# Reaction rate

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```					Reaction rate
A. Definition:
amount of reactant reacted
Reaction rate =
time interval
 [reac tan t ]
= lim
t 0       t
d[reac tan t ]
=
dt
amount of product produced
Reaction rate =
time interval
[ product ]
= lim
t 0      t
d[ product ]
=
dt

e.g.             2 H  (aq )  S 2 O3  (aq )   H2 O(l )  S ( s)  SO2 ( g )
2


d[ H ]
reaction rate =               mol dm3 s1 of H+ consuming
dt
d [ S 2 O3  ]
2

reaction rate =                  mol dm3 s1 of S 2 O3 consuming
2
dt
d [ PSO2 ]
reaction rate =           Pa s1 of SO2 forming
dt
dms 1
reaction rate =       g s of S forming
dt
Consider the following reaction:
2 A + B  A2B
d[ A]      d [ B]    d[ A2 B]
        2        2
dt         dt          dt
1 d[ A]     d[ B] d[ A2 B]
                 
2 dt          dt       dt
This is important to specify which species is taken in the rate expression, since the rate can be different for different species.
Ususally the rate of the reaction is defined as follow:
1
Reaction rate =    rate of change of [A]
2
=  rate of change of [B]
= rate of change of [A2B]

B. Collision theory:
1. The reaction occurs when particles collide.
2. The more the collisions, the faster the reaction is.
3. In order to occur a reaction, the molecules need a minimum energy (activation energy/threshold energy), below which a
collision cannot be successful, particles bounce apart again without reacting.
4. Increasing temperature increases the kinetic energy
of particles.
This causes
(i) collision would be more frequent;
(ii) more particles have an energy higher than the
activation energy.
Number of collision with energy higher than Ea
Ea

= Total number of collisione        RT

Reaction rate / page 1
C. Factors affecting the reaction rate:
1. concentration
2. temperature
3. pressure (for gas only)
4. surface area (for solid only)
5. catalyst
6. light

D. Concentration effect
Incresaing concentration means crowding of particles and decreasing the distance of collision.
concentration            collision frequency                  reaction rate 
1. Rate equation (rate law):
Ex. In the kinetic study of the following reaction:
CO (g) + NO2 (g)  CO2 (g) + NO (g)
the initial concentrations of the reactants and the initial reaction rates are determined in a number of experiments.
Experiment          Initial [CO] mol dm3      Initial [NO2] mol dm3 Initial rate mol dm3 s1
1                      0.10                       0.10                        0.015
2                      0.20                       0.10                        0.030
3                      0.40                       0.10                        0.060
4                      0.10                       0.20                        0.030
5                      0.10                       0.30                        0.045
From experiment 1, 2 and 3, reaction rate  [CO]
From experiment 1, 4 and 5, reaction rate  [NO2]
 reaction rate  [CO] [NO2]
d [ NO]
reaction rate =           = k[CO] [NO2]
dt
where k is called the rate constant, its unit is dm3 mol1 s1 in this experiment;
and the above expression is called the rate equation (rate law) of the reaction;
the rate order of the reaction is 2.

(a) First order reaction (Unimolecular reaction):
For the elementary step:            A (g)  X (g)
d[ A]
             k[ A]
dt
[ A]o [ A]   0kdt
[ A ] d [ A]      t

ln[A]o  ln[A] = kt

Rate                                                 ln[A]

[A]                                                     Time
slope = k                                              slope = k

Examples of the (a) First order reaction:
CH3                          CH3

CH3CCl + OH  CH3COH + Cl                                    SN1

CH3                            CH3
rate = k [(CH3)3CCl]
226
88       86
Ra   222 Rn 2 He
4

rate = k [Ra]

Half-life t 1 : The time taken for half of the reactant to be converted to the product.
2
For radioactive decay is known as first order reaction.
Assume t = 0      Initial concentration = [A]0
1
t = t1            concentration =      [A]0
2
2
Rate equation for the first order reaction :      ln[A]o  ln[A] = kt

Reaction rate / page 2
1
ln[A]o  ln [A]0 = k t 1
2         2
ln 2 = k t 1
2
ln 2 0.693
t1 =         
2
k     k

(b) Second order reaction (Bimolecular reaction):
For the elementary step:          2 A (g)  X (g)
d [ A]
             k[ A]2
dt
[ A]o [ A]2   0kdt
[ A ] d [ A]      t

1          1
         kt
[ A] [ A]0
Rate                                                 [A]1

[A]2                                         Time
slope = k                                             slope =  k
Examples of the second order reaction:
CH3Cl + OH  CH3OH + Cl                           SN2
rate = k [CH3Cl][ OH]
2 NO2  2 NO + O2
rate = k [NO2]2

(c) Zeroth order reaction:
For the elementary step:              A (g)  X (g)
d [ A]
           k[ A]0
dt
[ A] [ A]   0kdt
[ A]           t

o

[A]0  [A] = kt
Rate                                                   [A]

[A]                                           Time
slope = 0                                          slope = k
Example of the Zeroth order reaction:
Reaction involves solid catalyst.
2 HI  H2 + I2
rate = k
Technique to determine the rate order:
(a) Method of initial rate:
2            
Disappearance the cross in the reaction                             
S 2 O3 (aq )  2 H (aq )   H2 O(l )  SO2 ( g )  S ( s)
Decolorization of methyl red in the reaction

5Br  (aq )  BrO3 (aq )  6 H  (aq )   3Br2 (aq )  3H2 O(l )

(b) Method of excess reactant:
Refer the experiment in TAS to find the rate order of the reaction.
CH3COCH3 (aq) + I2 (aq)  CH3COCH2I (aq) + HI (aq)

Reaction rate / page 3
(c) Plotting a graph of log(rate) against log [A]           log (1/time)
For a reaction: A + B  X + Y
By means of initial rate method, let [B] >> [A]
Assume             rate = k [A]n
log (rate) = log k + n log [A]

Slope = n
Intercept = log k

log [A]

2. Reaction mechanism:
Reaction mechanism is the term used to describe the detailed step by step pathway of chemical reactions by which reactants
are converted to products.
Consider the following typical mechanism. To begin with, consider the relatively simple reaction of nitrogen oxide with
hydrogen to give nitrogen and water. The reaction is
2 NO (g) + 2 H2 (g)  N2 (g) + 2 H2O (g)
The rate is found experimentally as follow:
d[ NO]
           k[ NO]2 [ H2 ]
dt
The stoichiometry is not the same as the molecularity of the reaction. It can be explained by the following mechanism.
(1)         2 NO (g) + H2 (g)  N2 (g) + H2O2 (g)                   (slow)
(2)         H2O2 (g) + H2 (g)  2 H2O (g)                           (fast)
Overall:    2 NO (g) + 2 H2 (g)  N2 (g) + 2 H2O (g)
The overall reaction rate is determined by the slowest step (1) is called the rate-determining step.
d[ NO]
Reaction rate =              k[ NO]2 [ H2 ]
dt
Activated complex I
Energy
Activated complex II
Ea1
Ea2
N2 (g) + H2O2 (g) + H2 (g)
(Intermediate)
2 NO (g) + H2 (g) H

N2 (g) + 2 H2O (g)

Reaction Profile

Ex. Consider the reaction                 A (g) + B2 (g)  AB (g) + B (g)
Experimental findings show that the rate of formation of AB is proportional to the concentration of B 2 and the
concentration of a certain substance C but does not vary with the concentration of A.
(a) Deduce the rate law for this reaction.
(b) Suggest the reaction mechanism for this reaction.
(c) What might be the function of C? Why is it not written in the overall equation?
Difference between activated complex and intermediate:
Activated complex                      Intermediate
It is very unstable.                   It is meta-stable.
It cannot be isolated.                 It may be isolated.
Its structure is usually unkown. Its structure may be deduced.

E. Pressure effect (for gas only)
Pressure                Collision frequency                 Reaction rate 

F. Surface area effect (for solid only)
Surface area            Collision frequency                Reaction rate 

G. Temperature effect
(1) Temperature                   Kinetic energy            Collision frequency 
(2) Temperature                   Kinetic energy            Number of particles have energy higher than Ea,
the collisions are more effective.
Arrhenius equation:

Reaction rate / page 4
Ea

k  Ae         RT
where k is the rate constant of a rate equation,
Ea is the activation energy of the reaction,
R is the gas constant (8.314 J mol1 K1),
T is the absolute temperature.
e = 2.7183
Ea
Altermative form I:            ln k  ln A 
RT
The activation energy of a reaction can be determined by plotting a graph of ln(rate) against 1/T.

ln(rate)
E
slope   a
R
Ea=  R(slope)

Alternative form II:                                                                                   1/T
E
At temperature T1:              ln k1  ln A  a (1)
RT1
Ea
At temperature T2:              ln k 2  ln A      (2)
RT2
k        E 1 1
(1)-(2):                        ln( 1 )   a (  )
k2        R T1 T2
Remarks:
Raising 10C of temperature, the reaction rate becomes nearly double for most chemical reactions.
T
k 2  k1  2        10
(By approximation)
where k2 is the rate constant at T2C,
k1 is the rate constant at T1C,
T = T2  T1

*Arrhenius equation:
Ea

k  zpe        RT

H. Catalyst effect
Catalyst gives an alternative pathway requiring less (more) activation energy in a reaction.

Energy

with negative catalyst

(activated complex)                                 without catalyst

with positive catalyst

(product)

(reactant)

Reaction Coordinate

Reaction rate / page 5
Definition of Catalyst:
A substance, which is unchanged chemically at the end of the reaction, but changes the rate of a reaction.
Kinds of catalysts:
(a) Positive catalyst: the catalyst increases the reaction rate, e.g. manganese(IV) oxide for hydrogen peroixde.
(b) Negative catalyst: the catalyst decreases the reaction rate, e.g. preservatives to prevent spoilage, vitamin C for fruit
browning.

Characteristic of catalyst:
(a) Rate changed depends on the amount of the catalyst.
(b) It is selective to a special reaction.
(c) Mass and chemical properties do not change, but physical appearance may be changed.
(d) Small amounts of a certain impurities may oison” a catalyst. Usually reactants must be purified before using a expensive
catalyst, e.g. arsenic oxide for platinum in contact process.
(e) Many catalysts are transition metals, e.g. iron for Haber process, nickel for preparation of Town gas from naptha.
(f) There are two types of catalysts:
(i) homogeneous catalyst (same physical state with all reactants)
e.g. sulphuric acid is a homogeneous catalyst in esterification.
CH3COOH (l) + HOCH2CH3 (l)  CH3COOCH2CH3 (l) + H2O (l)
the catalyst and all reactants have the same physical state.
(ii) heterogeneous catalyst (different physical states with one of reactant)
e.g. nickel is a heterogeneous catalyst in the hydrogenation of alkene.
H2C=CH2 (g) + HH (g)  CH3CH3 (g)
Reactants are gaseous but catalyst is a solid.
(g) Enzyme is an organic catalyst in living cells.

Reaction mechanism of catalytic effect:
(a) Homogeneous catalyst: (Intermediate Formation)
Consider the decomposition of methanoic acid:
HCOOH (aq)  H2O (l) + CO (g)
The reaction is a simple reaction which has one elementary step only, its energy diagram is shown as following.

rate = k[HCOOH] a standard first order reaction
Consider the decomposition of methanoic acid with hydrogen ion as catalyst:

Reaction rate / page 6
The catalysed reaction involves the following mechanism:
O
fast

Step 1:        HCOOH  H  [ H  C  O  H ]

K

H
O

[ H  C  O  H ]  [ H  C  O]  H 2 O

slow
Step 2:
k1

H
[ H  C  O]  CO  H 

fast
Step 3:
k2
H
Overall:       HCOOH  CO  H 2 O
Rate equation:
From step 1:       Forward reaction rate = Backward reaction rate
Forward reaction rate = k11[HCOOH][H+]
Backward reaction rate = k11[HCOOH2+]
k11[HCOOH][H+] = k11[HCOOH2+]

k11        [ HCOOH 2 ]
K       
k 11 [ HCOOH ][ H  ]

[ HCOOH2 ]  K[ HCOOH ][ H  ]

Step 2 is the rate determining step, the overall reaction rate = k1 [ HCOOH2 ]

= k1 K[ HCOOH ][ H ]
The reaction rate involves [H+] though it is used as a catalyst.

Consider the contact process:

  2 SO3 (g)
Pt
2 SO2 (g) + O2 (g)

O=O                                           O      O
O=S O                                    O     SO

Activated site

The reaction involves that the solid catalyst absorbs the reactants SO2 and O2 on its surface. If the number of activated sites is
limited compared with [SO2] and [O2], the The reaction rate depends on the number of activated sites on the surface of the solid
catalyst.
rate = k’  [activated sites]
=k
The reaction becomes zero order with respect to the concentration of reactants.

Light:
Light is a form of energy. If the wavelength of the light is appropriate, it may cause the breaking of bonds in the original
molecules such that the reaction may then take place quickly.
 no observable change
in..dark
e.g.           H2 (g) + Cl2 (g)
h

H2 (g) + Cl2 (g)   2 HCl (g)       explosion

Reaction rate / page 7

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