Important Formulas: Chemical Kinetics

 Page 1


  
   
RATE/VELOCITY OF CHEMICAL REACTION :
Rate = 
t
c
?
?
 = 
sec
. lit / mol
 = mol lit
?1
 time
?1 
 = mol dm
?3
 time
?1
Types of Rates of chemical reaction :
For a reaction R ?? ? P
Average rate = 
taken time Total
ion concentrat in change Total
  
R
instantaneous
 = 
0 t
lim
?
 ?
?
?
?
?
?
?
?
t
c
 = 
dt
dc
 = ? 
dt
] R [ d
 = 
dt
] P [ d
RATE LAW (DEPENDENCE OF RATE ON CONCENTRATION OF
REACTANTS) :
Rate = K (conc.)
order
 ? differential rate equation or rate expression
Where K = Rate constant = specific reaction rate = rate of reaction when
concentration is unity
unit of K = (conc)
1? order
 time
?1
Order of reaction :
m
1
A + m
2
B ?? products.
R ? [A]
P
 [B]
q
Where p may or may not be equal to m
1
 & similarly q
may or may not be equal to m
2
.
p is order of reaction with respect to reactant A and q is order of reaction
with respect to reactant B and (p + q) is overall order of the reaction.
Page 2


  
   
RATE/VELOCITY OF CHEMICAL REACTION :
Rate = 
t
c
?
?
 = 
sec
. lit / mol
 = mol lit
?1
 time
?1 
 = mol dm
?3
 time
?1
Types of Rates of chemical reaction :
For a reaction R ?? ? P
Average rate = 
taken time Total
ion concentrat in change Total
  
R
instantaneous
 = 
0 t
lim
?
 ?
?
?
?
?
?
?
?
t
c
 = 
dt
dc
 = ? 
dt
] R [ d
 = 
dt
] P [ d
RATE LAW (DEPENDENCE OF RATE ON CONCENTRATION OF
REACTANTS) :
Rate = K (conc.)
order
 ? differential rate equation or rate expression
Where K = Rate constant = specific reaction rate = rate of reaction when
concentration is unity
unit of K = (conc)
1? order
 time
?1
Order of reaction :
m
1
A + m
2
B ?? products.
R ? [A]
P
 [B]
q
Where p may or may not be equal to m
1
 & similarly q
may or may not be equal to m
2
.
p is order of reaction with respect to reactant A and q is order of reaction
with respect to reactant B and (p + q) is overall order of the reaction.
  
INTEGRATED RATE LAWS :
C
0
 or  'a' is initial concentration and C
t
 or a ? x is concentration at time 't'
(a) zero order reactions :
Rate = k [conc.]º = constant
Rate = k = 
' t '
C C
t 0
?
or    C
t
 = C
0
 ? kt
Unit of K  = mol lit
?1
 sec
?1
,   Time for completion = 
k
C
0
at t
1/2
 , C
t
  = 
2
C
0
, so  kt
1/2
 = 
2
C
0
 
? t
1/2
 = 
k 2
C
0
? t
1/2
  ? C
0
(b) First Order Reactions :
(i) Let a 1
st
 order reaction is,  A    ?? ?  Products
t = 
k
303 . 2
 log 
x a
a
?
or k = 
t
303 . 2
 log 
t
0
C
C
? t
1/2
 = 
k
2 n ?
 = 
k
0.693
 = Independent of initial concentration.
t
Avg.
 = 
k
1
 = 1.44 t
1/2
 .
Graphical Representation :
t = 
k
303 . 2
? log C
t
 + 
2.303
k
 log C
0
?
log C /C
or log a/a-x
0 t
't'
tan = 2.303 ?
k
't'
tan =  ?
2.303
k
?
log C
t
(c) Second order reaction :
2
nd
 order Reactions
      Two types
A     +   A    ??  products A     +  B  ??   products.
a          a a         b 0
(a ? x)  (a ?x) a ? x   b ? x
? 
dt
dx
 = k (a?x)
2
dt
dx
 = k (a ? x) (b ? x)
? 
) x a (
1
?
 ? 
a
1
 = kt k =   
) b a ( t
303 . 2
?
 log 
) x b ( a
) x a ( b
?
?
Page 3


  
   
RATE/VELOCITY OF CHEMICAL REACTION :
Rate = 
t
c
?
?
 = 
sec
. lit / mol
 = mol lit
?1
 time
?1 
 = mol dm
?3
 time
?1
Types of Rates of chemical reaction :
For a reaction R ?? ? P
Average rate = 
taken time Total
ion concentrat in change Total
  
R
instantaneous
 = 
0 t
lim
?
 ?
?
?
?
?
?
?
?
t
c
 = 
dt
dc
 = ? 
dt
] R [ d
 = 
dt
] P [ d
RATE LAW (DEPENDENCE OF RATE ON CONCENTRATION OF
REACTANTS) :
Rate = K (conc.)
order
 ? differential rate equation or rate expression
Where K = Rate constant = specific reaction rate = rate of reaction when
concentration is unity
unit of K = (conc)
1? order
 time
?1
Order of reaction :
m
1
A + m
2
B ?? products.
R ? [A]
P
 [B]
q
Where p may or may not be equal to m
1
 & similarly q
may or may not be equal to m
2
.
p is order of reaction with respect to reactant A and q is order of reaction
with respect to reactant B and (p + q) is overall order of the reaction.
  
INTEGRATED RATE LAWS :
C
0
 or  'a' is initial concentration and C
t
 or a ? x is concentration at time 't'
(a) zero order reactions :
Rate = k [conc.]º = constant
Rate = k = 
' t '
C C
t 0
?
or    C
t
 = C
0
 ? kt
Unit of K  = mol lit
?1
 sec
?1
,   Time for completion = 
k
C
0
at t
1/2
 , C
t
  = 
2
C
0
, so  kt
1/2
 = 
2
C
0
 
? t
1/2
 = 
k 2
C
0
? t
1/2
  ? C
0
(b) First Order Reactions :
(i) Let a 1
st
 order reaction is,  A    ?? ?  Products
t = 
k
303 . 2
 log 
x a
a
?
or k = 
t
303 . 2
 log 
t
0
C
C
? t
1/2
 = 
k
2 n ?
 = 
k
0.693
 = Independent of initial concentration.
t
Avg.
 = 
k
1
 = 1.44 t
1/2
 .
Graphical Representation :
t = 
k
303 . 2
? log C
t
 + 
2.303
k
 log C
0
?
log C /C
or log a/a-x
0 t
't'
tan = 2.303 ?
k
't'
tan =  ?
2.303
k
?
log C
t
(c) Second order reaction :
2
nd
 order Reactions
      Two types
A     +   A    ??  products A     +  B  ??   products.
a          a a         b 0
(a ? x)  (a ?x) a ? x   b ? x
? 
dt
dx
 = k (a?x)
2
dt
dx
 = k (a ? x) (b ? x)
? 
) x a (
1
?
 ? 
a
1
 = kt k =   
) b a ( t
303 . 2
?
 log 
) x b ( a
) x a ( b
?
?
  
METHODS TO DETERMINE ORDER OF A REACTION
(a) Initial rate method :
r = k [A]
a
 [B]
b
 [C]
c
if [B] = constant
[C] = constant
then for two different initial concentrations of A we have
1
0
r
 = k [A
0
]
1
a
  ,
2
0
r
 = k [A
0
]
2
a
?
a
2 0
1 0
0
0
] A [
] A [
r
r
2
1
?
?
?
?
?
?
?
?
?
(b) Using integrated rate law : It is method of trial and error.
(c) Method of half lives :
for n
th
 order reaction t
1/2
  ? 1 n
0
] R [
1
?
(d) Ostwald Isolation Method :
rate = k [A]
a
 [B]
b
 [C]
c
 = k
0
 [A]
a
METHODS TO MONITOR THE PROGRESS OF THE REACTION :
(a) Progress of gaseous reaction can be monitored by measuring total
pressure at a fixed volume & temperature or by measuring total volume
of mixture under constant pressure and temperature.
? k =
t
2.303
 log 
t 0
0
P nP
1) (n P
?
?
{Formula is not applicable when n = 1, the value of n can be fractional also.}
(b) By titration method :
1. ?  a ? V
0
    a ? x ? V
t
? k = 
t
2.303
 log 
t
0
V
V
2. Study of acid hydrolysis of an easter.
k = 
t
303 . 2
 log 
t
0
V V
V V
?
?
?
?
(c) By measuring optical rotation produced by the reaction mixture :
k = 
t
303 . 2
 log 
?
?
?
?
?
?
?
?
? ? ?
? ? ?
?
?
t
0
Page 4


  
   
RATE/VELOCITY OF CHEMICAL REACTION :
Rate = 
t
c
?
?
 = 
sec
. lit / mol
 = mol lit
?1
 time
?1 
 = mol dm
?3
 time
?1
Types of Rates of chemical reaction :
For a reaction R ?? ? P
Average rate = 
taken time Total
ion concentrat in change Total
  
R
instantaneous
 = 
0 t
lim
?
 ?
?
?
?
?
?
?
?
t
c
 = 
dt
dc
 = ? 
dt
] R [ d
 = 
dt
] P [ d
RATE LAW (DEPENDENCE OF RATE ON CONCENTRATION OF
REACTANTS) :
Rate = K (conc.)
order
 ? differential rate equation or rate expression
Where K = Rate constant = specific reaction rate = rate of reaction when
concentration is unity
unit of K = (conc)
1? order
 time
?1
Order of reaction :
m
1
A + m
2
B ?? products.
R ? [A]
P
 [B]
q
Where p may or may not be equal to m
1
 & similarly q
may or may not be equal to m
2
.
p is order of reaction with respect to reactant A and q is order of reaction
with respect to reactant B and (p + q) is overall order of the reaction.
  
INTEGRATED RATE LAWS :
C
0
 or  'a' is initial concentration and C
t
 or a ? x is concentration at time 't'
(a) zero order reactions :
Rate = k [conc.]º = constant
Rate = k = 
' t '
C C
t 0
?
or    C
t
 = C
0
 ? kt
Unit of K  = mol lit
?1
 sec
?1
,   Time for completion = 
k
C
0
at t
1/2
 , C
t
  = 
2
C
0
, so  kt
1/2
 = 
2
C
0
 
? t
1/2
 = 
k 2
C
0
? t
1/2
  ? C
0
(b) First Order Reactions :
(i) Let a 1
st
 order reaction is,  A    ?? ?  Products
t = 
k
303 . 2
 log 
x a
a
?
or k = 
t
303 . 2
 log 
t
0
C
C
? t
1/2
 = 
k
2 n ?
 = 
k
0.693
 = Independent of initial concentration.
t
Avg.
 = 
k
1
 = 1.44 t
1/2
 .
Graphical Representation :
t = 
k
303 . 2
? log C
t
 + 
2.303
k
 log C
0
?
log C /C
or log a/a-x
0 t
't'
tan = 2.303 ?
k
't'
tan =  ?
2.303
k
?
log C
t
(c) Second order reaction :
2
nd
 order Reactions
      Two types
A     +   A    ??  products A     +  B  ??   products.
a          a a         b 0
(a ? x)  (a ?x) a ? x   b ? x
? 
dt
dx
 = k (a?x)
2
dt
dx
 = k (a ? x) (b ? x)
? 
) x a (
1
?
 ? 
a
1
 = kt k =   
) b a ( t
303 . 2
?
 log 
) x b ( a
) x a ( b
?
?
  
METHODS TO DETERMINE ORDER OF A REACTION
(a) Initial rate method :
r = k [A]
a
 [B]
b
 [C]
c
if [B] = constant
[C] = constant
then for two different initial concentrations of A we have
1
0
r
 = k [A
0
]
1
a
  ,
2
0
r
 = k [A
0
]
2
a
?
a
2 0
1 0
0
0
] A [
] A [
r
r
2
1
?
?
?
?
?
?
?
?
?
(b) Using integrated rate law : It is method of trial and error.
(c) Method of half lives :
for n
th
 order reaction t
1/2
  ? 1 n
0
] R [
1
?
(d) Ostwald Isolation Method :
rate = k [A]
a
 [B]
b
 [C]
c
 = k
0
 [A]
a
METHODS TO MONITOR THE PROGRESS OF THE REACTION :
(a) Progress of gaseous reaction can be monitored by measuring total
pressure at a fixed volume & temperature or by measuring total volume
of mixture under constant pressure and temperature.
? k =
t
2.303
 log 
t 0
0
P nP
1) (n P
?
?
{Formula is not applicable when n = 1, the value of n can be fractional also.}
(b) By titration method :
1. ?  a ? V
0
    a ? x ? V
t
? k = 
t
2.303
 log 
t
0
V
V
2. Study of acid hydrolysis of an easter.
k = 
t
303 . 2
 log 
t
0
V V
V V
?
?
?
?
(c) By measuring optical rotation produced by the reaction mixture :
k = 
t
303 . 2
 log 
?
?
?
?
?
?
?
?
? ? ?
? ? ?
?
?
t
0
  
EFFECT OF TEMPERATURE ON RATE OF REACTION.
T.C. = 
t 10
t
K
K
?
?
2 to 3 ( for most of the reactions)
Arhenius theroy of reaction rate.
Products
Reactants
SH
R
SH
P
Ea 1 Ea 2
Threshold enthalpy 
or energy
D S S H = H ? H = Ea ? Ea
p R 1 2
Enthalpy (H)
Progress of reaction (or reaction coordinate)
S
S
D
H = Summation of enthalpies of reactants
H = Summation of enthalpies of reactants
H = Enthalpy change during the reaction
Ea = Energy of activation of the forward reaction
Ea = Energy of activation of the backward reaction
R
P
1
2
E
P
 > E
r
? endothermic
E
P
 < E
r
? exothermic
?H = ( E
P
 ? E
r
 ) = enthalpy change
?H = E
af
 ? E
ab
E
threshold
 = E
af
 + E
r
 = E
b
 + E
p
Arhenius equation
RT E
a
Ae k
?
?
r = k [conc.]
order
dT
k ln d
 = 
2
a
RT
E
log k = 
A log
T
1
R  303 . 2
Ea
? ?
?
?
?
?
?
?
If k
1
 and k
2 
be the rate constant of a reaction at two different temperature
T
1
 and T
2
 respectively, then we have
?
?
?
?
?
?
?
?
? ?
2 1
a
1
2
T
1
T
1
.
R 303 . 2
E
k
k
log
? lnk = ln A ? 
RT
E
a
slope = ? 
InA
InK
E
R
a
1/T
E
a
 ? O
? T ? ? , K ? A. A.