§9.2 reaction rate and rate equation. the rate (r) of a chemical reaction is defined as the change...
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§9.2 Reaction rate and rate equation
The rate (r) of a chemical reaction is defined as the change
in concentration of a reactant or a product per unit time.
There are two kinds of reaction rates:
2 1
2 1
[A]=
c cr
t t t
2.1 expression of reaction rate
mean rate
instantaneous rate:
[A]dr
dt
Physical meaning:
the slope of the [A] ~ t curve at time t. t1 t
c
t
c
t1 t2
c1
c2
N2 + 3H2 == 2NH3
2
2
H
H
dcr
dt2
2
N
N
dcr
dt 3
3
NH
NH
dcr
dt
It is apparent that 2 2 3N H NH
1 1
3 2r r r
When expressed using different species, the rate of the reaction
may attain different values, which is not convenient and
sometimes may even cause confusion.
Definition: extent of reaction or advancement ()
i i,0
i
n n
where i is the stoichiometric coefficient of the reaction.
Definition: The true rate of the reaction or rate of conversion (J):
dt
dJ
aA + bB gG + hH
For general reaction:
aA + bB gG + hH
When the extent of reaction is d
GA B Hdndn dn dnd
a b g h
GA B H1 1 1 1dndn dn dndJ
dt a dt b dt g dt h dt
When the reaction takes place in a container with constant volume
Define rate V
Jr
dt
dn
hdt
dn
gdt
dn
bdt
dn
adt
dJ HGBA 1111
dt
d
hdt
d
gdt
d
bdt
d
ar
]H[1]G[1]A[1]A[1
dt
cdr i
i
][1
Unit: mol m-3 s-1
2.2 measurement of reaction rate
Physical meaning:
slope of the c ~ t curvei
r1
dt
cd i ][kinetic curve
0
tdt
dcr
ttdt
dcr
Initial rate
Rate at any time
tt = 0 t = t
c
The key subject of kinetic study is to measure the concentration of some species after arbitrary time intervals.
The concentration of the species can be measured using either chemical or physical methods.
CH3COOC2H5 + NaOH
CH3COONa + C2H5OH
The reaction can be stopped by removing
of CH3COOC2H5, and the consumption of
NaOH can be determined by chemical
titration.
For example:
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.
The first successful example for measuring concentration of reactant ph
ysically was made by Wilhelmy in 1850 .
He determined the residual concentration of sucrose by measuring th
e change of the rotation angle of a beam of plane-polarized light passin
g through the hydrolysis solution (optical activity).
C12H22O11 + H2O C12H22O11 + C12H22O11
sucrose glucose fructose
Substance sucrose glucose fructose
[]D25 +66.5 o +52 o - 92 o
The rotation angle of the 1:1
mixture of glucose and fructose
is –20 o
We still use in it in our physical
chemistry laboratory t1 t2
20
[]
[]2
[]1
66.5
t
CH3COOC2H5 + NaOH
CH3COONa + C2H5OH
CH3COOC2H5 + NaOH
CH3COONa + C2H5OH
the rate of which can be monitored using pH meter or conductometer.
N2O5 = N2O4 + 0.5 O2N2O5 = 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.
Stretch of epoxy group
FTIR spectroscopy
The physical parameters usually used for monitoring rea
ction process includes volume, pressure, electric conductanc
e, pH, refractive index, thermal conductivity, polarimetry, sp
ectrometry, chromatography, etc.
Analyzing methods:
1) Static method
2) Flow method
1) Real time analysis
2) Quenching
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.
Stable flow: l t
Flow method
Difficulties in study on kinetics
Mixer detector
Moving direction
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.
CBA
A cckcdt
dc
rate equation
Rate law
For example:
H2 + I2 = 2 HI 1 12 2[H ] [I ]r k
H2 + Cl2 = 2 HCl 1 0.52 2[H ] [Cl ]r k
AA B C
dcr kc c c
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.
1 0.52 2[H ] [Cl ]r k
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.
The overall order is 1.5.
1 0.52 2[H ] [Cl ]r k
2SO2 + O2 2SO3
13 2
2 3
[SO ]2 [SO ][SO ]
dr k
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.
AA B C
dcr kc c c
dt A
A B Ca b cdc
r kc c cdt
Partial order = stoichiometric coefficient
Reaction order = number of molecules involved in the reaction
For example: 2I + H2 = 2HI
22
1 [I][I] [H ]
2
dr k
dt
Law of mass action valid only for elementary reaction
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.
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