§9.2 Reaction rate and rate equation
2.1 expression of reaction rate
The rate (r): concentration change of a reactant or a product per
unit time.
c
mean rate
instantaneous rate:
c1
c2
Physical meaning:
t1
t2
t
Initial instantaneous rate?
c
N2 + 3H2 == 2NH3
rN 2
rNH3
rH 2
rN2
1
1
 rH2  rNH3
3
2
t1
t
Extent of reaction or advancement ()
 
ni  ni,0
where i is the stoichiometric
coefficient of the reaction.
i
True rate of the reaction or rate of conversion (J):
d
J 
dt
Unit?
For general reaction:
aA + bB  gG + hH
When the extent of reaction is d
dnA
dnB dnG dnH
d  



a
b
g
h
d
1 dnA
1 dnB 1 dnG 1 dnH
J




dt
a dt
b dt
g dt
h dt
When the reaction takes place in a container with constant
volume
Define rate
J
r 
V
d
1 dn A
1 dn B 1 dnG 1 dn H
J




dt
a dt
b dt
g dt
h dt
1 d [ A]
1 d [ A ] 1 d [G ] 1 d [ H ]
r



a dt
b dt
g dt
h dt
1 d [ci ]
r
 i dt
Unit?
2.2 measurement of reaction rate
r
1 d [ ci ]
i
dt
Physical meaning:
slope of the c ~ t curve
c
kinetic curve
(1) How to record time?
(2) How to measure instantaneous
concentration?
t=0
t=t
t
The concentration of the species can be measured
using either chemical or physical methods.
For example:
CH3COOC2H5 + NaOH 
CH3COONa + C2H5OH
The reaction can be stopped by removing
of CH3COOC2H5, and the consumption of
NaOH can be determined by chemical
titration.
t=0
t = t1
t = t2
The change in physical properties of the reaction system which relates
to the concentration of reactants or products can be usually chosen as
indicator of the progress of the reaction.
Wilhelmy in 1850 .
C12H22O11 + H2O 
C12H22O11 + C12H22O11
glucose
sucrose
fructose
Substance
sucrose
glucose
fructose
[]D25
+66.5 o
+52 o
- 92 o
[]
[]1
The rotation angle of the 1:1
mixture of glucose and fructose
is –20 o
[]2
We still use in it in our physical
20
chemistry laboratory
66.5
t1
t2
t
CH3COOC2H5 + NaOH 
CH3COONa + C2H5OH
the rate of which can be monitored using pH meter or
conductometer.
N2O5 = N2O4 + 0.5 O2
When this reaction takes place in a container with constant
volume, the rate of the reaction can be monitored by measuring
the pressure change. And when this reaction takes place under
constant pressure, the advance of the reaction can be monitored
by measuring the volume increase. dilatometer.
FTIR spectroscopy
Stretch of epoxy group
The physical parameters usually used for monitoring reaction
process includes volume, pressure, electric conductance, pH, refractive
index, thermal conductivity, polarimetry, spectrometry, chromatography,
etc.
1) Static method
1)
Real time analysis
2)
Quenching
Analyzing methods:
2) Flow method
All the above methods are valid only for reactions with half-lives
of at least a few seconds, i.e., “slow” reaction. For fast reaction of
half-lives ranging between 100 ~ 10-11 s, special methods are
required.
Flow method
Mixer
detector
Moving direction
Stable flow: l  t
Difficulties in study on kinetics
2.3 Rate equation and the law of mass action
The concentration-dependence of rate:
r = r(ci) = r(cA, cB, cC…)
Where ci represents concentration of individual specie present
in rate equation.
In many instances, the rate of a reaction is proportional to
the concentrations of the reactants raised to some power.
dc A

 kcA cB cC 
dt
rate equation
Rate law
For example:
H2 + I2 = 2 HI
r  k[H 2 ]1[I 2 ]1
H2 + Cl2 = 2 HCl
r  k[H 2 ]1[Cl2 ]0.5
dcA
  
r
 kcA cB cC
dt
Where rate coefficient/constant (k) is a proportionality constant
/coefficient independent of concentration.
The exponent shows the effect of concentration on the reaction
rate. In 1895, Noyes defined them as partial order of the reactant.
,  is the partial order of the reaction with respect to A or B,
respectively.
r  k[H 2 ] [Cl2 ]
1
0.5
This implies that the reaction obeying rate law is first-order in H2 and
0.5-order in Cl2.
the sum of the partial order n =  +  +  +… is the overall
order of the reaction, or more simply, the reaction order.
r  k[H 2 ] [Cl2 ]
1
0.5
The overall order is 1.5.
2SO2 + O2  2SO3
1

d [SO3 ]
r
 2k[SO2 ][SO3 ] 2
dt
is first-order in SO2, -0.5-order in SO3 and 0.5 order overall.
n, , , , etc., different from the stoichiometric coefficient, may
be integers, decimals, of plus or minus values.
Rate law must be determined from measurements of reaction
rate and cannot be deduced from the reaction stoichiometry.
For elementary reaction,  = a,  = b, etc.
dcA
r
 kcA cB cC
dt
dcA
r
 kcAa cBb cCc
dt
Partial order = stoichiometric coefficient
Reaction order = number of molecules involved in the reaction
For example:
2I + H2 = 2HI
1 d [I]
r
 k[I]2 [H 2 ]
2 dt
Law of mass action valid only for elementary reaction
An exercise
k1
k3
2A
B +C
D
k2
k4
d [A ]
dt
d [B]
dt
d [ C]
dt
E
d [D]
dt
d [E]
dt
Group work:
Write the differential form of rate equation and deduce the
integration rate equations of reactions with simple orders.
A member of a chosen group will be asked to deduce the
equation on blackboard this Thursday.