the rate of reaction. rate law relation between rate of reaction and concentration of the reactants
TRANSCRIPT
The rate of reaction
dt
Bd
dt
Ad
dt
Cd
dt
Dd
dt
dn
dnddt
d
i
i
ii
2
1
3
1
D3C2BA
1
Rate Law
• Relation between rate of reaction and concentration of the reactants
.............
..,.........,
ba BAk
BAf
Three important problems
• Determination of rate law and rate constant from experimental data.
• Construct reaction mechanism that are consistent with rate law.
• Value of rate constant and their temperature dependence
Determination of rate law
• Isolation method: Add large excess
• Methods of initial rate: measurement of rate of reaction for several different initial concentration of reactants.
Integrated Rate LawsConsider a simple 1st order rxn: A B
How much A is left after time t? Integrate:
Differential form:
Integrated Rate Laws
The integrated form of first order rate law:
Can be rearranged to give:
[A]0 is the initial concentration of A (t=0).[A]t is the concentration of A at some time, t, during the course of the reaction.
Integrated Rate Laws
Manipulating this equation produces…
…which is in the form y = mx + b
First-Order Processes
If a reaction is first-order, a plot of ln [A]t vs. t will yield a straight line with a slope of –k.
Second-Order Processes
Similarly, integrating the rate law for a process that is second-order in reactant A:
also in the form y = mx + b
Rearrange, integrate:
Second-Order Processes
So if a process is second-order in A, a plot of 1/[A] vs. t will yield a straight line with a slope of k.
Half-Life• Half-life is defined
as the time required for one-half of a reactant to react.
• Because [A] at t1/2 is one-half of the original [A],
[A]t = 0.5 [A]0.
Half-LifeFor a first-order process, set [A]t=0.5 [A]0 in integrated
rate equation:
NOTE: For a first-order process, the half-life does not depend on [A]0.
Half-Life- 2nd orderFor a second-order process, set
[A]t=0.5 [A]0 in 2nd order equation.
Outline: Kinetics
First order Second order Second order
Rate Laws
Integrated Rate Laws
complicated
Half-life complicated
Most important application of studying the order of a reaction is to establish the mechanism of reaction.
Reactions proceed in one or more elementary steps.
In elementary step molecularity = order of reaction
Reaction order and reaction mechanism
Overall order of reaction corresponds to stoichiometric equation => The reaction mechanism most probably involves one elementary step that is identical to stoichiometric equation.
When the reaction order does not corresponds to the stoichiometry of the reaction, the reaction certainly involves more than one elementary reaction.
When the reaction order does not corresponds to the stoichiometry of the reaction, the reaction certainly involves more than one elementary reaction.
Elementary Reaction(i) Reversible elementary reaction
A B
(ii) Consecutive elementary reaction
A B C
(iii) Parallel Reaction:
AB
C
Consecutive Reaction
IktkAkdt
Id
IkAkdt
Id
tkAAkdt
Ad
PIA
baa
ba
aa
kk ba
exp
expA
0
0
Consecutive Reaction
ab
abba
baba
a
aab
baa
kk
tkktkkA
IAAP
Atktkkk
kI
tkAkIkdt
Id
IktkAkdt
Id
expexp1
)exp()exp(
exp
exp
0
0
0
0
0
Consecutive Reaction
0
b
b
0
exp1
k Also
expexp
k if
expexp1 P
AtkP
kk
tktk
k
PIA
kk
tkktkkA
a
ba
ab
a
kk
ab
abba
ba
Consecutive Reaction
• Rate of formation of the final product P depends on only the smaller of two rate constants.
g)determinin (Rate IA Slow
Consecutive Reaction
PIA fastslow
A
I
P
Conc
Time
This is the basis of steady-State approximation.
0
dt
Id
Consecutive Reaction
PIA fastslow
0
0
)exp(1
exp
0
AtkP
tkAk
AkIkdt
Pd
Ak
kI
IkAkdt
Id
a
aa
ab
b
a
ba
PIA slowfast
[I]
[P]
Case II: when 12 kk
PIA fastslow
[P]
[I]
[I]
[I]
When are consecutive and Single-Step reactions distinguishable ?
01exp1 AtkP
Rate of formation of product is different from rate of decay of A
02exp1 AtkP
Rate of formation of product is same as rate of decay of A
Parallel Reaction
Parallel Reaction
Thermodynamic vs. Kinetic Control
k2 >k1, K2>K1 k2 < k1, K2>K1
k2 >k1, K2<K1k2 < k1, K2 < K1
A
BC
A
A A
B
B B
C
C C
Parallel Reaction
Reversible Reaction
Reversible reaction
Reversible reaction
Higher order reversible Reaction
