CHEMICAL KINETICS & REDIOACTIVITY

RATE/VELOCITY OF CHEMICAL REACTION :

c mol / lit.
Rate = = = mol lit–1 time–1 = mol dm–3 time–1
t sec

Types of Rates of chemical reaction :

For a reaction R  P

Total change in concentrat ion

Average rate = Total time taken

 c  dc d [R] d [P]
Rinstantaneous = tlim
0   = =– =

  t dt dt dt

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 :
m1A + m2B  products.
R  [A]P [B]q Where p may or may not be equal to m1 & similarly q
may or may not be equal to m2.
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.

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INTEGRATED RATE LAWS :
C0 or 'a' is initial concentration and Ct or a – x is concentration at time 't'
(a) zero order reactions :
Rate = k [conc.]º = constant
C0  Ct
Rate = k = or Ct = C0 – kt
' t'
C0
Unit of K = mol lit–1 sec–1, Time for completion =
k
C0 C0 C0
at t1/2 , Ct = , so kt1/2 =  t1/2 =  t1/2  C0
2 2 2k
(b) First Order Reactions :
(i) Let a 1st order reaction is, A  Products

2.303 a 2.303 C0
t= log or k= log C
k ax t t

n 2 0.693
 t1/2 = = = Independent of initial concentration.
k k
1
tAvg. = = 1.44 t1/2 .
k
Graphical Representation :
2.303 2.303
t=  log Ct + log C0
k k

tan= 2.303 tan= 2.303

't' k
k
 't'

log C0/Ct
or log a/a-x log Ct
(c) Second order reaction :
2nd order Reactions
Two types
A + A  products A + B  products.
a a a b 0
(a – x) (a –x) a–x b–x
dx dx
 = k (a–x)2 = k (a – x) (b – x)
dt dt
1 1 2.303 b(a  x )
 – = kt k= t( a  b )
log a(b  x )
(a  x ) a
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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
r01 = k [A0]1a , r02 = k [A0]2a

a
r01  [A ] 
   0 1 
r02  [ A 0 ]2 

(b) Using integrated rate law : It is method of trial and error.

(c) Method of half lives :
1
for nth order reaction t1/2 
[R 0 ]n 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.
2.303 P0 (n  1)
 k= log nP  P
t 0 t

{Formula is not applicable when n = 1, the value of n can be fractional also.}

(b) By titration method :
2.303 V0
1.  a  V0 a – x  Vt  k= log V
t t

2. Study of acid hydrolysis of an easter.

2.303 V  V0
k= log V  V
t  t

(c) By measuring optical rotation produced by the reaction mixture :

2.303  0    
k= log     

t  t  

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EFFECT OF TEMPERATURE ON RATE OF REACTION.
K t 10
T.C. =  2 to 3 ( for most of the reactions)
Kt

Arhenius theroy of reaction rate.

S HR = Summation of enthalpies of reactants

Threshold enthalpy
Enthalpy (H) Ea1 Ea2 or energy S HP = Summation of enthalpies of reactants
DH = Enthalpy change during the reaction
S HR
Reactants Ea1 = Energy of activation of the forward reaction
DH = S Hp – S HR = Ea1 – Ea2 Ea2 = Energy of activation of the backward reaction
S HP
Products

Progress of reaction (or reaction coordinate)

EP > Er  endothermic
EP < Er  exothermic
H = ( EP – Er ) = enthalpy change
H = Eaf – Eab
Ethreshold = Eaf + Er = Eb + Ep
Arhenius equation
k  AeE aRT r = k [conc.]order

d ln k Ea  Ea  1
= 2 log k =     log A
dT RT  2.303 R  T
If k1 and k2 be the rate constant of a reaction at two different temperature
T1 and T2 respectively, then we have
k2 Ea  1 1 
log  .  

k1 2 . 303 R  T1 T2 

InA
Ea Ea
 lnk = ln A – slope = – Ea  O
RT R

InK

1/T

 T   , K  A.

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