## Third order reaction-

source : SlideShare

## Third order reaction-

### ” A reaction is third order if rate of reaction is determined by variation of three concentration terms.”

### Ex –

1) 2NO +O_{2} ——–> 2NO_{2}

2) 2NO + Cl_{2} ———> 2NOCl

3) 2FeCl_{3} + SnCl_{2} ——–> 2FeCl_{2} + SnCl_{4}

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/ 2a ^{2}*

*Putting the value of ‘C’ in eq. 1*

*1 / 2(a – x) ^{2} = Kt + 1 / 2a^{2}*

*K = 1/ 2t [ (1 / (a- x) ^{2} – (1/a^{2})]*

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

K = 1/2t [ ( 2ax -x^{2} ) /{a^{2}(a-x)^{2}}

### K = 1/2t [ {x(2a- x) }/{a^{2}(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’ = litre*^{2} mole ^{-2} time^{-2}

^{2}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 = t _{1/2} then x = a/2*

*K = 1/ 2t _{1/2} [ {a/2} {2a- (a/2)}] / [ 2a^{2}(a -a/2)^{2}]*

*t _{1/2} = 1 / 2K [ (a/2) (3a/2)]/ [2a^{2}( a^{2}/4)]*

*t *_{1/2} = 3/ 2Ka^{2}

_{1/2}= 3/ 2Ka

^{2}

*t *_{1/2} ∝ 1 /a^{2}

_{1/2}∝ 1 /a

^{2}