## Order of reaction

source: SlidePlayer

## Order of reaction – Experimental determination-

### 1)  Graphical method-

#### This method is used when there is only one reactant . This method involves the following steps-

a) The concentration of the reactants are measured by some suitable method.

b) A graph is plotted between concentration and time.

c) The instantaneous rates of the reaction at different times are calculated by finding out the slopes of the tangents corresponding to different times.

d) The rate of reaction Vs concentration is plotted.

i) If rate of reaction remains constant in graph potted rate Vs concentration . Then it is concluded that rate is independent of the concentration of reactants.

Rate = K [A]0 = K

Hence reaction is zero order.

ii)  If a straight line is obtained in rate Vs concentration graph .  Then it is concluded that rate is directly proportional to the concentration of reactant.

Rate = K [A]

Hence reaction is first order.

iii)  If a straight line is obtained in rate Vs (conc.)2  graph .  Then it is concluded that rate is directly proportional to the square of the concentration of reactant.

Rate = K [A]2

Hence reaction is second  order.

iv)  If a straight line is obtained in rate Vs (conc.)3 graph .  Then it is concluded that rate is directly proportional to the cube of the concentration of reactant.

Rate = K [A]3

Hence reaction is third order.

### 2) Method of integration ( Hit and Trial method)-

It is simplest method . In this method a, x and t are determined and substituted in the kinetic equations of different orders. The equation gives the constant value of rate constant for different time intervals . In this way order of reaction is determined.

For first order reaction,

K = 2.303/t [log(a / a-x)

For second order reaction,

K = 1/t [( 1/a-x) – (1/a)]

For third order reaction,

K = 1/2t [(1/a-x )2 – (1/a2)

### 3) Half life method-

t1/2 ∝ 1 / an-1

n is the order of reaction.

Suppose , initial conc. = a1 and a2

half lives = (t1/2)1 and (t1/2)2

(t1/2)1  ∝  1 / a1n-1                        eq 1

(t1/2)2  ∝  1 / a2n-1                      eq 2

divide eq 1 by eq 2

(t1/2)1  /  (t1/2)2  =  (a2 / a1 )n-1

Taking log of both sides,

log [(t1/2)1  /  (t1/2)2]  = log [ (a2 / a1 )n-1]

log [(t1/2)1  –  (t1/2)2]  = (n-1 )  [log a2 – log  a1 ]

(n-1) = log [(t1/2)1  –  (t1/2)2]  /  [log a2 – log  a1 ]

#### n=   1 +[ log [(t1/2)1  –  (t1/2)2]  /  (log a2 – log  a1 )]

This formula is used to determine order of reaction.

### 4) Vant Hoff differential method-

‘n’ is order of reaction, A1 and A2 are different initial concentrations.

-dx1 /dt = KA1n          ——-eq.1

-dx2 /dt = KA2n        ———eq.2

taking log of both equations,

log [-dx1 /dt] = log KA1n

log [-dx1 /dt] = log K + n log A1     ———eq .3

log [-dx2 /dt] = log KA2n

log [-dx2 /dt] = log K + n log A2     ———-eq.4

Subtracting both equations,

log [-dx1 /dt] – log [-dx2 /dt] = log K +n log A1 – log K – n log A2

=  n ( log A1 – log A2)

n = log [-dx1 /dt] – log [-dx2 /dt] / [( log A1 – log A2)]

– dx1/dt and -dx2/dt are determined from graph conc. Vs time. So value of ‘n’ can be calculated.