## Third order reaction- source : SlideShare

## Third order reaction-

### Ex –

1)  2NO +O2 ——–> 2NO2

2) 2NO + Cl2 ———> 2NOCl

3) 2FeCl3 + SnCl2 ——–> 2FeCl2 + SnCl4

consider a reaction,

A+B+C ———> product

Rate of reaction,

dx/dt = K (a- x )(b- x )(c- x )

When ,

a = b = c , then

dx/dt ∝  (a- x )3

dx / (a – x )3 = K.dt

Taking integration of both sides,

∫ dx / (a – x )3 = K∫ dt

1 / 2 (a – x)2 = Kt + C          ——— eq.1

when t = 0 then  x = 0

1 / 2 ( a – 0)2 = K x 0 + C

C = 1/ 2a2

Putting the value of ‘C’ in eq. 1

1 / 2(a – x)2 = Kt + 1 / 2a2

K = 1/ 2t [ (1 / (a- x)2 – (1/a2)]

K = 1 / 2t {a2-(a2 +x2-2ax)}/ {a2(a-x)2}]

K = 1/2t [ ( 2ax -x2 ) /{a2(a-x)2}

### K = 1/2t [ {x(2a- x) }/{a2(a-x)2}

a = initial concentration

a – x = conc. of reactant after time ‘t’

## Characteristics of third order reaction –

#### 1) Unit of ‘K’-

K = 1 / 2t [x( 2a-x)/ a 2(a – x)2]

unit of ‘K’ = 1 / time ( mole  litre-1  ) (mole  litre-1)/( mole  litre-1 )2 x (mole litre-1)2

#### unit of ‘K’ = litre2 mole -2 time-2

2) The unit of velocity constant  depends upon  the units of concentration because,

unit of ‘K’ = litre 2mole -2 time-2

3) The time taken to complete a  half reaction( half life period )  is inversely proportional to the square of initial concentration of the reactant.

K = 1 / 2t [x( 2a-x)/ a 2(a – x)2]

If  t = t1/2 then x = a/2

K =  1/ 2t1/2  [ {a/2} {2a- (a/2)}] / [ 2a2(a -a/2)2]

t 1/2 =  1 / 2K  [ (a/2) (3a/2)]/ [2a2( a2/4)]