is first-order in N2O5 and determine the rate constant.
Solution: To confirm that a reaction is first order, plot ln([A]/[A]0) against
time and expect a straight line:
t/s
0
200
400
600
1000
ln([A]/[A]0)
0
-0.410 -0.829 -1.23
-2.06
0
0
200
400
600
800
1000
1200
-0.5
-1
Series1
-1.5
-2
-2.5
Half-lives and time constant
• For the first order reaction, the half-live equals:

t1 / 2
ln 2
k
therefore, is independent of the initial concentration.
• Time constant, τ, the time required for the concentration of a
reactant to fall to 1/e of its initial value.


1
k
for the first order reaction.